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Title: The Life of Galileo Galilei, with Illustrations of the Advancement of Experimental Philosophy

Author: John Elliot Drinkwater Bethune

Release date: October 3, 2013 [eBook #43877]

Language: English

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Transcriber's Note.

Variable spelling and hyphenation have been retained. Minor punctuation
inconsistencies have been silently repaired. The author's corrections,
additions and comments have been applied in the text. Changes made by
the transcriber can be found at the end of the book. The original text
is printed in a two-column layout. Formatting and special characters are
indicated as follows:

    Letters in superscript are presented ^{like this}.
    _italic_
    [Greek]




[Illustration: Galileo Galilei]




                                  THE
                                  LIFE
                                   OF
                            GALILEO GALILEI,
                                  WITH
                    ILLUSTRATIONS OF THE ADVANCEMENT
                                   OF
                        EXPERIMENTAL PHILOSOPHY.

                               MDCCCXXX.

                                LONDON.




LIFE OF GALILEO:

WITH ILLUSTRATIONS OF THE ADVANCEMENT OF EXPERIMENTAL PHILOSOPHY.




CHAPTER I.

    _Introduction._


THE knowledge which we at present possess of the phenomena of nature and
of their connection has not by any means been regularly progressive, as
we might have expected, from the time when they first drew the attention
of mankind. Without entering into the question touching the scientific
acquirements of eastern nations at a remote period, it is certain that
some among the early Greeks were in possession of several truths,
however acquired, connected with the economy of the universe, which were
afterwards suffered to fall into neglect and oblivion. But the
philosophers of the old school appear in general to have confined
themselves at the best to observations; very few traces remain of their
having instituted _experiments_, properly so called. This putting of
nature to the torture, as Bacon calls it, has occasioned the principal
part of modern philosophical discoveries. The experimentalist may so
order his examination of nature as to vary at pleasure the circumstances
in which it is made, often to discard accidents which complicate the
general appearances, and at once to bring any theory which he may form
to a decisive test. The province of the mere observer is necessarily
limited: the power of selection among the phenomena to be presented is
in great measure denied to him, and he may consider himself fortunate if
they are such as to lead him readily to a knowledge of the laws which
they follow.

Perhaps to this imperfection of method it may be attributed that natural
philosophy continued to be stationary, or even to decline, during a long
series of ages, until little more than two centuries ago. Within this
comparatively short period it has rapidly reached a degree of perfection
so different from its former degraded state, that we can hardly
institute any comparison between the two. Before that epoch, a few
insulated facts, such as might first happen to be noticed, often
inaccurately observed and always too hastily generalized, were found
sufficient to excite the naturalist's lively imagination; and having
once pleased his fancy with the supposed fitness of his artificial
scheme, his perverted ingenuity was thenceforward employed in forcing
the observed phenomena into an imaginary agreement with the result of
his theory; instead of taking the more rational, and it should seem, the
more obvious, method of correcting the theory by the result of his
observations, and considering the one merely as the general and
abbreviated expression of the other. But natural phenomena were not then
valued on their own account, and for the proofs which they afford of a
vast and beneficent design in the structure of the universe, so much as
for the fertile topics which the favourite mode of viewing the subject
supplied to the spirit of scholastic disputation: and it is a
humiliating reflection that mankind never reasoned so ill as when they
most professed to cultivate the art of reasoning. However specious the
objects, and alluring the announcements of this art, the then prevailing
manner of studying it curbed and corrupted all that is free and noble in
the human mind. Innumerable fallacies lurked every where among the most
generally received opinions, and crowds of dogmatic and self-sufficient
pedants fully justified the lively definition, that "logic is the art of
talking unintelligibly on things of which we are ignorant."[1]

The error which lay at the root of the philosophy of the middle ages was
this:--from the belief that general laws and universal principles might
be discovered, of which the natural phenomena were _effects_, it was
thought that the proper order of study was, first to detect the general
_cause_, and then to pursue it into its consequences; it was considered
absurd to begin with the effect instead of the cause; whereas the real
choice lay between proceeding from particular facts to general facts,
or from general facts to particular facts; and it was under this
misrepresentation of the real question that all the sophistry lurked. As
soon as it is well understood that the general _cause_ is no other than
a single fact, common to a great number of phenomena, it is necessarily
perceived that an accurate scrutiny of these latter must precede any
safe reasoning with respect to the former. But at the time of which we
are speaking, those who adopted this order of reasoning, and who began
their inquiries by a minute and sedulous investigation of facts, were
treated with disdain, as men who degraded the lofty name of philosophy
by bestowing it upon mere mechanical operations. Among the earliest and
noblest of these was Galileo.

It is common, especially in this country, to name Bacon as the founder
of the present school of experimental philosophy; we speak of the
Baconian or inductive method of reasoning as synonimous and convertible
terms, and we are apt to overlook what Galileo had already done before
Bacon's writings appeared. Certainly the Italian did not range over the
circle of the sciences with the supreme and searching glance of the
English philosopher, but we find in every part of his writings
philosophical maxims which do not lose by comparison with those of
Bacon; and Galileo deserves the additional praise, that he himself gave
to the world a splendid practical illustration of the value of the
principles which he constantly recommended. In support of this view of
the comparative deserts of these two celebrated men, we are able to
adduce the authority of Hume, who will be readily admitted as a
competent judge of philosophical merit, where his prejudices cannot bias
his decision. Discussing the character of Bacon, he says, "If we
consider the variety of talents displayed by this man, as a public
speaker, a man of business, a wit, a courtier, a companion, an author, a
philosopher, he is justly the object of great admiration. If we consider
him merely as an author and philosopher, the light in which we view him
at present, though very estimable, he was yet inferior to his
contemporary Galileo, perhaps even to Kepler. Bacon pointed out at a
distance the road to true philosophy: Galileo both pointed it out to
others, and made himself considerable advances in it. The Englishman was
ignorant of geometry: the Florentine revived that science, excelled in
it, and was the first that applied it, together with experiment, to
natural philosophy. The former rejected with the most positive disdain
the system of Copernicus: the latter fortified it with new proofs
derived both from reason and the senses."[2]

If we compare them from another point of view, not so much in respect of
their intrinsic merit, as of the influence which each exercised on the
philosophy of his age, Galileo's superior talent or better fortune, in
arresting the attention of his contemporaries, seems indisputable. The
fate of the two writers is directly opposed the one to the other;
Bacon's works seem to be most studied and appreciated when his readers
have come to their perusal, imbued with knowledge and a philosophical
spirit, which, however, they have attained independently of his
assistance. The proud appeal to posterity which he uttered in his will,
"For my name and memory, I leave it to men's charitable speeches, and to
foreign nations, and the next ages," of itself indicates a consciousness
of the fact that his contemporary countrymen were but slightly affected
by his philosophical precepts. But Galileo's personal exertions changed
the general character of philosophy in Italy: at the time of his death,
his immediate pupils had obtained possession of the most celebrated
universities, and were busily engaged in practising and enforcing the
lessons which he had taught them; nor was it then easy to find there a
single student of natural philosophy who did not readily ascribe the
formation of his principles to the direct or remote influence of
Galileo's example. Unlike Bacon's, his reputation, and the value of his
writings, were higher among his contemporaries than they have since
become. This judgment perhaps awards the highest intellectual prize to
him whose disregarded services rise in estimation with the advance of
knowledge; but the praise due to superior usefulness belongs to him who
succeeded in training round him a school of imitators, and thereby
enabled his imitators to surpass himself.

The biography of men who have devoted themselves to philosophical
pursuits seldom affords so various and striking a succession of
incidents as that of a soldier or statesman. The life of a man who is
shut up during the greater part of his time in his study or laboratory
supplies but scanty materials for personal details; and the lapse of
time rapidly removes from us the opportunities of preserving such
peculiarities as might have been worth recording. An account of it will
therefore consist chiefly in a review of his works and opinions, and of
the influence which he and they have exercised over his own and
succeeding ages. Viewed in this light, few lives can be considered more
interesting than that of Galileo; and if we compare the state in which
he found, with that in which he left, the study of nature, we shall feel
how justly an enthusiastic panegyric pronounced upon the age immediately
following him may be transferred to this earlier period. "This is the
age wherein all men's minds are in a kind of fermentation, and the
spirit of wisdom and learning begins to mount and free itself from those
drossie and terrene impediments wherewith it has been so long clogged,
and from the insipid phlegm and _caput mortuum_ of useless notions in
which it hath endured so violent and long a fixation. This is the age
wherein, methinks, philosophy comes in with a spring tide, and the
peripatetics may as well hope to stop the current of the tide, or, with
Xerxes, to fetter the ocean, as hinder the overflowing of free
philosophy. Methinks I see how all the old rubbish must be thrown away,
and the rotten buildings be overthrown and carried away, with so
powerful an inundation. These are the days that must lay a new
foundation of a more magnificent philosophy, never to be overthrown,
that will empirically and sensibly canvass the phenomena of nature,
deducing the causes of things from such originals in nature as we
observe are producible by art, and the infallible demonstration of
mechanics: and certainly this is the way, and no other, to build a true
and permanent philosophy."[3]


FOOTNOTES:

[1] Ménage.

[2] Hume's England, James I.

[3] Power's Experimental Philosophy, 1663.




CHAPTER II.

    _Galileo's Birth--Family--Education--Observation of the
      Pendulum--Pulsilogies--Hydrostatical Balance--Lecturer at Pisa._


GALILEO GALILEI was born at Pisa, on the 15th day of February, 1564, of
a noble and ancient Florentine family, which, in the middle of the
fourteenth century, adopted this surname instead of Bonajuti, under
which several of their ancestors filled distinguished offices in the
Florentine state. Some misapprehension has occasionally existed, in
consequence of the identity of his proper name with that of his family;
his most correct appellation would perhaps be Galileo de' Galilei, but
the surname usually occurs as we have written it. He is most commonly
spoken of by his Christian name, agreeably to the Italian custom; just
as Sanzio, Buonarotti, Sarpi, Reni, Vecelli, are universally known by
their Christian names of Raphael, Michel Angelo, Fra Paolo, Guido, and
Titian.

Several authors have followed Rossi in styling Galileo illegitimate, but
without having any probable grounds even when they wrote, and the
assertion has since been completely disproved by an inspection of the
registers at Pisa and Florence, in which are preserved the dates of his
birth, and of his mother's marriage, eighteen months previous to it.[4]

His father, Vincenzo Galilei, was a man of considerable talent and
learning, with a competent knowledge of mathematics, and particularly
devoted to the theory and practice of music, on which he published
several esteemed treatises. The only one which it is at present easy to
procure--his Dialogue on ancient and modern music--exhibits proofs, not
only of a thorough acquaintance with his subject, but of a sound and
vigorous understanding applied to other topics incidentally discussed.
There is a passage in the introductory part, which becomes interesting
when considered as affording some traces of the precepts by which
Galileo was in all probability trained to reach his preeminent station
in the intellectual world. "It appears to me," says one of the speakers
in the dialogue, "that they who in proof of any assertion rely simply on
the weight of authority, without adducing any argument in support of it,
act very absurdly: I, on the contrary, wish to be allowed freely to
question and freely to answer you without any sort of adulation, as well
becomes those who are truly in search of truth." Sentiments like these
were of rare occurrence at the close of the sixteenth century, and it is
to be regretted that Vincenzo hardly lived long enough to witness his
idea of a true philosopher splendidly realized in the person of his son.
Vincenzo died at an advanced age, in 1591. His family consisted of three
sons, Galileo, Michel Angelo, and Benedetto, and the same number of
daughters, Giulia, Virginia, and Livia. After Vincenzo's death the chief
support of the family devolved upon Galileo, who seems to have assisted
them to his utmost power. In a letter to his mother, dated 1600,
relative to the intended marriage of his sister Livia with a certain
Pompeo Baldi, he agrees to the match, but recommends its temporary
postponement, as he was at that time exerting himself to furnish money
to his brother Michel Angelo, who had received the offer of an
advantageous settlement in Poland. As the sum advanced to his brother,
which prevented him from promoting his sister's marriage, did not exceed
200 crowns, it may be inferred that the family were in a somewhat
straitened condition. However he promises, as soon as his brother should
repay him, "to take measures for the young lady, since she too is bent
upon _coming out_ to prove the miseries of this world."--As Livia was at
the date of this letter in a convent, the last expression seems to
denote that she had been destined to take the veil. This proposed
marriage never took place, but Livia was afterwards married to Taddeo
Galletti: her sister Virginia married Benedetto Landucci. Galileo
mentions one of his sisters, (without naming her) as living with him in
1619 at Bellosguardo. Michel Angelo is probably the same brother of
Galileo who is mentioned by Liceti as having communicated from Germany
some observations on natural history.[5] He finally settled in the
service of the Elector of Bavaria; in what situation is not known, but
upon his death the Elector granted a pension to his family, who then
took up their abode at Munich. On the taking of that city in 1636, in
the course of the bloody thirty years' war, which was then raging
between the Austrians and Swedes, his widow and four of his children
were killed, and every thing which they possessed was either burnt or
carried away. Galileo sent for his two nephews, Alberto and a younger
brother, to Arcetri near Florence, where he was then living. These two
were then the only survivors of Michel Angelo's family; and many of
Galileo's letters about that date contain allusions to the assistance he
had been affording them. The last trace of Alberto is on his return into
Germany to the Elector, in whose service his father had died. These
details include almost every thing which is known of the rest of
Vincenzo's family.

Galileo exhibited early symptoms of an active and intelligent mind, and
distinguished himself in his childhood by his skill in the construction
of ingenious toys and models of machinery, supplying the deficiencies of
his information from the resources of his own invention; and he
conciliated the universal good-will of his companions by the ready good
nature with which he employed himself in their service and for their
amusement. It is worthy of observation, that the boyhood of his great
follower Newton, whose genius in many respects so closely resembled his
own, was marked by a similar talent. Galileo's father was not opulent,
as has been already stated: he was burdened with a large family, and was
unable to provide expensive instructors for his son; but Galileo's own
energetic industry rapidly supplied the want of better opportunities;
and he acquired, under considerable disadvantages, the ordinary
rudiments of a classical education, and a competent knowledge of the
other branches of literature which were then usually studied. His
leisure hours were applied to music and drawing; for the former
accomplishment he inherited his father's talent, being an excellent
performer on several instruments, especially on the lute; this continued
to be a favourite recreation during the whole of his life. He was also
passionately fond of painting, and at one time he wished to make it his
profession: and his skill and judgment of pictures were highly esteemed
by the most eminent contemporary artists, who did not scruple to own
publicly their deference to young Galileo's criticism.

When he had reached his nineteenth year, his father, becoming daily more
sensible of his superior genius, determined, although at a great
personal sacrifice, to give him the advantages of an university
education. Accordingly, in 1581, he commenced his academical studies in
the university of his native town, Pisa, his father at this time
intending that he should adopt the profession of medicine. In the
matriculation lists at Pisa, he is styled Galileo, the son of Vincenzo
Galilei, a Florentine, Scholar in Arts. His instructor was the
celebrated botanist, Andreas Cæsalpinus, who was professor of medicine
at Pisa from 1567 to 1592. Hist. Acad. Pisan.; Pisis, 1791. It is dated
5th November, 1581. Viviani, his pupil, friend, and panegyrist, declares
that, almost from the first day of his being enrolled on the lists of
the academy, he was noticed for the reluctance with which he listened to
the dogmas of the Aristotelian philosophy, then universally taught; and
he soon became obnoxious to the professors from the boldness with which
he promulgated what they styled his philosophical paradoxes. His early
habits of free inquiry were irreconcileable with the mental quietude of
his instructors, whose philosophic doubts, when they ventured to
entertain any, were speedily lulled by a quotation from Aristotle.
Galileo thought himself capable of giving the world an example of a
sounder and more original mode of thinking; he felt himself destined to
be the founder of a new school of rational and experimental philosophy.
Of this we are now securely enjoying the benefits; and it is difficult
at this time fully to appreciate the obstacles which then presented
themselves to free inquiry: but we shall see, in the course of this
narrative, how arduous their struggle was who happily effected this
important revolution. The vindictive rancour with which the partisans of
the old philosophy never ceased to assail Galileo is of itself a
sufficient proof of the prominent station which he occupied in the
contest.

Galileo's earliest mechanical discovery, to the superficial observer
apparently an unimportant one, occurred during the period of his studies
at Pisa. His attention was one day arrested by the vibrations of a lamp
swinging from the roof of the cathedral, which, whether great or small,
seemed to recur at equal intervals. The instruments then employed for
measuring time were very imperfect: Galileo attempted to bring his
observation to the test before quitting the church, by comparing the
vibrations with the beatings of his own pulse, and his mind being then
principally employed upon his intended profession, it occurred to him,
when he had further satisfied himself of their regularity by repeated
and varied experiments, that the process he at first adopted might be
reversed, and that an instrument on this principle might be usefully
employed in ascertaining the rate of the pulse, and its variation from
day to day. He immediately carried the idea into execution, and it was
for this sole and limited purpose that the first pendulum was
constructed. Viviani tells us, that the value of the invention was
rapidly appreciated by the physicians of the day, and was in common use
in 1654, when he wrote.

[Illustration: Instrument No. 1, No. 2, No. 3]

Santorio, who was professor of medicine at Padua, has given
representations of four different forms of these instruments, which he
calls pulsilogies, (_pulsilogias_,) and strongly recommends to medical
practitioners.[6] These instruments seem to have been used in the
following manner: No. 1 consists merely of a weight fastened to a string
and a graduated scale. The string being gathered up into the hand till
the vibrations of the weight coincided with the beatings of the
patient's pulse, the length was ascertained from the scale, which, of
course, if great, indicated a languid, if shorter, a more lively action.
In No. 2 the improvement is introduced of connecting the scale and
string, the length of the latter is regulated by the turns of a peg at
_a_, and a bead upon the string at _b_ showed the measure. No. 3 is
still more compact, the string being shortened by winding upon an axle
at the back of the dial-plate. The construction of No. 4, which Santorio
claims as his own improvement, is not given, but it is probable that the
principal index, by its motion, shifted a weight to different distances
from the point of suspension, and that the period of vibration was
still more accurately adjusted by a smaller weight connected with the
second index. Venturi seems to have mistaken the third figure for that
of a pendulum clock, as he mentions this as one of the earliest
adaptations of Galileo's principle to that purpose;[7] but it is
obvious, from Santorio's description, that it is nothing more than a
circular scale, the index showing, by the figure to which it points, the
length of string remaining unwound upon the axis. We shall, for the
present, postpone the consideration of the invention of pendulum clocks,
and the examination of the different claims to the honour of their first
construction.

At the time of which we are speaking, Galileo was entirely ignorant of
mathematics, the study of which was then at a low ebb, not only in
Italy, but in every part of Europe. Commandine had recently revived a
taste for the writings of Euclid and Archimedes, and Vieta Tartalea and
others had made considerable progress in algebra, Guido Ubaldi and
Benedetti had done something towards establishing the principles of
statics, which was the only part of mechanics as yet cultivated; but
with these inconsiderable exceptions the application of mathematics to
the phenomena of nature was scarcely thought of. Galileo's first
inducement to acquire a knowledge of geometry arose from his partiality
for drawing and music, and from the wish to understand their principles
and theory. His father, fearful lest he should relax his medical
studies, refused openly to encourage him in this new pursuit; but he
connived at the instruction which his son now began to receive in the
writings of Euclid, from the tuition of an intimate friend, named
Ostilio Ricci, who was one of the professors in the university.
Galileo's whole attention was soon directed to the enjoyment of the new
sensations thus communicated to him, insomuch that Vincenzo, finding his
prognostics verified, began to repent his indirect sanction, and
privately requested Ricci to invent some excuse for discontinuing his
lessons. But it was fortunately too late; the impression was made and
could not be effaced; from that time Hippocrates and Galen lay unheeded
before the young physician, and served only to conceal from his father's
sight the mathematical volumes on which the whole of his time was really
employed. His progress soon revealed the true nature of his pursuits:
Vincenzo yielded to the irresistible predilection of his son's mind, and
no longer attempted to turn him from the speculations to which his whole
existence was thenceforward abandoned.

After mastering the elementary writers, Galileo proceeded to the study
of Archimedes, and, whilst perusing the Hydrostatics of that author,
composed his earliest work,--an Essay on the Hydrostatical Balance. In
this he explains the method probably adopted by Archimedes for the
solution of Hiero's celebrated question[8], and shows himself already
well acquainted with the true principles of specific gravities. This
essay had an immediate and important influence on young Galileo's
fortunes, for it introduced him to the approving notice of Guido Ubaldi,
then one of the most distinguished mathematicians of Italy. At his
suggestion Galileo applied himself to consider the position of the
centre of gravity in solid bodies, a choice of subject that sufficiently
showed the estimate Ubaldi had formed of his talents; for it was a
question on which Commandine had recently written, and which engaged at
that time the attention of geometricians of the highest order. Galileo
tells us himself that he discontinued these researches on meeting with
Lucas Valerio's treatise on the same subject. Ubaldi was so much struck
with the genius displayed in the essay with which Galileo furnished him,
that he introduced him to his brother, the Cardinal Del Monte: by this
latter he was mentioned to Ferdinand de' Medici, the reigning Duke of
Tuscany, as a young man of whom the highest expectations might be
entertained. By the Duke's patronage he was nominated, in 1589, to the
lectureship of mathematics at Pisa, being then in his twenty-sixth year.
His public salary was fixed at the insignificant sum of sixty crowns
annually, but he had an opportunity of greatly adding to his income by
private tuition.


FOOTNOTES:

[4] Erythræus, Pinacotheca, vol. i.; Salusbury's Life of Galileo. Nelli,
Vita di Gal. Galilei.

[5] De his quæ diu vivunt. Patavii, 1612.

[6] Comment, in Avicennam. Venetiis, 1625.




CHAPTER III.

    _Galileo at Pisa--Aristotle--Leonardo da Vinci--Galileo becomes a
      Copernican--Urstisius--Bruno--Experiments on falling
      bodies--Galileo at Padua--Thermometer._


NO sooner was Galileo settled in his new office than he renewed his
inquiries into the phenomena of nature with increased diligence. He
instituted a course of experiments for the purpose of putting to the
test the mechanical doctrines of Aristotle, most of which he found
unsupported even by the pretence of experience. It is to be regretted
that we do not more frequently find detailed his method of
experimenting, than occasionally in the course of his dialogues, and it
is chiefly upon the references which he makes to the results with which
the experiments furnished him, and upon the avowed and notorious
character of his philosophy, that the truth of these accounts must be
made to depend. Venturi has found several unpublished papers by Galileo
on the subject of motion, in the Grand Duke's private library at
Florence, bearing the date of 1590, in which are many of the theorems
which he afterwards developed in his Dialogues on Motion. These were not
published till fifty years afterwards, and we shall reserve an account
of their contents till we reach that period of his life.

Galileo was by no means the first who had ventured to call in question
the authority of Aristotle in matters of science, although he was
undoubtedly the first whose opinions and writings produced a very marked
and general effect. Nizzoli, a celebrated scholar who lived in the early
part of the 16th century, had condemned Aristotle's philosophy,
especially his Physics, in very unequivocal and forcible terms,
declaring that, although there were many excellent truths in his
writings, the number was scarcely less of false, useless, and ridiculous
propositions.[9] About the time of Galileo's birth, Benedetti had
written expressly in confutation of several propositions contained in
Aristotle's mechanics, and had expounded in a clear manner some of the
doctrines of statical equilibrium.[10] Within the last forty years it
has been established that the celebrated painter Leonardo da Vinci, who
died in 1519, amused his leisure hours in scientific pursuits; and many
ideas appear to have occurred to him which are to be found in the
writings of Galileo at a later date. It is not impossible (though there
are probably no means of directly ascertaining the fact) that Galileo
may have been acquainted with Leonardo's investigations, although they
remained, till very lately, almost unknown to the mathematical world.
This supposition is rendered more probable from the fact, that Mazenta,
the preserver of Leonardo's manuscripts, was, at the very time of their
discovery, a contemporary student with Galileo at Pisa. Kopernik, or, as
he is usually called, Copernicus, a native of Thorn in Prussia, had
published his great work, De Revolutionibus, in 1543, restoring the
knowledge of the true theory of the solar system, and his opinions were
gradually and silently gaining ground.

It is not satisfactorily ascertained at what period Galileo embraced
the new astronomical theory. Gerard Voss attributes his conversion
to a public lecture of Mæstlin, the instructor of Kepler; and later
writers (among whom is Laplace) repeat the same story, but without
referring to any additional sources of information, and in most
instances merely transcribing Voss's words, so as to shew indisputably
whence they derived their account. Voss himself gives no authority,
and his general inaccuracy makes his mere word not of much weight. The
assertion appears, on many accounts, destitute of much probability.
If the story were correct, it seems likely that some degree of
acquaintance, if not of friendly intercourse, would have subsisted
between Mæstlin, and his supposed pupil, such as in fact we find
subsisting between Mæstlin and his acknowledged pupil Kepler, the
devoted friend of Galileo; but, on the contrary, we find Mæstlin
writing to Kepler himself of Galileo as an entire stranger, and in
the most disparaging terms. If Mæstlin could lay claim to the honour
of so celebrated a disciple, it is not likely that he could fail so
entirely to comprehend the distinction it must confer upon himself as
to attempt diminishing it by underrating his pupil's reputation. There
is a passage in Galileo's works which more directly controverts the
claim advanced for Mæstlin, although Salusbury, in his life of Galileo,
having apparently an imperfect recollection of its tenor, refers to
this very passage in confirmation of Voss's statement. In the second
part of the dialogue on the Copernican system, Galileo makes Sagredo,
one of the speakers in it, give the following account:--"Being very
young, and having scarcely finished my course of philosophy, which I
left off as being set upon other employments, there chanced to come
into these parts a certain foreigner of Rostoch, _whose name, as I
remember, was Christianus Urstisius_, a follower of Copernicus, who,
in an academy, gave two or three lectures upon this point, to whom
many flocked as auditors; but I, thinking they went more for the
novelty of the subject than otherwise, did not go to hear him; for I
had concluded with myself that that opinion could be no other than a
solemn madness; and questioning some of those who had been there, I
perceived they all made a jest thereof, except one, who told me that
the business was not altogether to be laughed at: and because the man
was reputed by me to be very intelligent and wary, I repented that I
was not there, and began from that time forward, as oft as I met with
any one of the Copernican persuasion, to demand of them if they had
been always of the same judgment. Of as many as I examined I found not
so much as one who told me not that he had been a long time of the
contrary opinion, but to have changed it for this, as convinced by the
strength of the reasons proving the same; and afterwards questioning
them one by one, to see whether they were well possessed of the reasons
of the other side, I found them all to be very ready and perfect in
them, so that I could not truly say that they took this opinion out
of ignorance, vanity, or to show the acuteness of their wits. On the
contrary, of as many of the Peripatetics and Ptolemeans as I have
asked, (and out of curiosity I have talked with many,) what pains they
had taken in the book of Copernicus, I found very few that had so much
as superficially perused it, but of those who I thought had understood
the same, not one: and, moreover, I have inquired amongst the followers
of the Peripatetic doctrine, if ever any of them had held the contrary
opinion, and likewise found none that had. Whereupon, considering that
there was no man who followed the opinion of Copernicus that had not
been first on the contrary side, and that was not very well acquainted
with the reasons of Aristotle and Ptolemy, and, on the contrary, that
there was not one of the followers of Ptolemy that had ever been of
the judgment of Copernicus, and had left that to embrace this of
Aristotle;--considering, I say, these things, I began to think that
one who leaveth an opinion imbued with his milk and followed by very
many, to take up another, owned by very few, and denied by all the
schools, and that really seems a great paradox, must needs have been
moved, not to say forced, by more powerful reasons. For this cause I
am become very curious to dive, as they say, into the bottom of this
business." It seems improbable that Galileo should think it worth while
to give so detailed an account of the birth and growth of opinion in
any one besides himself; and although Sagredo is not the personage who
generally in the dialogue represents Galileo, yet as the real Sagredo
was a young nobleman, a pupil of Galileo himself, the account cannot
refer to him. The circumstance mentioned of the intermission of his
philosophical studies, though in itself trivial, agrees very well with
Galileo's original medical destination. Urstisius is not a fictitious
name, as possibly Salusbury may have thought, when alluding to this
passage; he was mathematical professor at Bâle, about 1567, and several
treatises by him are still extant. According to Kästner, his German name
was Wursteisen. In 1568 Voss informs us that he published some new
questions on Purbach's Theory of the Planets. He died at Bâle in 1586,
when Galileo was about twenty-two years old.

It is not unlikely that Galileo also, in part, owed his emancipation
from popular prejudices to the writings of Giordano Bruno, an
unfortunate man, whose unsparing boldness in exposing fallacies and
absurdities was rewarded by a judicial murder, and by the character of
heretic and infidel, with which his executioners endeavoured to
stigmatize him for the purpose of covering over their own atrocious
crime. Bruno was burnt at Rome in 1600, but not, as Montucla supposes,
on account of his "Spaccio della Bestia trionfante." The title of this
book has led him to suppose that it was directed against the church of
Rome, to which it does not in the slightest degree relate. Bruno
attacked the fashionable philosophy alternately with reason and
ridicule, and numerous passages in his writings, tedious and obscure as
they generally are, show that he had completely outstripped the age in
which he lived. Among his astronomical opinions, he believed that the
universe consisted of innumerable systems of suns with assemblages of
planets revolving round each of them, like our own earth, the smallness
of which, alone, prevented their being observed by us. He remarked
further, "that it is by no means improbable that there are yet other
planets revolving round our own sun, which we have not yet noticed,
either on account of their minute size or too remote distance from us."
He declined asserting that all the apparently fixed stars are really so,
considering this as not sufficiently proved, "because at such enormous
distances the motions become difficult to estimate, and it is only by
long observation that we can determine if any of these move round each
other, or what other motions they may have." He ridiculed the
Aristotelians in no very measured terms--"They harden themselves, and
heat themselves, and embroil themselves for Aristotle; they call
themselves his champions, they hate all but Aristotle's friends, they
are ready to live and die for Aristotle, and yet they do not understand
so much as the titles of Aristotle's chapters." And in another place he
introduces an Aristotelian inquiring, "Do you take Plato for an
ignoramus--Aristotle for an ass?" to whom he answers, "My son, I neither
call them asses, nor you mules,--them baboons, nor you apes,--as you
would have me: I told you that I esteem them the heroes of the world,
but I will not credit them without sufficient reason; and if you were
not both blind and deaf, you would understand that I must disbelieve
their absurd and contradictory assertions."[11] Bruno's works, though in
general considered those of a visionary and madman, were in very
extensive circulation, probably not the less eagerly sought after from
being included among the books prohibited by the Romish church; and
although it has been reserved for later observations to furnish complete
verification of his most daring speculations, yet there was enough,
abstractedly taken, in the wild freedom of his remarks, to attract a
mind like Galileo's; and it is with more satisfaction that we refer the
formation of his opinions to a man of undoubted though eccentric genius,
like Bruno, than to such as Maestlin, who, though a diligent and careful
observer, seems seldom to have taken any very enlarged views of the
science on which he was engaged.

With a few exceptions similar to those above mentioned, the rest of
Galileo's contemporaries well deserved the contemptuous epithet which he
fixed on them of Paper Philosophers, for, to use his own words, in a
letter to Kepler on this subject, "this sort of men fancied philosophy
was to be studied like the Æneid or Odyssey, and that the true reading
of nature was to be detected by the collation of texts." Galileo's own
method of philosophizing was widely different; seldom omitting to bring
with every new assertion the test of experiment, either directly in
confirmation of it, or tending to show its probability and consistency.
We have already seen that he engaged in a series of experiments to
investigate the truth of some of Aristotle's positions. As fast as he
succeeded in demonstrating the falsehood of any of them, he denounced
them from his professorial chair with an energy and success which
irritated more and more against him the other members of the academic
body.

There seems something in the stubborn opposition which he encountered in
establishing the truth of his mechanical theorems, still more stupidly
absurd than in the ill will to which, at a later period of his life, his
astronomical opinions exposed him: it is intelligible that the vulgar
should withhold their assent from one who pretended to discoveries in
the remote heavens, which few possessed instruments to verify, or
talents to appreciate; but it is difficult to find terms for
stigmatizing the obdurate folly of those who preferred the evidence of
their books to that of their senses, in judging of phenomena so obvious
as those, for instance, presented by the fall of bodies to the ground.
Aristotle had asserted, that if two different weights of the same
material were let fall from the same height, the heavier one would reach
the ground sooner than the other, in the proportion of their weights.
The experiment is certainly not a very difficult one, but nobody thought
of that method of argument, and consequently this assertion had been
long received, upon his word, among the axioms of the science of motion.
Galileo ventured to appeal from the authority of Aristotle to that of
his own senses, and maintained that, with the exception of an
inconsiderable difference, which he attributed to the disproportionate
resistance of the air, they would fall in the same time. The
Aristotelians ridiculed and refused to listen to such an idea. Galileo
repeated his experiments in their presence from the famous leaning tower
at Pisa: and with the sound of the simultaneously falling weights still
ringing in their ears, they could persist in gravely maintaining that a
weight of ten pounds would reach the ground in a tenth part of the time
taken by one of a single pound, because they were able to quote chapter
and verse in which Aristotle assures them that such is the fact. A
temper of mind like this could not fail to produce ill will towards him
who felt no scruples in exposing their wilful folly; and the watchful
malice of these men soon found the means of making Galileo desirous of
quitting his situation at Pisa. Don Giovanni de' Medici, a natural son
of Cosmo, who possessed a slight knowledge of mechanics on which he
prided himself, had proposed a contrivance for cleansing the port of
Leghorn, on the efficiency of which Galileo was consulted. His opinion
was unfavourable, and the violence of the inventor's disappointment,
(for Galileo's judgment was verified by the result,) took the somewhat
unreasonable direction of hatred towards the man whose penetration had
foreseen the failure. Galileo's situation was rendered so unpleasant by
the machinations of this person, that he decided on accepting overtures
elsewhere, which had already been made to him; accordingly, under the
negotiation of his staunch friend Guido Ubaldi, and with the consent of
Ferdinand, he procured from the republic of Venice a nomination for six
years to the professorship of mathematics in the university of Padua,
whither he removed in September 1592.

Galileo's predecessor in the mathematical chair at Padua was Moleti, who
died in 1588, and the situation had remained unfilled during the
intervening four years. This seems to show that the directors attributed
but little importance to the knowledge which it was the professor's duty
to impart. This inference is strengthened by the fact, that the amount
of the annual salary attached to it did not exceed 180 florins, whilst
the professors of philosophy and civil law, in the same university, were
rated at the annual stipends of 1400 and 1680 florins.[12] Galileo
joined the university about a year after its triumph over the Jesuits,
who had established a school in Padua about the year 1542, and,
increasing yearly in influence, had shown symptoms of a design to get
the whole management of the public education into the hands of their own
body.[13] After several violent disputes it was at length decreed by the
Venetian senate, in 1591, that no Jesuit should be allowed to give
instruction at Padua in any of the sciences professed in the university.
It does not appear that after this decree they were again troublesome to
the university, but this first decree against them was followed, in
1606, by a second more peremptory, which banished them entirely from the
Venetian territory. Galileo would of course find his fellow-professors
much embittered against that society, and would naturally feel inclined
to make common cause with them, so that it is not unlikely that the
hatred which the Jesuits afterwards bore to Galileo on personal
considerations, might be enforced by their recollection of the
university to which he had belonged.

Galileo's writings now began to follow each other with great rapidity,
but he was at this time apparently so careless of his reputation, that
many of his works and inventions, after a long circulation in manuscript
among his pupils and friends, found their way into the hands of those
who were not ashamed to publish them as their own, and to denounce
Galileo's claim to the authorship as the pretence of an impudent
plagiarist. He was, however, so much beloved and esteemed by his
friends, that they vied with each other in resenting affronts of this
nature offered to him, and in more than one instance he was relieved, by
their full and triumphant answers, from the trouble of vindicating his
own character.

To this epoch of Galileo's life may be referred his re-invention of the
thermometer. The original idea of this useful instrument belongs to the
Greek mathematician Hero; and Santorio himself, who has been named as
the inventor by Italian writers, and at one time claimed it himself,
refers it to him. In 1638, Castelli wrote to Cesarini that "he
remembered an experiment shown to him more than thirty-five years back
by Galileo, who took a small glass bottle, about the size of a hen's
egg, the neck of which was twenty-two inches long, and as narrow as a
straw. Having well heated the bulb in his hands, and then introducing
its mouth into a vessel in which was a little water, and withdrawing the
heat of his hand from the bulb, the water rose in the neck of the bottle
more than eleven inches above the level in the vessel, and Galileo
employed this principle in the construction of an instrument for
measuring heat and cold."[14] In 1613, a Venetian nobleman named
Sagredo, who has been already mentioned as Galileo's friend and pupil,
writes to him in the following words: "I have brought the instrument
which you invented for measuring heat into several convenient and
perfect forms, so that the difference of temperature between two rooms
is seen as far as 100 degrees."[15] This date is anterior to the claims
both of Santorio and Drebbel, a Dutch physician, who was the first to
introduce it into Holland.

Galileo's thermometer, as we have just seen, consisted merely of a glass
tube ending in a bulb, the air in which, being partly expelled by heat,
was replaced by water from a glass into which the open end of the tube
was plunged, and the different degrees of temperature were indicated by
the expansion of the air which yet remained in the bulb, so that the
scale would be the reverse of that of the thermometer now in use, for
the water would stand at the highest level in the coldest weather. It
was, in truth, a barometer also, in consequence of the communication
between the tube and external air, although Galileo did not intend it
for this purpose, and when he attempted to determine the relative weight
of the air, employed a contrivance still more imperfect than this rude
barometer would have been. A passage among his posthumous fragments
intimates that he subsequently used spirit of wine instead of water.

Viviani attributes an improvement of this imperfect instrument, but
without specifying its nature, to Ferdinand II., a pupil and subsequent
patron of Galileo, and, after the death of his father Cosmo, reigning
duke of Florence. It was still further improved by Ferdinand's younger
brother, Leopold de' Medici, who invented the modern process of
expelling all the air from the tube by boiling the spirit of wine in it,
and of hermetically sealing the end of the tube, whilst the contained
liquid is in this expanded state, which deprived it of its barometrical
character, and first made it an accurate thermometer. The final
improvement was the employment of mercury instead of spirit of wine,
which is recommended by Lana so early as 1670, on account of its equable
expansion.[16] For further details on the history and use of this
instrument, the reader may consult the Treatises on the THERMOMETER and
PYROMETER.


FOOTNOTES:

[7] Essai sur les Ouvrages de Leonard da Vinci. Paris, 1797.

[8] See Treatise on HYDROSTATICS.

[9] Antibarbarus Philosophicus. Francofurti, 1674.

[10] Speculationum liber. Venetiis, 1585.

[11] De l'Infinito Universo. Dial. 3. La Cena de le Cenere, 1584.

[12] Riccoboni, Commentarii de Gymnasio Patavino, 1598.

[13] Nelli.

[14] Nelli.

[15] Venturi. Memorie e Lettere di Gal. Galilei. Modena, 1821.

[16] Prodromo all' Arte Maestra. Brescia, 1670.




CHAPTER IV.

    _Astronomy before Copernicus--Fracastoro--Bacon--Kepler--Galileo's
      Treatise on the Sphere._


THIS period of Galileo's lectureship at Padua derives interest from its
including the first notice which we find of his having embraced the
doctrines of the Copernican astronomy. Most of our readers are aware of
the principles of the theory of the celestial motions which Copernicus
restored; but the number of those who possess much knowledge of the
cumbrous and unwieldy system which it superseded is perhaps more
limited. The present is not a fit opportunity to enter into many details
respecting it; these will find their proper place in the History of
Astronomy: but a brief sketch of its leading principles is necessary to
render what follows intelligible.

The earth was supposed to be immoveably fixed in the centre of the
universe, and immediately surrounding it the atmospheres of air and
fire, beyond which the sun, moon, and planets, were thought to be
carried round the earth, fixed each to a separate orb or heaven of solid
but transparent matter. The order of distance in which they were
supposed to be placed with regard to the central earth was as follows:
The Moon, Mercury, Venus, The Sun, Mars, Jupiter, and Saturn. It became
a question in the ages immediately preceding Copernicus, whether the Sun
was not nearer the Earth than Mercury, or at least than Venus; and this
question was one on which the astronomical theorists were then chiefly
divided.

We possess at this time a curious record of a former belief in this
arrangement of the Sun and planets, in the order in which the days of
the week have been named from them. According to the dreams of
Astrology, each planet was supposed to exert its influence in
succession, reckoning from the most distant down to the nearest, over
each hour of the twenty-four. The planet which was supposed to
predominate over the first hour, gave its name to that day.[17] The
general reader will trace this curious fact more easily with the French
or Latin names than with the English, which have been translated into
the titles of the corresponding Saxon deities. Placing the Sun and
planets in the following order, and beginning, for instance, with
Monday, or the Moon's day; Saturn ruled the second hour of that day,
Jupiter the third, and so round till we come again and again to the Moon
on the 8th, 15th, and 22d hours; Saturn ruled the 23d, Jupiter the
24th, so that the next day would be the day of Mars, or, as the Saxons
translated it, Tuisco's day, or Tuesday. In the same manner the
following days would belong respectively to Mercury or Woden, Jupiter or
Thor, Venus or Frea, Saturn or Seater, the Sun, and again the Moon. In
this manner the whole week will be found to complete the cycle of the
seven planets.

[Illustration: Cycle of the seven planets.]

The other stars were supposed to be fixed in an outer orb, beyond which
were two crystalline spheres, (as they were called,) and on the outside
of all, the _primum mobile_ or _first moveable_, which sphere was
supposed to revolve round the earth in twenty-four hours, and by its
friction, or rather, as most of the philosophers of that day chose to
term it, by the sort of heavenly influence which it exercised on the
interior orbs, to carry them round with a similar motion. Hence the
diversity of day and night. But beside this principal and general
motion, each orb was supposed to have one of its own, which was intended
to account for the apparent changes of position of the planets with
respect to the fixed stars and to each other. This supposition, however,
proving insufficient to account for all the irregularities of motion
observed, two hypotheses were introduced.--First, that to each planet
belonged several concentric spheres or heavens, casing each other like
the coats of an onion, and, secondly, that the centres of these solid
spheres, with which the planet revolved, were placed in the
circumference of a secondary revolving sphere, the centre of which
secondary sphere was situated at the earth. They thus acquired the names
of Eccentrics or Epicycles, the latter word signifying a circle upon a
circle. The whole art of astronomers was then directed towards inventing
and combining different eccentric and epicyclical motions, so as to
represent with tolerable fidelity the ever varying phenomena of the
heavens. Aristotle had lent his powerful assistance in this, as in other
branches of natural philosophy, in enabling the false system to prevail
against and obliterate the knowledge of the true, which, as we gather
from his own writings, was maintained by some philosophers before his
time. Of these ancient opinions, only a few traces now remain,
principally preserved in the works of those who were adverse to them.
Archimedes says expressly that Aristarchus of Samos, who lived about 300
B. C., taught the immobility of the sun and stars, and that the earth is
carried round the central sun.[18] Aristotle's words are: "Most of those
who assert that the whole concave is finite, say that the earth is
situated in the middle point of the universe: those who are called
Pythagoreans, who live in Italy, are of a contrary opinion. For they say
that fire is in the centre, and that the earth, which, according to
them, is one of the stars, occasions the change of day and night by its
own motion, with which it is carried about the centre." It might be
doubtful, upon this passage alone, whether the Pythagorean theory
embraced more than the diurnal motion of the earth, but a little
farther, we find the following passage: "Some, as we have said, make the
earth to be one of the stars: others say that it is placed in the centre
of the Universe, and revolves on a central axis."[19] From which, in
conjunction with the former extract, it very plainly appears that the
Pythagoreans maintained both the diurnal and annual motions of the
earth.

Some idea of the supererogatory labour entailed upon astronomers by the
adoption of the system which places the earth in the centre, may be
formed in a popular manner by observing, in passing through a thickly
planted wood, in how complicated a manner the relative positions of the
trees appear at each step to be continually changing, and by considering
the difficulty with which the laws of their apparent motions could be
traced, if we were to attempt to refer these changes to a real motion of
the trees instead of the traveller. The apparent complexity in the
heavens is still greater than in the case suggested; because, in
addition to the earth's motions, with which all the stars appear to be
impressed, each of the planets has also a real motion of its own, which
of course greatly contributes to perplex and complicate the general
appearances. Accordingly the heavens rapidly became, under this system,

    "With centric and eccentric scribbled o'er,
    Cycle and epicycle, orb in orb;"[20]

crossing and penetrating each other in every direction. Maestlin has
given a concise enumeration of the principal orbs which belonged to this
theory. After warning the readers that "they are not mere fictions which
have nothing to correspond with them out of the imagination, but that
they exist really, and bodily in the heavens,"[21] he describes seven
principal spheres belonging to each planet, which he classes as
Eccentrics, Epicycles, and Concentrepicycles, and explains their use in
accounting for the planet's revolutions, motions of the apogee, and
nodes, &c. &c. In what manner this multitude of solid and crystalline
orbs were secured from injuring or interfering with each other was not
very closely inquired into.

The reader will cease to expect any very intelligible explanation of
this and numberless other difficulties which belong to this unwieldy
machinery when he is introduced to the reasoning by which it was upheld.
Gerolamo Fracastoro, who lived in the sixteenth century, writes in the
following terms, in his work entitled Homocentrica, (certainly one of
the best productions of the day,) in which he endeavours to simplify the
necessary apparatus, and to explain all the phenomena (as the title of
his book implies) by concentric spheres round the earth. "There are
some, not only of the ancients but also among the moderns, who believe
that the stars move freely without any such agency; but it is difficult
to conceive in what manner they have imbued themselves with this notion,
_since not only reason, but the very senses, inform us that all the
stars are carried round fastened to solid spheres_." What ideas
Fracastoro entertained of the evidence of the "senses" it is not now
easy to guess, but he goes on to give a specimen of the "reasoning"
which appeared to him so incontrovertible. "The planets are observed to
move one while forwards, then backwards, now to the right, now to the
left, quicker and slower by turns; which variety is consistent with a
compound structure like that of an animal, which possesses in itself
various springs and principles of action, but is totally at variance
with our notion of a simple and undecaying substance like the heavens
and heavenly bodies. For that which is simple, is altogether single, and
singleness is of one only nature, and one nature can be the cause of
only one effect; and therefore it is altogether impossible that the
stars of themselves should move with such variety of motion. And
besides, if the stars move by themselves, they either move in an empty
space, or in a fluid medium like the air. But there cannot be such a
thing as empty space, and if there were such a medium, the motion of the
star would occasion condensation and rarefaction in different parts of
it, which is the property of corruptible bodies and where they exist
some violent motion is going on; but the heavens are incorruptible and
are not susceptible of violent motion, and hence, and from many other
similar reasons, any one who is not obstinate may satisfy himself that
the stars cannot have any independent motion."

Some persons may perhaps think that arguments of this force are
unnecessarily dragged from the obscurity to which they are now for the
most part happily consigned; but it is essential, in order to set
Galileo's character and merits in their true light, to show how low at
this time philosophy had fallen. For we shall form a very inadequate
notion of his powers and deserts if we do not contemplate him in the
midst of men who, though of undoubted talent and ingenuity, could so far
bewilder themselves as to mistake such a string of unmeaning phrases for
argument: we must reflect on the difficulty every one experiences in
delivering himself from the erroneous impressions of infancy, which will
remain stamped upon the imagination in spite of all the efforts of
matured reason to erase them, and consider every step of Galileo's
course as a triumph over difficulties of a like nature. We ought to be
fully penetrated with this feeling before we sit down to the perusal of
his works, every line of which will then increase our admiration of the
penetrating acuteness of his invention and unswerving accuracy of his
judgment. In almost every page we discover an allusion to some new
experiment, or the germ of some new theory; and amid all this wonderful
fertility it is rarely indeed that we find the exuberance of his
imagination seducing him from the rigid path of philosophical induction.
This is the more remarkable as he was surrounded by friends and
contemporaries of a different temperament and much less cautious
disposition. A disadvantageous contrast is occasionally furnished even
by the sagacious Bacon, who could so far deviate from the sound
principles of inductive philosophy, as to write, for instance, in the
following strain, bordering upon the worst manner of the
Aristotelians:--"Motion in a circle has no limit, and seems to emanate
from the appetite of the body, which moves only for the sake of moving,
and that it may follow itself and seek its own embraces, and put in
action and enjoy its own nature, and exercise its peculiar operation: on
the contrary, motion in a straight line seems transitory, and to move
towards a limit of cessation or rest, and that it may reach some point,
and then put off its motion."[22] Bacon rejected all the machinery of
the _primum mobile_ and the solid spheres, the eccentrics and the
epicycles, and carried his dislike of these doctrines so far as to
assert that nothing short of their gross absurdity could have driven
theorists to the extravagant supposition of the motion of the earth,
which, said he, "we know to be most false."[23] Instances of extravagant
suppositions and premature generalizations are to be found in almost
every page of his other great contemporary, Kepler.

It is with pain that we observe Delambre taking every opportunity, in
his admirable History of Astronomy, to undervalue and sneer at Galileo,
seemingly for the sake of elevating the character of Kepler, who appears
his principal favourite, but whose merit as a philosopher cannot safely
be brought into competition with that of his illustrious contemporary.
Delambre is especially dissatisfied with Galileo, for taking no notice,
in his "System of the World," of the celebrated laws of the planetary
motions which Kepler discovered, and which are now inseparably connected
with his name. The analysis of Newton and his successors has now
identified those apparently mysterious laws with the general phenomena
of motion, and has thus entitled them to an attention of which, before
that time, they were scarcely worthy; at any rate not more than is at
present the empirical law which includes the distances of all the
planets from the sun (roughly taken) in one algebraical formula. The
observations of Kepler's day were scarcely accurate enough to prove that
the relations which he discovered between the distances of the planets
from the sun and the periods of their revolutions around him were
necessarily to be received as demonstrated truths; and Galileo surely
acted most prudently and philosophically in holding himself altogether
aloof from Kepler's fanciful devices and numeral concinnities, although,
with all the extravagance, they possessed much of the genius of the
Platonic reveries, and although it did happen that Galileo, by
systematically avoiding them, failed to recognise some important truths.
Galileo probably was thinking of those very laws, when he said of
Kepler, "He possesses a bold and free genius, perhaps too much so; but
his mode of philosophizing is widely different from mine." We shall have
further occasion in the sequel to recognise the justice of this remark.

In the treatise on the Sphere which bears Galileo's name, and which, if
he be indeed the author of it, was composed during the early part of his
residence at Padua, he also adopts the Ptolemaic system, placing the
earth immoveable in the centre, and adducing against its motion the
usual arguments, which in his subsequent writings he ridicules and
refutes. Some doubts have been expressed of its authenticity; but,
however this may be, we have it under Galileo's own hand that he taught
the Ptolemaic system, in compliance with popular prejudices, for some
time after he had privately become a convert to the contrary opinions.
In a letter, apparently the first which he wrote to Kepler, dated from
Padua, 1597, he says, acknowledging the receipt of Kepler's Mysterium
Cosmographicum, "I have as yet read nothing beyond the preface of your
book, from which however I catch a glimpse of your meaning, and feel
great joy on meeting with so powerful an associate in the pursuit of
truth, and consequently such a friend to truth itself, for it is
deplorable that there should be so few who care about truth, and who do
not persist in their perverse mode of philosophizing; but as this is not
the fit time for lamenting the melancholy condition of our times, but
for congratulating you on your elegant discoveries in confirmation of
the truth, I shall only add a promise to peruse your book
dispassionately, and with a conviction that I shall find in it much to
admire. _This I shall do the more willingly because many years ago I
became a convert to the opinions of Copernicus_,[24] and by that theory
have succeeded in fully explaining many phenomena, which on the contrary
hypothesis are altogether inexplicable. I have arranged many arguments
and confutations of the opposite opinions, _which however I have not yet
dared to publish_, fearing the fate of our master Copernicus, who,
although he has earned immortal fame among a few, yet by an infinite
number (for so only can the number of fools be measured) is exploded and
derided. If there were many such as you, I would venture to publish my
speculations; but, since that is not so, I shall take time to consider
of it." This interesting letter was the beginning of the friendship of
these two great men, which lasted uninterruptedly till 1630, the date of
Kepler's death. That extraordinary genius never omitted an opportunity
of testifying his admiration of Galileo, although there were not wanting
persons envious of their good understanding, who exerted themselves to
provoke coolness and quarrel between them. Thus Brutius writes to Kepler
in 1602[25]: "Galileo tells me he has written to you, and has got your
book, which however he denied to Magini, and I abused him for praising
you with too many qualifications. I know it to be a fact that, both in
his lectures, and elsewhere, he is publishing your inventions as his
own; but I have taken care, and shall continue to do so, that all this
shall redound not to his credit but to yours." The only notice which
Kepler took of these repeated insinuations, which appear to have been
utterly groundless, was, by renewed expressions of respect and
admiration, to testify the value he set upon his friend and
fellow-labourer in philosophy.


FOOTNOTES:

[17] Dion Cassius, lib. 37.

[18] The pretended translation by Roberval of an Arabic version of
Aristarchus, "De Systemate Mundi," in which the Copernican system is
fully developed, is spurious. Menage asserts this in his observations on
Diogen. Laert. lib. 8, sec. 85, tom. ii., p. 389. (Ed. Amst. 1692.) The
commentary contains many authorities well worth consulting. Delambre,
Histoire de l'Astronomie, infers it from its not containing some
opinions which Archimedes tells us were held by Aristarchus. A more
direct proof may be gathered from the following blunder of the supposed
translator. Astronomers had been long aware that the earth in different
parts of her orbit is at different distances from the sun. Roberval
wished to claim for Aristarchus the credit of having known this, and
introduced into his book, not only the mention of the fact, but an
explanation of its cause. Accordingly he makes Aristarchus give a reason
"why the sun's apogee (or place of greatest distance from the earth)
must always be at the north summer solstice." In fact, it was there, or
nearly so, in Roberval's time, and he knew not but that it had always
been there. It is however moveable, and, when Aristarchus lived, was
nearly half way between the solstices and equinoxes. He therefore would
hardly have given a reason for the necessity of a phenomenon of which,
if he observed anything on the subject, he must have observed the
contrary. The change in the obliquity of the earth's axis to the
ecliptic was known in the time of Roberval, and he accordingly has
introduced the proper value which it had in Aristarchus's time.

[19] De Coelo. lib. 2.

[20] Paradise Lost, b. viii. v. 83.

[21] Itaque tam circulos primi motus quam orbes secundorum mobilium
reverâ in coelesti corpore esse concludimus, &c. Non ergo sunt mera
figmenta, quibus extra mentem nihil correspondeat. M. Maestlini, De
Astronomiæ Hypothesibus disputatio. Heidelbergæ, 1582.

[22] Opuscula Philosophica, Thema Coeli.

[23] "Nobis constat falsissimum esse." De Aug. Scient. lib. iii. c. 3,
1623.

[24] Id autum eò libentius faciam, quod in Copernici sententiam multis
abhinc annis venerim.--Kepl. Epistolæ.

[25] Kepleri Epistolæ.




CHAPTER V.

    _Galileo re-elected Professor at Padua--New star--Compass of
      proportion--Capra--Gilbert--Proposals to return to Pisa--Lost
      writings--Cavalieri._


GALILEO'S reputation was now rapidly increasing: his lectures were
attended by many persons of the highest rank; among whom were the
Archduke Ferdinand, afterwards Emperor of Germany, the Landgrave of
Hesse, and the Princes of Alsace and Mantua. On the expiration of the
first period for which he had been elected professor, he was rechosen
for a similar period, with a salary increased to 320 florins. The
immediate occasion of this augmentation is said by Fabroni[26], to have
arisen out of the malice of an ill wisher of Galileo, who, hoping to do
him disservice, apprized the senate that he was not married to Marina
Gamba, then living with him, and the mother of his son Vincenzo. Whether
or not the senate might consider themselves entitled to inquire into the
morality of his private life, it was probably from a wish to mark their
sense of the informer's impertinence, that they returned the brief
answer, that "if he had a family to provide for, he stood the more in
need of an increased stipend."

During Galileo's residence at Padua, and, according to Viviani's
intimation, towards the thirtieth year of his age, that is to say in
1594, he experienced the first attack of a disease which pressed
heavily on him for the rest of his life. He enjoyed, when a young man, a
healthy and vigorous constitution, but chancing to sleep one afternoon
near an open window, through which was blowing a current of air cooled
artificially by the fall of water, the consequences were most disastrous
to him. He contracted a sort of chronic complaint, which showed itself
in acute pains in his limbs, chest, and back, accompanied with frequent
hæmorrhages and loss of sleep and appetite; and this painful disorder
thenceforward never left him entirely, but recurred intermittingly, with
greater or less violence, as long as he lived. Others of the party did
not even escape so well, but died shortly after committing this
imprudence.

In 1604, the attention of astronomers was called to the contemplation of
a new star, which appeared suddenly with great splendour in the
constellation Serpentarius, or Ophiuchus, as it is now more commonly
called. Maestlin, who was one of the earliest to notice it, relates his
observations in the following words: "How wonderful is this new star! I
am certain that I did not see it before the 29th of September, nor
indeed, on account of several cloudy nights, had I a good view till the
6th of October. Now that it is on the other side of the sun, instead of
surpassing Jupiter as it did, and almost rivalling Venus, it scarcely
matches the Cor Leonis, and hardly surpasses Saturn. It continues
however to shine with the same bright and strongly sparkling light, and
changes its colours almost with every moment; first tawny, then yellow,
presently purple and red, and, when it has risen above the vapours, most
frequently white." This was by no means an unprecedented phenomenon; and
the curious reader may find in Riccioli[27] a catalogue of the principal
new stars which have at different times appeared. There is a tradition
of a similar occurrence as early as the times of the Greek astronomer
Hipparchus, who is said to have been stimulated by it to the formation
of his catalogue of the stars; and only thirty-two years before, in
1572, the same remarkable phenomenon in the constellation Cassiopeia was
mainly instrumental in detaching the celebrated Tycho Brahe from the
chemical studies, which till then divided his attention with astronomy.
Tycho's star disappeared at the end of two years; and at that time
Galileo was a child. On the present occasion, he set himself earnestly
to consider the new phenomenon, and embodied the results of his
observations in three lectures, which have been unfortunately lost. Only
the exordium of the first has been preserved: in this he reproaches his
auditors with their general insensibility to the magnificent wonders of
creation daily exposed to their view, in no respect less admirable than
the new prodigy, to hear an explanation of which they had hurried in
crowds to his lecture room. He showed, from the absence of parallax,
that the new star could not be, as the vulgar hypothesis represented, a
mere meteor engendered in our atmosphere and nearer the earth than the
moon, but must be situated among the most remote heavenly bodies. This
was inconceivable to the Aristotelians, whose notions of a perfect,
simple, and unchangeable sky were quite at variance with the
introduction of any such new body; and we may perhaps consider these
lectures as the first public declaration of Galileo's hostility to the
old Ptolemaic and Aristotelian astronomy.

In 1606 he was reappointed to the lectureship, and his salary a second
time increased, being raised to 520 florins. His public lectures were at
this period so much thronged that the ordinary place of meeting was
found insufficient to contain his auditors, and he was on several
occasions obliged to adjourn to the open air,--even from the school of
medicine, which was calculated to contain one thousand persons.

About this time he was considerably annoyed by a young Milanese, of the
name of Balthasar Capra, who pirated an instrument which Galileo had
invented some years before, and had called the geometrical and military
compass. The original offender was a German named Simon Mayer, whom we
shall meet with afterwards arrogating to himself the merit of one of
Galileo's astronomical discoveries; but on this occasion, as soon as he
found Galileo disposed to resent the injury done to him, he hastily
quitted Italy, leaving his friend Capra to bear alone the shame of the
exposure which followed. The instrument is of simple construction,
consisting merely of two straight rulers, connected by a joint; so that
they can be set to any required angle. This simple and useful
instrument, now called the Sector, is to be found in almost every case
of mathematical instruments. Instead of the trigonometrical and
logarithmic lines which are now generally engraved upon it, Galileo's
compass merely contained, on one side, three pairs of lines, divided in
simple, duplicate, and triplicate proportion, with a fourth pair on
which were registered the specific gravities of several of the most
common metals. These were used for multiplications, divisions, and the
extraction of roots; for finding the dimensions of equally heavy balls
of different materials, &c. On the other side were lines contrived for
assisting to describe any required polygon on a given line; for finding
polygons of one kind equal in area to those of another; and a multitude
of other similar operations useful to the practical engineer.

Unless the instrument, which is now called Gunter's scale, be much
altered from what it originally was, it is difficult to understand on
what grounds Salusbury charges Gunter with plagiarism from Galileo's
Compass. He declares that he has closely compared the two, and can find
no difference between them.[28] There has also been some confusion, by
several writers, between this instrument and what is now commonly called
the Proportional Compass. The latter consists of two slips of metal
pointed at each end, and connected by a pin which, sliding in a groove
through both, can be shifted to different positions. Its use is to find
proportional lines; for it is obvious that the openings measured by each
pair of legs will be in the same proportion in which the slips are
divided by the centre. The divisions usually marked on it are calculated
for finding the submultiples of straight lines, and the chords of
submultiple arcs. Montucla has mentioned this mistake of one instrument
for the other, and charges Voltaire with the more inexcusable error of
confounding Galileo's with the Mariner's Compass. He refers to a
treatise by Hulsius for his authority in attributing the Proportional
Compass to Burgi, a Swiss astronomer of some celebrity. Horcher also has
been styled the inventor; but he did no more than describe its form and
application. In the frontispiece of his book is an engraving of this
compass exactly similar to those which are now used.[29] To the
description which Galileo published of his compass, he added a short
treatise on the method of measuring heights and distances with the
quadrant and plumb line. The treatise, which is printed by itself at the
end of the first volume of the Padua edition of Galileo's works,
contains nothing more than the demonstrations belonging to the same
operations. They are quite elementary, and contain little or nothing
that was new even at that time.

Such an instrument as Galileo's Compass was of much more importance
before the grand discovery of logarithms than it can now be considered:
however it acquires an additional interest from the value which he
himself set on it. In 1607, Capra, at the instigation of Mayer,
published as his own invention what he calls the proportional hoop,
which is a mere copy of Galileo's instrument. This produced from Galileo
a long essay, entitled "A Defence of Galileo against the Calumnies and
Impostures of Balthasar Capra." His principal complaint seems to have
been of the misrepresentations which Capra had published of his lectures
on the new star already mentioned, but he takes occasion, after pointing
out the blunders and falsehoods which Capra had committed on that
occasion, to add a complete proof of his piracy of the geometrical
compass. He showed, from the authenticated depositions of workmen, and
of those for whom the instruments had been fabricated, that he had
devised them as early as the year 1597, and had explained their
construction and use both to Balthasar himself and to his father Aurelio
Capra, who was then residing in Padua. He gives, in the same essay, the
minutes of a public meeting between himself and Capra, in which he
proved, to the satisfaction of the university, that wherever Capra had
endeavoured to introduce into his book propositions which were not to be
met with in Galileo's, he had fallen into the greatest absurdities, and
betrayed the most complete ignorance of his subject. The consequence of
this public exposure, and of the report of the famous Fra Paolo Sarpi,
to whom the matter had been referred, was a formal prohibition by the
university of Capra's publication, and all copies of the book then on
hand were seized, and probably destroyed, though Galileo has preserved
it from oblivion by incorporating it in his own publication.

Nearly at the same time, 1607, or immediately after, he first turned his
attention towards the loadstone, on which our countryman Gilbert had
already published his researches, conducted in the true spirit of the
inductive method. Very little that is original is to be found in
Galileo's works on this subject, except some allusions to his method of
arming magnets, in which, as in most of his practical and mechanical
operations, he appears to have been singularly successful. Sir Kenelm
Digby[30] asserts, that the magnets armed by Galileo would support twice
as great a weight as one of Gilbert's of the same size. Galileo was well
acquainted, as appears from his frequent allusions in different parts of
his works, with what Gilbert had done, of whom he says, "I extremely
praise, admire, and envy this author;--I think him, moreover, worthy of
the greatest praise for the many new and true observations that he has
made to the disgrace of so many vain and fabling authors, who write, not
from their own knowledge only, but repeat every thing they hear from the
foolish vulgar, without attempting to satisfy themselves of the same by
experience, perhaps that they may not diminish the size of their books."

Galileo's reputation being now greatly increased, proposals were made to
him, in 1609, to return to his original situation at Pisa. He had been
in the habit of passing over to Florence during the academic vacation,
for the purpose of giving mathematical instruction to the younger
members of Ferdinand's family; and Cosmo, who had now succeeded his
father as duke of Tuscany, regretted that so masterly a genius had been
allowed to leave the university which he naturally should have graced. A
few extracts from Galileo's answers to these overtures will serve to
show the nature of his situation at Padua, and the manner in which his
time was there occupied. "I will not hesitate to say, having now
laboured during twenty years, and those the best of my life, in dealing
out, as one may say, in detail, at the request of any body, the little
talent which God has granted to my assiduity in my profession, that my
wish certainly would be to have sufficient rest and leisure to enable
me, before my life comes to its close, to conclude three great works
which I have in hand, and to publish them; which might perhaps bring
some credit to me, and to those who had favoured me in this undertaking,
and possibly may be of greater and more frequent service to students
than in the rest of my life I could personally afford them. Greater
leisure than I have here I doubt if I could meet with elsewhere, so long
as I am compelled to support my family from my public and private
lectures, (nor would I willingly lecture in any other city than this,
for several reasons which would be long to mention) nevertheless not
even the liberty I have here is sufficient, where I am obliged to spend
many, and often the best hours of the day at the request of this and
that man.--My public salary here is 520 florins, which I am almost
certain will be advanced to as many crowns upon my re-election, and
these I can greatly increase by receiving pupils, and from private
lectures, to any extent that I please. My public duty does not confine
me during more than 60 half hours in the year, and even that not so
strictly but that I may, on occasion of any business, contrive to get
some vacant days; the rest of my time is absolutely at my own disposal;
but because my private lectures and domestic pupils are a great
hindrance and interruption of my studies, I wish to live entirely exempt
from the former, and in great measure from the latter: for if I am to
return to my native country, I should wish the first object of his
Serene Highness to be, that leisure and opportunity should be given me
to complete my works without employing myself in lecturing.--And, in
short, I should wish to gain my bread from my writings, which I would
always dedicate to my Serene Master.--The works which I have to finish
are principally--two books on the system or structure of the Universe,
an immense work, full of philosophy, astronomy, and geometry; three
books on Local Motion, a science entirely new, no one, either ancient or
modern, having discovered any of the very many admirable accidents which
I demonstrate in natural and violent motions, so that I may with very
great reason call it a new science, and invented by me from its very
first principles; three books of Mechanics, two on the demonstration of
principles and one of problems; and although others have treated this
same matter, yet all that has been hitherto written, neither in
quantity, nor otherwise, is the quarter of what I am writing on it. I
have also different treatises on natural subjects; On sound and speech;
On light and colours; On the tide; On the composition of continuous
quantity; On the motions of animals;--And others besides. I have also
an idea of writing some books relating to the military art, giving not
only a model of a soldier, but teaching with very exact rules every
thing which it is his duty to know that depends upon mathematics; as the
knowledge of castrametation, drawing up battalions, fortifications,
assaults, planning, surveying, the knowledge of artillery, the use of
instruments, &c. I also wish to reprint the 'Use of my Geometrical
Compass,' which is dedicated to his highness, and which is no longer to
be met with; for this instrument has experienced such favour from the
public, that in fact no other instruments of this kind are now made, and
I know that up to this time several thousands of mine have been made.--I
say nothing as to the amount of my salary, feeling convinced that as I
am to live upon it, the graciousness of his highness would not deprive
me of any of those comforts, which, however, I feel the want of less
than many others; and therefore I say nothing more on the subject.
Finally, on the title and profession of my service, I should wish that
to the name of Mathematician, his highness would add that of
Philosopher, as I profess to have studied a greater number of years in
philosophy than months in pure mathematics; and how I have profited by
it, and if I can or ought to deserve this title, I may let their
highnesses see as often as it shall please them to give me an
opportunity of discussing such subjects in their presence with those who
are most esteemed in this knowledge." It may perhaps be seen in the
expressions of this letter, that Galileo was not inclined to undervalue
his own merits, but the peculiar nature of the correspondence should be
taken into account, which might justify his indulging a little more than
usual in self-praise, and it would have been perhaps almost impossible
for him to have remained entirely blind to his vast superiority over his
contemporaries.

Many of the treatises which Galileo here mentions, as well as another on
dialling, have been irrecoverably lost, through the superstitious
weakness of some of his relations, who after his death suffered the
family confessor to examine his papers, and to destroy whatever seemed
to him objectionable; a portion which, according to the notions then
prevalent, was like to comprise the most valuable part of the papers
submitted to this expurgation. It is also supposed that many were burnt
by his infatuated grandson Cosimo, who conceived he was thus offering a
proper and pious sacrifice before devoting himself to the life of a
missionary. A Treatise on Fortification, by Galileo, was found in 1793,
and is contained among the documents published by Venturi. Galileo does
not profess in it to give much original matter, but to lay before his
readers a compendium of the most approved principles then already known.
It has been supposed that Gustavus Adolphus of Sweden attended Galileo's
lectures on this subject, whilst in Italy; but the fact is not
satisfactorily ascertained. Galileo himself mentions a Prince Gustavus
of Sweden to whom he gave instruction in mathematics, but the dates
cannot well be made to agree. The question deserves notice only from its
having been made the subject of controversy.

The loss of Galileo's Essay on Continuous Quantity is particularly to be
regretted, as it would be highly interesting to see how far he succeeded
in methodizing his thoughts on this important topic. It is to his pupil
Cavalieri (who refused to publish his book so long as he hoped to see
Galileo's printed) that we owe "The Method of Indivisibles," which is
universally recognized as one of the first germs of the powerful methods
of modern analysis. Throughout Galileo's works we find many indications
of his having thought much on the subject, but his remarks are vague,
and bear little, if at all, on the application of the method. To this
the chief part of Cavalieri's book is devoted, though he was not so
entirely regardless of the principles on which his method of measuring
spaces is founded, as he is sometimes represented. This method consisted
in considering lines as made up of an infinite number of points,
surfaces in like manner as composed of lines, and solids of surfaces;
but there is an observation at the beginning of the 7th book, which
shews clearly that Cavalieri had taken a much more profound view of the
subject than is implied in this superficial exposition, and had
approached very closely to the apparently more exact theories of his
successors. Anticipating the objections to his hypothesis, he argues,
that "there is no necessity to suppose the continuous quantities made up
of these indivisible parts, _but only that they will observe the same
ratios as those parts do_." It ought not to be omitted, that Kepler also
had given an impulse to Cavalieri in his "New method of Gauging," which
is the earliest work with which we are acquainted, where principles of
this sort are employed.[31]


FOOTNOTES:

[26] Vitæ Italorum Illustrium.

[27] Almagestum Novum, vol. i.

[28] Math. Coll. vol. ii.

[29] Constructio Circini Proportionum. Moguntiæ, 1605.

[30] Treatise of the Nature of Bodies. London, 1665.

[31] Nova Stereometria Doliorum--Lincii, 1615.




CHAPTER VI.

    _Invention of the telescope--Fracastoro--Porta--Reflecting
      telescope--Roger Bacon--Digges--De
      Dominis--Jansen--Lipperhey--Galileo constructs
      telescopes--Microscopes--Re-elected Professor at Padua for life._


THE year 1609 was signalized by Galileo's discovery of the telescope,
which, in the minds of many, is the principal, if not the sole invention
associated with his name. It cannot be denied that his fame, as the
founder of the school of experimental philosophy, has been in an
unmerited degree cast into the shade by the splendour of his
astronomical discoveries; yet Lagrange[32] surely errs in the opposite
extreme, when he almost denies that these form any real or solid part of
the glory of this great man; and Montucla[33] omits an important
ingredient in his merit, when he (in other respects very justly)
remarks, that it required far less genius to point a telescope towards
the heavens than to trace the unheeded, because daily recurring,
phenomena of motion up to its simple and primary laws. We are to
remember that in the days of Galileo a telescope could scarcely be
pointed to the heavens with impunity, and that a courageous mind was
required to contradict, and a strong one to bear down, a party, who,
when invited to look on any object in the heavens which Aristotle had
never suspected, immediately refused all credit to those senses, to
which, on other occasions, they so confidently appealed. It surely is a
real and solid part of Galileo's glory that he consumed his life in
laborious and indefatigable observations, and that he persevered in
announcing his discoveries undisgusted by the invectives, and undismayed
by the persecutions, to which they subjected him. Plagiarist! liar!
impostor! heretic! were among the expressions of malignant hatred
lavished upon him, and although he also was not without some violent and
foul-mouthed partisans, yet it must be told to his credit that he
himself seldom condescended to notice these torrents of abuse, otherwise
than by good-humoured retorts, and by prosecuting his observations with
renewed assiduity and zeal.

The use of single lenses in aid of the sight had been long known.
Spectacles were in common use at the beginning of the fourteenth
century, and there are several hints, more or less obscure, in many
early writers, of the effects which might be expected from a combination
of glasses; but it does not appear with certainty that any of these
authors had attempted to reduce their ideas to practice. After the
discovery of the telescope, almost every country endeavoured to find in
the writings of its early philosophers traces of the knowledge of such
an instrument, but in general with success very inadequate to the zeal
of their national prepossessions. There are two authors especially to
whom the attention of Kepler and others was turned, immediately upon the
promulgation of the discovery, as containing the germ of it in their
works. These are Baptista Porta, and Gerolamo Fracastoro. We have
already had occasion to quote the Homocentrica of Fracastoro, who died
in 1553; the following expressions, though they seem to refer to actual
experiment, yet fall short of the meaning with which it has been
attempted to invest them. After explaining and commenting on some
phenomena of refraction through different media, to which he was led by
the necessity of reconciling his theory with the variable magnitudes of
the planets, he goes on to say--"For which reason, those things which
are seen at the bottom of water, appear greater than those which are at
the top; and if any one look through two eyeglasses, _one placed upon
the other_, he will see every thing much larger and nearer."[34] It
should seem that this passage (as Delambre has already remarked) rather
refers to the close application of one glass upon another, and it may
fairly be doubted whether anything analogous to the composition of the
telescope was in the writer's thoughts. Baptista Porta writes on the
same subject more fully;--"Concave lenses show distant objects most
clearly, convex those which are nearer, whence they may be used to
assist the sight. With a concave glass distant objects will be seen,
small, but distinct; with a convex one those near at hand, larger, but
confused; _if you know rightly how to combine one of each sort, you
will see both far and near objects larger and clearer_."[35] These words
show, if Porta really was then unacquainted with the telescope, how
close it is possible to pass by an invention without lighting on it, for
of precisely such a combination of a convex and concave lens, fitted to
the ends of an organ pipe by way of tube, did the whole of Galileo's
telescope consist. If Porta had stopped here he might more securely have
enjoyed the reputation of the invention, but he then professes to
describe the construction of his instrument, which has no relation
whatever to his previous remarks. "I shall now endeavour to show in what
manner we may contrive to recognize our friends at the distance of
several miles, and how those of weak sight may read the most minute
letters from a distance. It is an invention of great utility, and
grounded on optical principles, nor is it at all difficult of execution;
but it must be so divulged as not to be understood by the vulgar, and
yet be clear to the sharpsighted." The description which follows seems
far enough removed from the apprehended danger of being too clear, and
indeed every writer who has hitherto quoted it has merely given the
passage in its original Latin, apparently despairing of an intelligible
translation. With some alterations in the punctuation, which appear
necessary to bring it into any grammatical construction,[36] it may be
supposed to bear something like the following meaning:--"Let a view be
contrived in the centre of a mirror, where it is most effective. All the
solar rays are exceedingly dispersed, and do not in the least come
together (in the true centre); but there is a concourse of all the rays
in the central part of the said mirror, half way towards the other
centre, where the cross diameters meet. This view is contrived in the
following manner. A concave cylindrical mirror placed directly in front,
but with its axis inclined, must be adapted to that focus: and let
obtuse angled or right angled triangles be cut out with two cross lines
on each side drawn from the centre, and a glass (_specillum_) will be
completed fit for the purposes we mentioned." If it were not for the
word "_specillum_," which, in the passage immediately preceding this,
Porta[37] contrasts with "_speculum_," and which he afterwards explains
to mean a glass lens, it would be very clear that the foregoing passage
(supposing it to have any meaning) must be referred to a reflecting
telescope, and it is a little singular that while this obscure passage
has attracted universal attention, no one, so far as we are aware, has
taken any notice of the following unequivocal description of the
principal part of Newton's construction of the same instrument. It is in
the 5th chapter of the 17th book, where Porta explains by what device
exceedingly minute letters may be read without difficulty. "Place a
concave mirror so that the back of it may lie against your breast;
opposite to it, and within the burning point, place the writing; put a
plane mirror behind it, that may be under your eyes. Then the images of
the letters which are in the concave mirror, and which the concave has
magnified, will be reflected in the plane mirror, so that you may read
without difficulty."

We have not been able to meet with the Italian translation of Porta's
Natural Magic, which was published in 1611, under his own
superintendence; but the English translator of 1658 would probably have
known if any intelligible interpretation were there given of the
mysterious passage above quoted, and his translation is so devoid of
meaning as strongly to militate against this idea. Porta, indeed,
claimed the invention as his own, and is believed to have hastened his
death, (which happened in 1615, he being then 80 years old,) by the
fatigue of composing a Treatise on the Telescope, in which he had
promised to exhaust the subject. We do not know whether this is the same
work which was published after his death by Stelliola,[38] but which
contains no allusion to Porta's claim, and possibly Stelliola may have
thought it most for his friend's reputation to suppress it. Schott[39]
says, a friend of his had seen Porta's book in manuscript, and that it
did at that time contain the assertion of Porta's title to the
invention. After all it is not improbable that he may have derived his
notions of magnifying distant objects from our celebrated countryman
Roger Bacon, who died about the year 1300. He has been supposed, not
without good grounds, to have been one of the first who recognised the
use of single lenses in producing distinct vision, and he has some
expressions with respect to their combination which promise effects
analogous to those held out by Porta. In "The Admirable Force of Art and
Nature," he says, "Physical figurations are far more strange, for in
such manner may we frame perspects and looking-glasses that one thing
shall appear to be many, as one man shall seeme a whole armie; and
divers sunnes and moones, yea, as many as we please, shall appeare at
one time, &c. And so may the perspects be framed, that things most farre
off may seeme most nigh unto us, and clean contrarie, soe that we may
reade very small letters an incredible distance from us, and behold
things how little soever they be, and make stars to appeare wheresoever
we will, &c. And, besides all these, we may so frame perspects that any
man entering into a house he shall indeed see gold, and silver, and
precious stones, and what else he will, but when he maketh haste to the
place he shall find just nothing." It seems plain, that the author is
here speaking solely of mirrors, and we must not too hastily draw the
conclusion, because in the first and last of these assertions he is, to
a certain extent, borne out by facts, that he therefore was in
possession of a method of accomplishing the middle problem also. In the
previous chapter, he gives a long list of notable things, (much in the
style of the Marquis of Worcester's Century of Inventions) which if we
can really persuade ourselves that he was capable of accomplishing, we
must allow the present age to be still immeasurably inferior to him in
science.

Thomas Digges, in the preface to his Pantometria, (published in 1591)
declares, "My father, by his continuall painfull practises, assisted
with demonstrations mathematicall, was able, and sundry times hath by
proportionall glasses, duely situate in convenient angles, not only
discouered things farre off, read letters, numbered peeces of money,
with the verye coyne and superscription thereof, cast by some of his
freends of purpose, upon downes in open fields; but also, seuen miles
off, declared what hath beene doone at that instant in priuate places.
He hath also sundrie times, by the sunne beames, fired powder and
dischargde ordnance halfe a mile and more distante; which things I am
the boulder to report, for that there are yet living diverse (of these
his dooings) occulati testes, (eye witnesses) and many other matters
farre more strange and rare, which I omit as impertinent to this place."

We find another pretender to the honour of the discovery of the
telescope in the celebrated Antonio de Dominis, Archbishop of Spalatro,
famous in the annals of optics for being one of the first to explain the
theory of the rainbow. Montucla, following P. Boscovich, has scarcely
done justice to De Dominis, whom he treats as a mere pretender and
ignorant person. The indisposition of Boscovich towards him is
sufficiently accounted for by the circumstance of his being a Catholic
prelate who had embraced the cause of Protestantism. His nominal
reconciliation with the Church of Rome would probably not have saved him
from the stake, had not a natural death released him when imprisoned on
that account at Rome. Judgment was pronounced upon him notwithstanding,
and his body and books were publicly burnt in the Campo de Fiori, in
1624. His treatise, De Radiis, (which is very rarely to be met with) was
published by Bartolo after the acknowledged invention of the telescope
by Galileo; but Bartolo tells us, in the preface, that the manuscript
was communicated to him from a collection of papers written 20 years
before, on his inquiring the Archbishop's opinion with respect to the
newly discovered instrument, and that he got leave to publish it, "with
the addition of one or two chapters." The treatise contains a complete
description of a telescope, which, however, is professed merely to be an
improvement on spectacles, and if the author's intention had been to
interpolate an afterwritten account, in order to secure to himself the
undeserved honour of the invention, it seems improbable that he would
have suffered an acknowledgment of additions, previous to publication,
to be inserted in the preface. Besides, the whole tone of the work is
that of a candid and truth-seeking philosopher, very far indeed removed
from being, as Montucla calls him, conspicuous for ignorance even among
the ignorant men of his age. He gives a drawing of a convex and concave
lens, and traces the passage of the rays through them; to which he
subjoins, that he has not satisfied himself with any determination of
the precise distance to which the glasses should be separated, according
to their convexity and concavity, but recommends the proper distance to
be found by actual experiment, and tells us, that the effect of the
instrument will be to prevent the confusion arising from the
interference of the direct and refracted rays, and to magnify the object
by increasing the visible angle under which it is viewed. These, among
the many claimants, are certainly the authors who approached the most
nearly to the discovery: and the reader may judge, from the passages
cited, whether the knowledge of the telescope can with probability be
referred to a period earlier than the commencement of the 17th century.
At all events, we can find no earlier trace of its being applied to any
practical use; the knowledge, if it existed, remained speculative and
barren.

In 1609, Galileo, then being on a visit to a friend at Venice, heard a
rumour of the recent invention, by a Dutch spectacle-maker, of an
instrument which was said to represent distant objects nearer than they
usually appeared. According to his own account, this general rumour,
which was confirmed to him by letters from Paris, was all that he
learned on the subject; and returning to Padua, he immediately applied
himself to consider the means by which such an effect could be produced.
Fuccarius, in an abusive letter which he wrote on the subject, asserts
that one of the Dutch telescopes had been at that time actually brought
to Venice, and that he (Fuccarius) had seen it; which, even if true, is
perfectly consistent with Galileo's statement; and in fact the question,
whether or not Galileo saw the original instrument, becomes important
only from his expressly asserting the contrary, and professing to give
the train of reasoning by which he discovered its principle; so that any
insinuation that he had actually seen the Dutch glass, becomes a direct
impeachment of his veracity. It is certain, from the following extract
of a letter from Lorenzo Pignoria to Paolo Gualdo, that one at least of
the Dutch glasses had been sent to Italy. It is dated Padua, 31st
August, 1609.[40] "We have no news, except the return of His Serene
Highness, and the re-election of the lecturers, among whom Sign. Galileo
has contrived to get 1000 florins for life; and it is said to be on
account of an eyeglass, _like the one which was sent from Flanders to
Cardinal Borghese_. We have seen some here, and truly they succeed
well."

It is allowed by every one that the Dutchman, or rather Zealander, made
his discovery by mere accident, which greatly derogates from any honour
attached to it; but even this diminished degree of credit has been
fiercely disputed. According to one account, which appears consistent
and probable, it had been made for sometime before its importance was in
the slightest degree understood or appreciated, but was set up in the
optician's shop as a curious philosophical toy, showing a large and
inverted image of a weathercock, towards which it was directed. The
Marquis Spinola, chancing to see it, was struck with the phenomenon,
purchased the instrument, and presented it either to the Archduke Albert
of Austria, or to Prince Maurice of Nassau, whose name appears in every
version of the story, and who first entertained the idea of employing it
in military reconnoissances.

Zacharias Jansen, and Henry Lipperhey, two spectacle-makers, living
close to each other, near the church of Middleburg, have both had
strenuous supporters of their title to the invention. A third pretender
appeared afterwards in the person of James Metius of Alkmaer, who is
mentioned by Huyghens and Des Cartes, but his claims rest upon no
authority whatever comparable to that which supports the other two.
About half a century afterwards, Borelli was at the pains to collect and
publish a number of letters and depositions which he procured, as well
on one side as on the other.[41] It seems that the truth lies between
them, and that one, probably Jansen, was the inventor of the
_microscope_, which application of the principle was unquestionably of
an earlier date, perhaps as far back as 1590. Jansen gave one of his
microscopes to the Archduke, who gave it to Cornelius Drebbel, a
salaried mathematician at the court of our James the first, where
William Borelli (not the author above mentioned) saw it many years
afterwards, when ambassador from the United Provinces to England, and
got from Drebbel this account of the quarter whence it came. Lipperhey
afterwards, in 1609, accidentally hit upon the _telescope_, and on the
fame of this discovery it would not be difficult for Jansen, already in
possession of an instrument so much resembling it, to perceive the
slight difference between them, and to construct a telescope
independently of Lipperhey, so that each, with some show of reason,
might claim the priority of the invention. A notion of this kind
reconciles the testimony of many conflicting witnesses on the subject,
some of whom do not seem to distinguish very accurately whether the
telescope or microscope is the instrument to which their evidence
refers. Borelli arrives at the conclusion, that Jansen was the inventor;
but not satisfied with this, he endeavours, with a glaring partiality
which makes his former determination suspicious, to secure for him and
his son the more solid reputation of having anticipated Galileo in the
useful employment of the invention. He has however inserted in his
collections a letter from John the son of Zacharias, in which John,
omitting all mention of his father, speaks of his own observation of the
satellites of Jupiter, evidently seeking to insinuate that they were
earlier than Galileo's; and in this sense the letter has since been
quoted,[42] although it appears from John's own deposition, preserved in
the same collection, that at the time of their discovery he could not
have been more than six years old. An oversight of this sort throws
doubt on the whole of the pretended observations, and indeed the letter
has much the air of being the production of a person imperfectly
informed on the subject on which he writes, and probably was compiled to
suit Borelli's purposes, which were to make Galileo's share in the
invention appear as small as possible.

Galileo himself gives a very intelligible account of the process of
reasoning, by which he detected the secret.--"I argued in the following
manner. The contrivance consists either of one glass or of more--one is
not sufficient, since it must be either convex, concave, or plane; the
last does not produce any sensible alteration in objects, the concave
diminishes them: it is true that the convex magnifies, but it renders
them confused and indistinct; consequently, one glass is insufficient to
produce the desired effect. Proceeding to consider two glasses, and
bearing in mind that the plane glass causes no change, I determined that
the instrument could not consist of the combination of a plane glass
with either of the other two. I therefore applied myself to make
experiments on combinations of the two other kinds, and thus obtained
that of which I was in search." It has been urged against Galileo that,
if he really invented the telescope on theoretical principles, the same
theory ought at once to have conducted him to a more perfect instrument
than that which he at first constructed;[43] but it is plain, from this
statement, that he does not profess to have theorized beyond the
determination of the species of glass which he should employ in his
experiments, and the rest of his operations he avows to have been purely
empirical. Besides, we must take into account the difficulty of grinding
the glasses, particularly when fit tools were yet to be made, and
something must be attributed to Galileo's eagerness to bring his results
to the test of actual experiment, without waiting for that improvement
which a longer delay might and did suggest. Galileo's language bears a
resemblance to the first passage which we quoted from Baptista Porta,
sufficiently close to make it not improbable that he might be assisted
in his inquiries by some recollection of it, and the same passage seems,
in like manner, to have recurred to the mind of Kepler, as soon as he
heard of the invention. Galileo's telescope consisted of a plano-convex
and plano-concave lens, the latter nearest the eye, distant from each
other by the difference of their focal lengths, being, in principle,
exactly the same with the modern opera-glass. He seems to have thought
that the Dutch glass was the same, but this could not be the case, if
the above quoted particular of the _inverted_ weathercock, which belongs
to most traditions of the story, be correct; because it is the
peculiarity of this kind of telescope not to invert objects, and we
should be thus furnished with a demonstrative proof of the falsehood of
Fuccarius's insinuation: in that case the Dutch glass must have been
similar to what was afterwards called the astronomical telescope,
consisting of two convex glasses distant from each other by the sum of
their focal lengths. This supposition is not controverted by the fact,
that this sort of telescope was never employed by astronomers till long
afterwards; for the fame of Galileo's observations, and the superior
excellence of the instruments constructed under his superintendence,
induced every one in the first instance to imitate his constructions as
closely as possible. The astronomical telescope was however eventually
found to possess superior advantages over that which Galileo imagined,
and it is on this latter principle that all modern refracting telescopes
are constructed; the inversion being counteracted in those which are
intended for terrestrial observations, by the introduction of a second
pair of similar glasses, which restore the inverted image to its
original position. For further details on the improvements which have
been subsequently introduced, and on the reflecting telescope, which was
not brought into use till the latter part of the century, the reader is
referred to the Treatise on OPTICAL INSTRUMENTS.

Galileo, about the same time, constructed microscopes on the same
principle, for we find that, in 1612, he presented one to Sigismund,
King of Poland; but his attention being principally devoted to the
employment and perfection of his telescope, the microscope remained a
long time imperfect in his hands: twelve years later, in 1624, he wrote
to P. Federigo Cesi, that he had delayed to send the microscope, the use
of which he there describes, because he had only just brought it to
perfection, having experienced some difficulty in working the glasses.
Schott tells an amusing story, in his "Magic of Nature," of a Bavarian
philosopher, who, travelling in the Tyrol with one of the newly invented
microscopes about him, was taken ill on the road and died. The
authorities of the village took possession of his baggage, and were
proceeding to perform the last duties to his body, when, on examining
the little glass instrument in his pocket, which chanced to contain a
flea, they were struck with the greatest astonishment and terror, and
the poor Bavarian, condemned by acclamation as a sorcerer who was in the
habit of using a portable familiar, was declared unworthy of Christian
burial. Fortunately for his character, some bold sceptic ventured to
open the instrument, and discovered the true nature of the imprisoned
fiend.

As soon as Galileo's first telescope was completed, he returned with it
to Venice, and the extraordinary sensation which it excited tends also
strongly to refute Fuccarius's assertion that the Dutch glass was
already known there. During more than a month Galileo's whole time was
employed in exhibiting his instrument to the principal inhabitants of
Venice, who thronged to his house to satisfy themselves of the truth of
the wonderful stories in circulation; and at the end of that time the
Doge, Leonardo Donati, caused it to be intimated to him that such a
present would not be deemed unacceptable by the senate. Galileo took the
hint, and his complaisance was rewarded by a mandate confirming him for
life in his professorship at Padua, at the same time doubling his yearly
salary, which was thus made to amount to 1000 florins.

It was long before the phrenzy of public curiosity abated. Sirturi
describes a ludicrous violence which was done to himself, when, with the
first telescope which he had succeeded in making, he went up into the
tower of St. Mark, at Venice, in the vain hope of being there entirely
unmolested. Unluckily he was seen by some idlers in the street: a crowd
soon collected round him, who insisted on taking possession of his
instrument, and, handing it one to the other, detained him there for
several hours till their curiosity was satiated, when he was allowed to
return home. Hearing them also inquire eagerly at what inn he lodged, he
thought it better to quit Venice early the next morning, and prosecute
his observations in a less inquisitive neighbourhood.[44] Instruments of
an inferior description were soon manufactured, and vended every where
as philosophical playthings, much in the way in which, in our own time,
the kaleidoscope spread over Europe as fast as travellers could carry
them. But the fabrication of a better sort was long confined, almost
solely, to Galileo and those whom he immediately instructed; and so late
as the year 1637, we find Gaertner, or as he chose to call himself,
Hortensius, assuring Galileo that none could be met with in Holland
sufficiently good to show Jupiter's disc well defined; and in 1634
Gassendi begs for a telescope from Galileo, informing him that he was
unable to procure a good one either in Venice, Paris, or Amsterdam.

The instrument, on its first invention, was generally known by the names
of Galileo's tube, the perspective, the double eye-glass: the names of
telescope and microscope were suggested by Demisiano, as we are told by
Lagalla in his treatise on the Moon.[45]


FOOTNOTES:

[32] Mecanique Analytique.

[33] Histoire des Mathématiques, tom. ii.

[34] "Per duo specilla ocularia si quis perspiciat, altero alteri
superposito, majora multo et propinquiora videbit omnia."--Fracast.
Homocentrica, § 2, c. 8.

[35] Si utrumque recte componere noveris, et longinqua et proxima majora
et clara videbis.--Mag. Nat. lib. 17.

[36] The passage in the original, which is printed alike in the editions
of 1598, 1607, 1619, and 1650, is as follows: Visus constituatur centro
valentissimus speculi, ubi fiet, et valentissimè universales solares
radii disperguntur, et coeunt minimè, sed centro prædicti speculi in
illius medio, ubi diametri transversales, omnium ibi concursus.
Constituitur hoc modo speculum concavum columnare æquidistantibus
lateribus, sed lateri uno obliquo sectionibus illis accomodetur,
trianguli vero obtusianguli, vel orthogonii secentur, hinc inde duobus
transversalibus lineis, ex-centro eductis. Et confectum erit specillum,
ad id, quod diximus utile.

[37] Diximus de Ptolemæi _speculo_, sive _specillo_ potius, quo per
sexcentena millia pervenientes naves conspiciebat.

[38] Il Telescopio, 1627.

[39] Magia Naturæ et Artis Herbipoli, 1657.

[40] Lettère d'Uomini illustri. Venezia, 1744.

[41] Borelli. De vero Telescopii inventore, 1655.

[42] Encyclopædia Britannica. Art. TELESCOPE.

[43] Ibid.

[44] Telescopium, Venetiis, 1619.

[45] De phænomenis in orbe Lunæ. Venetiis, 1612.




CHAPTER VII.

    _Discovery of Jupiter's
      satellites--Kepler--Sizzi--Astrologers--Mæstlin--Horky--Mayer._


AS soon as Galileo had provided himself with a second instrument, he
began a careful examination of the heavenly bodies, and a series of
splendid discoveries soon rewarded his diligence. After considering the
beautiful appearances which the varied surface of the moon presented to
this new instrument, he turned his telescope towards Jupiter, and his
attention was soon arrested by the singular position of three small
stars, near the body of that planet, which appeared almost in a straight
line with it, and in the direction of the ecliptic. The following
evening he was surprised to find that two of the three which had been to
the eastward of the planet, now appeared on the contrary side, which he
could not reconcile with the apparent motion of Jupiter among the fixed
stars, as given by the tables. Observing these night after night, he
could not fail to remark that they changed their relative positions. A
fourth also appeared, and in a short time he could no longer refuse to
believe that these small stars were four moons, revolving round Jupiter
in the same manner in which our earth is accompanied by its single
attendant. In honour of his patron Cosmo, he named them the Medicæan
stars. As they are now hardly known by this appellation, his doubts,
whether he should call them Medicæan, after Cosmo's family, or Cosmical,
from his individual name, are become of less interest.

An extract from a letter which Galileo received on this occasion from
the court of France, will serve to show how highly the honour of giving
a name to these new planets was at that time appreciated, and also how
much was expected from Galileo's first success in examining the heavens.
"The second request, but the most pressing one which I can make to you,
is, that you should determine, if you discover any other fine star, to
call it by the name of the great star of France, as well as the most
brilliant of all the earth; and, if it seems fit to you, call it rather
by his proper name of Henri, than by the family name of Bourbon: thus
you will have an opportunity of doing a thing just and due and proper in
itself, and at the same time will render yourself and your family rich
and powerful for ever." The writer then proceeds to enumerate the
different claims of Henri IV. to this honour, not forgetting that he
married into the family of the Medici, &c.

The result of these observations was given to the world, in an Essay
which Galileo entitled _Nuncius Sidereus_, or the Intelligencer of the
Stars; and it is difficult to describe the extraordinary sensation which
its publication produced. Many doubted, many positively refused to
believe, so novel an announcement; all were struck with the greatest
astonishment, according to their respective opinions, either at the new
view of the universe thus offered to them, or at the daring audacity of
Galileo in inventing such fables. We shall proceed to extract a few
passages from contemporary writers relative to this book, and the
discoveries announced in it.

Kepler deserves precedence, both from his own celebrity, and from the
lively and characteristic account which he gives of his first receiving
the intelligence:--"I was sitting idle at home, thinking of you, most
excellent Galileo, and your letters, when the news was brought me of the
discovery of four planets by the help of the double eye-glass.
Wachenfels stopped his carriage at my door to tell me, when such a fit
of wonder seized me at a report which seemed so very absurd, and I was
thrown into such agitation at seeing an old dispute between us decided
in this way, that between his joy, my colouring, and the laughter of
both, confounded as we were by such a novelty, we were hardly capable,
he of speaking, or I of listening. My amazement was increased by the
assertion of Wachenfels, that those who sent this news from Galileo were
celebrated men, far removed by their learning, weight, and character,
above vulgar folly; that the book was actually in the press, and would
be published immediately. On our separating, the authority of Galileo
had the greatest influence on me, earned by the accuracy of his
judgment, and excellence of his understanding; so I immediately fell to
thinking how there could be any addition to the number of the planets
without overturning my Mysterium Cosmographicum, published thirteen
years ago, according to which Euclid's five regular solids do not allow
more than six planets round the sun."

This was one of the many wild notions of Kepler's fanciful brain, among
which he was lucky enough at length to hit upon the real and principal
laws of the planetary motions. His theory may be briefly given in his
own words:--"The orbit of the earth is the measure of the rest. About it
circumscribe a dodecahedron. The sphere including this will be that of
Mars. About Mars' orbit describe a tetrahedron: the sphere containing
this will be Jupiter's orbit. Round Jupiter's describe a cube: the
sphere including this will be Saturn's. Within the earth's orbit
inscribe an icosahedron: the sphere inscribed in it will be Venus's
orbit. In Venus inscribe an octahedron: the sphere inscribed in it will
be Mercury's. You have now the reason of the number of the planets:" for
as there are no more than the five regular solids here enumerated,
Kepler conceived this to be a satisfactory reason why there could be
neither more nor less than six planets. His letter continues:--"I am so
far from disbelieving the existence of the four circumjovial planets,
that I long for a telescope to anticipate you, if possible, in
discovering two round Mars, (as the proportion seems to me to require,)
six or eight round Saturn, and perhaps one each round Mercury and
Venus."

The reader has here an opportunity of verifying Galileo's observation,
that Kepler's method of philosophizing differed widely from his own. The
proper line is certainly difficult to hit between the mere theorist and
the mere observer. It is not difficult at once to condemn the former,
and yet the latter will deprive himself of an important, and often
indispensable assistance, if he neglect from time to time to consolidate
his observations, and thence to conjecture the course of future
observation most likely to reward his assiduity. This cannot be more
forcibly expressed than in the words of Leonardo da Vinci:[46] "Theory
is the general, experiments are the soldiers. The interpreter of the
works of nature is experiment; that is never wrong; it is our judgment
which is sometimes deceived, because we are expecting results which
experiment refuses to give. We must consult experiment, and vary the
circumstances, till we have deduced general rules, for it alone can
furnish us with them. But you will ask, what is the use of these general
rules? I answer, that they direct us in our inquiries into nature and
the operations of art. They keep us from deceiving ourselves and others,
by promising ourselves results which we can never obtain."

In the instance before us, it is well known that, adopting some of the
opinions of Bruno and Brutti, Galileo, even before he had seen the
satellites of Jupiter, had allowed the possibility of the discovery of
new planets; and we can scarcely suppose that they had weakened his
belief in the probability of further success, or discouraged him from
examining the other heavenly bodies. Kepler on the contrary had taken
the opposite side of the argument; but no sooner was the fallacy of his
first position undeniably demonstrated, than, passing at once from one
extreme to the other, he framed an unsupported theory to account for the
number of satellites which were round Jupiter, and for those which he
expected to meet with elsewhere. Kepler has been styled the legislator
of the skies; his laws were promulgated rather too arbitrarily, and they
often failed, as all laws must do which are not drawn from a careful
observation of the nature of those who are to be governed by them.
Astronomers have reason to be grateful for the theorems which he was the
first to establish; but so far as regards the progress of the science of
inductive reasoning, it is perhaps to be regretted, that the seventeen
years which he wasted in random and unconnected guesses should have been
finally rewarded, by discoveries splendid enough to shed deceitful
lustre upon the method by which he arrived at them.

Galileo himself clearly perceived the fallacious nature of these
speculations on numbers and proportions, and has expressed his
sentiments concerning them very unequivocally. "How great and common an
error appears to me the mistake of those who persist in making their
knowledge and apprehension the measure of the apprehension and knowledge
of God; as if that alone were perfect, which they understand to be so.
But I, on the contrary, observe that Nature has other scales of
perfection, which we cannot comprehend, and rather seem disposed to
class among imperfections. For instance, among the relations of
different numbers, those appear to us most perfect which exist between
numbers nearly related to each other; as the double, the triple, the
proportion of three to two, &c.; those appear less perfect which exist
between numbers remote from, and prime to each other; as 11 to 7, 17 to
13, 53 to 37, &c.; and most imperfect of all do those appear which exist
between incommensurable quantities, which by us are nameless and
inexplicable. Consequently, if the task had been given to a man, of
establishing and ordering the rapid motions of the heavenly bodies,
according to his notions of perfect proportions, I doubt not that he
would have arranged them according to the former rational proportions;
but, on the contrary, God, with no regard to our imaginary symmetries,
has ordered them in proportions not only incommeasurable and irrational,
but altogether inappreciable by our intellect. A man ignorant of
geometry may perhaps lament, that the circumference of a circle does not
happen to be exactly three times the diameter, or in some other
assignable proportion to it, rather than such that we have not yet been
able to explain what the ratio between them is; but one who has more
understanding will know that if they were other than they are, thousands
of admirable conclusions would have been lost, and that none of the
other properties of the circle would have been true: the surface of the
sphere would not be quadruple of a great circle, nor the cylinder be to
the sphere as three to two: in short, no part of geometry would be true,
and as it now is. If one of our most celebrated architects had had to
distribute this vast multitude of fixed stars through the great vault of
heaven, I believe he would have disposed them with beautiful
arrangements of squares, hexagons, and octagons; he would have dispersed
the larger ones among the middle sized and the less, so as to correspond
exactly with each other; and then he would think he had contrived
admirable proportions: but God, on the contrary, has shaken them out
from His hand as if by chance, and we, forsooth, must think that He has
scattered them up yonder without any regularity, symmetry, and
elegance."

It is worth remarking that the dangerous ideas of aptitude and
congruence of numbers had taken such deep and general root, that long
afterwards, when the reality of Jupiter's satellites was incontestably
established, and Huyghens had discovered a similar satellite near
Saturn, he was so rash as to declare his belief, (unwarned by the vast
progress which astronomy had made in his own time,) that no more
satellites would be discovered, since the one which he discovered near
Saturn, with Jupiter's four, and our moon, made up the number six,
exactly equal to the number of the principal planets. Every reader knows
that this notion, so unworthy the genius of Huyghens, has been since
exploded by the discovery both of new planets, and new satellites.

Francesco Sizzi, a Florentine astronomer, took the matter up in a
somewhat different strain from Kepler.[47]--"There are seven windows
given to animals in the domicile of the head, through which the air is
admitted to the rest of the tabernacle of the body, to enlighten, to
warm, and nourish it, which are the principal parts of the [mikrokosmos]
(or little world); two nostrils, two eyes, two ears, and a mouth; so in
the heavens, as in a [makrokosmos] (or great world), there are two
favourable stars, two unpropitious, two luminaries, and Mercury alone
undecided and indifferent. From which and many other similar phenomena
of nature, such as the seven metals, &c., which it were tedious to
enumerate, we gather that the number of planets is necessarily seven.
Moreover, the satellites are invisible to the naked eye, and therefore
can exercise no influence on the earth, and therefore would be useless,
and therefore do not exist. Besides, as well the Jews and other ancient
nations as modern Europeans have adopted the division of the week into
seven days, and have named them from the seven planets: now if we
increase the number of the planets this whole system falls to the
ground." To these remarks Galileo calmly replied, that whatever their
force might be, as a reason for believing beforehand that no more than
seven planets would be discovered, they hardly seemed of sufficient
weight to destroy the new ones when actually seen.

Others, again, took a more dogged line of opposition, without venturing
into the subtle analogies and arguments of the philosopher just cited.
They contented themselves, and satisfied others, with the simple
assertion, that such things were not, and could not be, and the manner
in which they maintained themselves in their incredulity was
sufficiently ludicrous. "Oh, my dear Kepler,"[48] says Galileo, "how I
wish that we could have one hearty laugh together. Here, at Padua, is
the principal professor of philosophy, whom I have repeatedly and
urgently requested to look at the moon and planets through my glass,
which he pertinaciously refuses to do. Why are you not here? what shouts
of laughter we should have at this glorious folly! and to hear the
professor of philosophy at Pisa labouring before the grand duke with
logical arguments, as if with magical incantations, to charm the new
planets out of the sky."

Another opponent of Galileo deserves to be named, were it only for the
singular impudence of the charge he ventures to bring against him. "We
are not to think," says Christmann, in the Appendix to his _Nodus
Gordius_, "that Jupiter has four satellites given him by nature, in
order, by revolving round him, to immortalize the name of the Medici,
who first had notice of the observation. These are the dreams of _idle
men_, who love ludicrous ideas better than our laborious and industrious
correction of the heavens.--Nature abhors so horrible a chaos, and to
the truly wise such vanity is detestable."

Galileo was also urged by the astrologers to attribute some influence,
according to their fantastic notions, to the satellites, and the account
which he gives his friend Dini of his answer to one of this class is
well worth extracting, as a specimen of his method of uniting sarcasm
with serious expostulation; "I must," says he, "tell you what I said a
few days back to one of those nativity-casters, who believe that God,
when he created the heavens and the stars, had no thoughts beyond what
they can themselves conceive, in order to free myself from his tedious
importunity; for he protested, that unless I would declare to him the
effect of the Medicæan planets, he would reject and deny them as
needless and superfluous. I believe this set of men to be of Sizzi's
opinion, that astronomers discovered the other seven planets, not by
seeing them corporally in the skies, but only from their effects on
earth,--much in the manner in which some houses are discovered to be
haunted by evil spirits, not by seeing them, but from the extravagant
pranks which are played there. I replied, that he ought to reconsider
the hundred or thousand opinions which, in the course of his life, he
might have given, and particularly to examine well the events which he
had predicted with the help of Jupiter, and if he should find that all
had succeeded conformably to his predictions, I bid him prophecy merrily
on, according to his old and wonted rules; for I assured him that the
new planets would not in any degree affect the things which are already
past, and that in future he would not be a less fortunate conjuror than
he had been: but if, on the contrary, he should find the events
depending on Jupiter, in some trifling particulars not to have agreed
with his dogmas and prognosticating aphorisms, he ought to set to work
to find new tables for calculating the constitution of the four Jovial
circulators at every bygone moment, and, perhaps, from the diversity of
their aspects, he would be able, with accurate observations and
multiplied conjunctions, to discover the alterations and variety of
influences depending upon them; and I reminded him, that in ages past
they had not acquired knowledge with little labour, at the expense of
others, from written books, but that the first inventors acquired the
most excellent knowledge of things natural and divine with study and
contemplation of the vast book which nature holds ever open before those
who have eyes in their forehead and in their brain; and that it was a
more honourable and praiseworthy enterprize with their own watching,
toil, and study, to discover something admirable and new among the
infinite number which yet remain concealed in the darkest depths of
philosophy, than to pass a listless and lazy existence, labouring only
to darken the toilsome inventions of their neighbours, in order to
excuse their own cowardice and inaptitude for reasoning, while they cry
out that nothing can be added to the discoveries already made."

The extract given above from Kepler, is taken from an Essay, published
with the later editions of the _Nuncius_, the object and spirit of which
seem to have been greatly misunderstood, even by some of Kepler's
intimate friends.--They considered it as a covert attack upon Galileo,
and, accordingly, Maestlin thus writes to him:--"In your Essay (which I
have just received) you have plucked Galileo's feathers well; I mean,
that you have shown him not to be the inventor of the telescope, not to
have been the first who observed the irregularities of the moon's
surface, not to have been the first discoverer of more worlds than the
ancients were acquainted with, &c. One source of exultation was still
left him, from the apprehension of which Martin Horky has now entirely
delivered me." It is difficult to discover in what part of Kepler's book
Maestlin found all this, for it is one continued encomium upon Galileo;
insomuch that Kepler almost apologizes in the preface for what may seem
his intemperate admiration of his friend. "Some might wish I had spoken
in more moderate terms in praise of Galileo, in consideration of the
distinguished men who are opposed to his opinions, but I have written
nothing fulsome or insincere. I praise him, for myself; I leave other
men's judgments free; and shall be ready to join in condemnation when
some one wiser than myself shall, by sound reasoning, point out his
errors." However, Maestlin was not the only one who misunderstood
Kepler's intentions: the Martin Horky of whom he speaks, a young German,
also signalized himself by a vain attack upon the book which he thought
his patron Kepler condemned. He was then travelling in Italy, whence he
wrote to Kepler his first undetermined thoughts about the new
discoveries. "They are wonderful; they are stupendous; whether they are
true or false I cannot tell."[49] He seems soon to have decided that
most reputation was to be gained on the side of Galileo's opponents, and
his letters accordingly became filled with the most rancorous abuse of
him. At the same time, that the reader may appreciate Horky's own
character, we shall quote a short sentence at the end of one of his
letters, where he writes of a paltry piece of dishonesty with as great
glee as if he had solved an ingenious and scientific problem. After
mentioning his meeting Galileo at Bologna, and being indulged with a
trial of his telescope, which, he says, "does wonders upon the earth,
but represents celestial objects falsely;"[50] he concludes with the
following honourable sentence:--"I must confide to you a theft which I
committed. I contrived to take a mould of the glass in wax, without the
knowledge of any one, and, when I get home, I trust to make a telescope
even better than Galileo's own."

Horky having declared to Kepler, "I will never concede his four new
planets to that Italian from Padua though I die for it," followed up
this declaration by publishing a book against Galileo, which is the one
alluded to by Maestlin, as having destroyed the little credit which,
according to his view, Kepler's publication had left him. This book
professes to contain the examination of four principal questions
touching the alleged planets; 1st, Whether they exist? 2nd, What they
are? 3rd, What they are like? 4th, Why they are? The first question is
soon disposed of, by Horky's declaring positively that he has examined
the heavens with Galileo's own glass, and that no such thing as a
satellite about Jupiter exists. To the second, he declares solemnly,
that he does not more surely know that he has a soul in his body, than
that reflected rays are the sole cause of Galileo's erroneous
observations. In regard to the third question, he says, that these
planets are like the smallest fly compared to an elephant; and, finally,
concludes on the fourth, that the only use of them is to gratify
Galileo's "thirst of gold," and to afford himself a subject of
discussion.[51]

Galileo did not condescend to notice this impertinent folly; it was
answered by Roffini, a pupil of Magini, and by a young Scotchman of the
name of Wedderburn, then a student at Padua, and afterwards a physician
at the Court of Vienna. In the latter reply we find it mentioned, that
Galileo was also using his telescope for the examination of insects,
&c.[52] Horky sent his performance triumphantly to Kepler, and, as he
returned home before receiving an answer, he presented himself before
his patron in the same misapprehension under which he had written, but
the philosopher received him with a burst of indignation which rapidly
undeceived him. The conclusion of the story is characteristic enough to
be given in Kepler's own account of the matter to Galileo, in which,
after venting his wrath against this "scum of a fellow," whose
"obscurity had given him audacity," he says, that Horky begged so hard
to be forgiven, that "I have taken him again into favour upon this
preliminary condition, to which he has agreed:--that I am to shew him
Jupiter's satellites, AND HE IS TO SEE THEM, and own that they are
there."

In the same letter Kepler writes, that although he has himself perfect
confidence in the truth of Galileo's assertions, yet he wishes he could
furnish him with some corroborative testimonies, which Kepler could
quote in arguing the point with others. This request produced the
following reply, from which the reader will also learn the new change
which had now taken place in Galileo's fortunes, the result of the
correspondence with Florence, part of which we have already
extracted.[53] "In the first place, I return you my thanks that you
first, and almost alone, before the question had been sifted (such is
your candour and the loftiness of your mind), put faith in my
assertions. You tell me you have some telescopes, but not sufficiently
good to magnify distant objects with clearness, and that you anxiously
expect a sight of mine, which magnifies images more than a thousand
times. It is mine no longer, for the Grand Duke of Tuscany has asked it
of me, and intends to lay it up in his museum, among his most rare and
precious curiosities, in eternal remembrance of the invention: I have
made no other of equal excellence, for the mechanical labour is very
great: I have, however, devised some instruments for figuring and
polishing them which I am unwilling to construct here, as they could not
conveniently be carried to Florence, where I shall in future reside. You
ask, my dear Kepler, for other testimonies:--I produce, for one, the
Grand Duke, who, after observing the Medicæan planets several times with
me at Pisa during the last months, made me a present, at parting, worth
more than a thousand florins, and has now invited me to attach myself to
him with the annual salary of one thousand florins, and with the title
of Philosopher and Principal Mathematician to His Highness; without the
duties of any office to perform, but with the most complete leisure; so
that I can complete my Treatises on Mechanics, on the Constitution of
the Universe, and on Natural and Violent Local Motion, of which I have
demonstrated geometrically many new and admirable phenomena. I produce,
for another witness, myself, who, although already endowed in this
college with the noble salary of one thousand florins, such as no
professor of mathematics ever before received, and which I might
securely enjoy during my life, even if these planets had deceived me and
should disappear, yet quit this situation, and betake me where want and
disgrace will be my punishment should I prove to have been mistaken."

It is difficult not to regret that Galileo should be thus called on to
resign his best glasses, but it appears probable that on becoming more
familiar with the Grand Duke, he ventured to suggest that this telescope
would be more advantageously employed in his own hands, than pompously
laid up in a museum; for in 1637 we find him saying, in answer to a
request from his friend Micanzio to send him a telescope--"I am sorry
that I cannot oblige you with the glasses for your friend, but I am no
longer capable of making them, and I have just parted with two tolerably
good ones which I had, reserving only my old discoverer of celestial
novelties which is already promised to the Grand Duke." Cosmo was dead
in 1637, and it is his son Ferdinand who is here meant, who appears to
have inherited his father's love of science. Galileo tells us, in the
same letter, that Ferdinand had been amusing himself for some months
with making object-glasses, and always carried one with him to work at
wherever he went.

When forwarding this telescope to Cosmo in the first instance, Galileo
adds, with a very natural feeling--"I send it to his highness unadorned
and unpolished, as I made it for my own use, and beg that it may always
be left in the same state; for none of the old parts ought to be
displaced to make room for new ones, which will have had no share in the
watchings and fatigues of these observations." A telescope was in
existence, though with the object glass broken, at the end of the last
century, and probably still is in the Museum at Florence, which was
shewn as the discoverer of Jupiter's satellites. Nelli, on whose
authority this is mentioned, appears to question its genuineness. The
first reflecting telescope, made with Newton's own hands, and scarcely
possessing less interest than the first of Galileo's, is preserved in
the library of the Royal Society.

By degrees the enemies of Galileo and of the new stars found it
impossible to persevere in their disbelief, whether real or pretended,
and at length seemed resolved to compensate for the sluggishness of
their perception, by its acuteness when brought into action. Simon Mayer
published his "Mundus Jovialis" in 1614, in which he claims to have been
an original observer of the satellites, but, with an affectation of
candour, allows that Galileo observed them probably about the same time.
The earliest observation which he has recorded is dated 29th December,
1609, but, not to mention the total want of probability that Mayer would
not have immediately published so interesting a discovery, it is to be
observed, that, as he used the old style, this date of 29th December
agrees with the 8th January, 1610, of the new style, which was the date
of Galileo's second observation, and Galileo ventured to declare his
opinion, that this pretended observation was in fact a plagiarism.

Scheiner counted five, Rheita nine, and other observers, with increasing
contempt for Galileo's imperfect announcements, carried the number as
high as twelve.[54] In imitation of Galileo's nomenclature, and to
honour the sovereigns of the respective observers, these supposed
additional satellites were dignified with the names of Vladislavian,
Agrippine, Urbanoctavian, and Ferdinandotertian planets; but a very
short time served to show it was as unsafe to exceed as to fall short of
the number which Galileo had fixed upon, for Jupiter rapidly removed
himself from the neighbourhood of the fixed stars, which gave rise to
these pretended discoveries, carrying with him only his four original
attendants, which continued in every part of his orbit to revolve
regularly about him.

Perhaps we cannot better wind up this account of the discovery of
Jupiter's satellites, and of the intense interest they have at all times
inspired, than in the words of one who inherits a name worthy to be
ranked with that of Galileo in the list of astronomical discoverers, and
who takes his own place among the most accomplished mathematicians of
the present times. "The discovery of these bodies was one of the first
brilliant results of the invention of the telescope; one of the first
great facts which opened the eyes of mankind to the system of the
universe, which taught them the comparative insignificance of their own
planet, and the superior vastness and nicer mechanism of those other
bodies, which had before been distinguished from the stars only by their
motion, and wherein none but the boldest thinkers had ventured to
suspect a community of nature with our own globe. This discovery gave
the holding turn to the opinions of mankind respecting the Copernican
system; the analogy presented by these little bodies (little however
only in comparison with the great central body about which they revolve)
performing their beautiful revolutions in perfect harmony and order
about it, being too strong to be resisted. This elegant system was
watched with all the curiosity and interest the subject naturally
inspired. The eclipses of the satellites speedily attracted attention,
and the more when it was discerned, as it speedily was, by Galileo
himself, that they afforded a ready method of determining the difference
of longitudes of distant places on the earth's surface, by observations
of the instants of their disappearances and reappearances,
simultaneously made. Thus the first astronomical solution of the great
problem of the longitude, the first mighty step which pointed out a
connection between speculative astronomy and practical utility, and
which, replacing the fast dissipating dreams of astrology by nobler
visions, showed how the stars might really, and without fiction, be
called arbiters of the destinies of empires, we owe to the satellites of
Jupiter, those atoms imperceptible to the naked eye, and floating like
motes in the beam of their primary--itself an atom to our sight, noticed
only by the careless vulgar as a large star, and by the philosophers of
former ages as something moving among the stars, they knew not what, nor
why: perhaps only to perplex the wise with fruitless conjectures, and
harass the weak with fears as idle as their theories."[55]


FOOTNOTES:

[46] Venturi. Essai sur les ouvrages de Leo. da Vinci.

[47] Dianoia Astronomica, Venetiis, 1610.

[48] Kepleri Epistolæ.

[49] Kepleri Epistolæ.

[50] It may seem extraordinary that any one could support an argument by
this partial disbelief in the instrument, which was allowed on all hands
to represent terrestrial objects correctly. A similar instance of
obstinacy, in an almost identical case though in a more unpretending
station, once came under the writer's own observation. A farmer in
Cambridgeshire, who had acquired some confused notions of the use of the
quadrant, consulted him on a new method of determining the distances and
magnitudes of the sun and moon, which he declared were far different
from the quantities usually assigned to them. After a little
conversation, the root of his error, certainly sufficiently gross,
appeared to be that he had confounded the angular measure of a degree,
with 69½ miles, the linear measure of a degree on the earth's surface.
As a short way of showing his mistake, he was desired to determine, in
the same manner, the height of his barn which stood about 30 yards
distant; he lifted the quadrant to his eye, but perceiving, probably,
the monstrous size to which his principles were forcing him, he said,
"Oh, Sir, the quadrant's only true for the sky." He must have been an
objector of this kind, who said to Galileo,--"Oh, Sir, the telescope's
only true for the earth."

[51] Venturi.

[52] Quatuor probl. confut. per J. Wedderbornium, Scotobritannum.
Patavii, 1610.

[53] See page 18.

[54] Sherburne's Sphere of Manilius. London, 1675.

[55] Herschel's Address to the Astronomical Society, 1827.




CHAPTER VIII.

    _Observations on the Moon--Nebulæ--Saturn--Venus--Mars._


THERE were other discoveries announced in Galileo's book of great and
unprecedented importance, and which scarcely excited less discussion
than the controverted Medicæan planets. His observations on the moon
threw additional light on the constitution of the solar system, and
cleared up the difficulties which encumbered the explanation of the
varied appearance of her surface. The different theories current at that
day, to account for these phenomena, are collected and described by
Benedetti, and also with some liveliness, in a mythological poem, by
Marini.[56] We are told, that, in the opinion of some, the dark shades
on the moon's surface arise from the interposition of opaque bodies
floating between her and the sun, which prevents his light from reaching
those parts: others thought, that on account of her vicinity to the
earth, she was partly tainted with the imperfection of our terrestrial
and elementary nature, and was not of that entirely pure and refined
substance of which the more remote heavens consist: a third party looked
on her as a vast mirror, and maintained that the dark parts of her
surface were the reflected images of our earthly forests and mountains.

Galileo's glass taught him to believe that the surface of this planet,
far from being smooth and polished, as was generally taken for granted,
really resembled our earth in its structure; he was able distinctly to
trace on it the outlines of mountains and other inequalities, the
summits of which reflected the rays of the sun before these reached the
lower parts, and the sides of which, turned from his beams, lay buried
in deep shadow. He recognised a distribution into something similar to
continents of land, and oceans of water, which reflect the sun's light
to us with greater or less vivacity, according to their constitution.
These conclusions were utterly odious to the Aristotelians; they had
formed a preconceived notion of what the moon ought to be, and they
loathed the doctrines of Galileo, who took delight, as they said, in
distorting and ruining the fairest works of nature. It was in vain he
argued, as to the imaginary perfection of the spherical form, that
although the moon, or the earth, were it absolutely smooth, would indeed
be a more perfect sphere than in its present rough state, yet touching
the perfection of the earth, considered as a natural body calculated for
a particular purpose, every one must see that absolute smoothness and
sphericity would make it not only less perfect, but as far from being
perfect as possible. "What else," he demanded, "would it be but a vast
unblessed desert, void of animals, of plants, of cities and of men; the
abode of silence and inaction; senseless, lifeless, soulless, and stript
of all those ornaments which make it now so various and so beautiful?"

He reasoned to no purpose with the slaves of the ancient schools:
nothing could console them for the destruction of their smooth
unalterable surface, and to such an absurd length was this hallucination
carried, that one opponent of Galileo, Lodovico delle Colombe,
constrained to allow the evidence of the sensible inequalities of the
moon's surface, attempted to reconcile the old doctrine with the new
observations, by asserting, that every part of the moon, which to the
terrestrial observer appeared hollow and sunken, was in fact entirely
and exactly filled up with a clear crystal substance, perfectly
imperceptible by the senses, but which restored to the moon her
accurately spherical and smooth surface. Galileo met the argument in the
manner most fitting, according to one of Aristotle's own maxims, that
"it is foolish to refute absurd opinions with too much curiosity."
"Truly," says he, "the idea is admirable, its only fault is that it is
neither demonstrated nor demonstrable; but I am perfectly ready to
believe it, provided that, with equal courtesy, I may be allowed to
raise upon your smooth surface, crystal mountains (which nobody can
perceive) ten times higher than those which I have actually seen and
measured." By threatening to proceed to such extremities, he seems to
have scared the opposite party into moderation, for we do not find that
the crystalline theory was persevered in.

In the same essay, Galileo also explained at some length the cause of
that part of the moon being visible, which is unenlightened directly by
the sun in her first and last quarter. Maestlin, and before him Leonardo
da Vinci, had already declared this to arise from what may be called
_earthshine_, or the reflection of the sun's light from the terrestrial
globe, exactly similar to that which the moon affords us when we are
similarly placed between her and the sun; but the notion had not been
favourably received, because one of the arguments against the earth
being a planet, revolving like the rest round the sun, was, that it did
not shine like them, and was therefore of a different nature; and this
argument, weak as it was in itself, the theory of terrestrial reflection
completely overturned. The more popular opinions ascribed this feeble
light, some to the fixed stars, some to Venus, some to the rays of the
sun, penetrating and shining through the moon. Even the sagacious
Benedetti adopted the notion of this light being caused by Venus, in the
same sentence in which he explains the true reason of the faint light
observed during a total eclipse of the moon, pointing out that it is
occasioned by those rays of the sun, which reach the moon, after being
bent round the sides of the earth by the action of our atmosphere.[57]

Galileo also announced the detection of innumerable stars, invisible to
the unassisted sight; and those remarkable appearances in the heavens,
generally called nebulæ, the most considerable of which is familiar to
all under the name of the milky way, when examined by his instrument,
were found to resolve themselves into a vast collection of minute stars,
too closely congregated to produce a separate impression upon the
unassisted eye.[58] Benedetti, who divined that the dark shades on the
moon's surface arose from the constitution of those parts which suffered
much of the light to pass into them, and consequently reflected a less
portion of it, had maintained that the milky way was the result of the
converse of the same phenomenon, and declared, in the language of his
astronomy, that it was a part of the eighth orb, which did not, like the
rest, allow the sun's light to traverse it freely, but reflected a small
part feebly to our sight.

The Anti-Copernicans would probably have been well pleased, if by these
eternally renewed discussions and disputes, they could have occupied
Galileo's time sufficiently to detain his attention from his telescope
and astronomical observations; but he knew too well where his real
strength lay, and they had scarcely time to compound any thing like an
argument against him and his theories, before they found him in
possession of some new facts, which they were unprepared to meet,
otherwise than by the never-failing resource of abuse and affected
contempt. The year had not expired before Galileo had new intelligence
to communicate of the highest importance. Perhaps he had been taught
caution from the numerous piracies which had been committed upon his
discoveries, and he first announced his new discoveries enigmatically,
veiling their real import by transpositions of the letters in the words
which described them, (a practice then common, and not disused even at a
much later date,) and inviting all astronomers to declare, within a
certain time, if they had noted any thing new in the heavens worthy of
observation. The transposed letters which he published were--

    "_Smaismrmilme poeta leumi bvne nugttaviras._"

Kepler, in the true spirit of his riddling philosophy, endeavoured to
decypher the meaning, and fancied he had succeeded when he formed a
barbarous Latin verse,

    "_Salve umbistineum geminatum Martia proles_,"

conceiving that the discovery, whatever it might be, related to the
planet Mars, to which Kepler's attention had before been particularly
directed. The reader, however, need not weary himself in seeking a
translation of this solution, for at the request of the Emperor Rodolph,
Galileo speedily sent to him the real reading--

    _Altissimum planetam tergeminum observavi_;

that is, "I have observed that the most distant planet is triple," or,
as he further explains the matter, "I have with great admiration
observed that Saturn is not a single star, but three together, which as
it were touch each other; they have no relative motion, and are
constituted in this form [Symbol: oOo] the middle being somewhat larger
than the lateral ones. If we examine them with an eye-glass which
magnifies the surface less than 1000 times, the three stars do not
appear very distinctly, but Saturn has an oblong appearance, like the
appearance of an olive, thus [Symbol: horizontal 0]. Now I have
discovered a court for Jupiter, and two servants for this old man, who
aid his steps and never quit his side." Galileo was, however, no match
in this style of writing for Kepler, who disapproved his friend's
metaphor, and, in his usual fanciful and amusing strain,--"I will not,"
said he, "make an old man of Saturn, nor slaves of his attendant globes,
but rather let this tricorporate form be Geryon, so shall Galileo be
Hercules, and the telescope his club; armed with which, he has conquered
that distant planet, and dragged him from the remotest depths of nature,
and exposed him to the view of all." Galileo's glass was not of
sufficient power to shew him the real constitution of this extraordinary
planet; it was reserved for Huyghens, about the year 1656, to declare to
the world that these supposed attendant stars are in fact part of a ring
which surrounds, and yet is completely distinct from the body of
Saturn;[59] and the still more accurate observations of Herschel have
ascertained that it consists of two concentric rings revolving round the
planet, and separated from each other by a space which our most powerful
telescopes scarcely enable us to measure.

Galileo's second statement concluded with the remark, that "in the other
planets nothing new was to be observed;" but a month had scarcely
elapsed, before he communicated to the world another enigma,

    _Hæc immatura à me jam frustra leguntur oy_,

which, as he said, contained the announcement of a new phenomenon, in
the highest degree important to the truth of the Copernican system. The
interpretation of this is,

    _Cynthiæ figuras æmulatur mater amorum_,

that is to say,--Venus rivals the appearances of the moon--for Venus
being now arrived at that part of her orbit in which she is placed
between the earth and the sun, and consequently, with only a part of her
enlightened surface turned towards the earth, the telescope shewed her
in a crescent form, like the moon in a similar position, and tracing her
through the whole of her orbit round the sun, or at least so long as she
was not invisible from his overpowering light, Galileo had the
satisfaction of seeing the enlightened portion in each position assume
the form appropriate to that hypothesis. It was with reason, therefore,
that he laid stress on the importance of this observation, which also
established another doctrine scarcely less obnoxious to the
Anti-Copernicans, namely, that a new point of resemblance was here found
between the earth and one of the principal planets; and as the
reflection from the earth upon the moon had shewn it to be luminous like
the planets when subjected to the rays of the sun, so this change of
apparent figure demonstrated that one of the planets not near the earth,
and therefore probably all, were in their own nature not luminous, and
only reflected the sun's light which fell upon them; an inference, of
which the probability was still farther increased a few years later by
the observation of the transit of Mercury over the sun's disc.

It is curious that only twenty-five years before this discovery of the
phases (or appearances) of Venus, a commentator of Aristotle, under the
name of Lucillus Philalthæus, had advanced the doctrine that all the
planets except the moon are luminous of themselves, and in proof of his
assertion had urged, "that if the other planets and fixed stars received
their light from the sun, they would, as they approached and receded
from him, or as he approached and receded from them, assume the same
phases as the moon, which, he adds, we have never yet observed."--He
further remarks, "that Mercury and Venus would, in the supposed case of
their being nearer the earth than the sun, eclipse it occasionally, just
as eclipses are occasioned by the moon." Perhaps it is still more
remarkable, that these very passages, in which the reasoning is so
correct, though the facts are too hastily taken for granted, (the common
error of that school,) are quoted by Benedetti, expressly to shew the
ignorance and presumption of the author. Copernicus, whose want of
instruments had prevented him from observing the horned appearance of
Venus when between the earth and sun, had perceived how formidable an
obstacle the non-appearance of this phenomenon presented to his system;
he endeavoured, though unsatisfactorily, to account for it by supposing
that the rays of the sun passed freely through the body of the planet,
and Galileo takes occasion to praise him for not being deterred from
adopting the system, which, on the whole, appeared to agree best with
the phenomena, by meeting with some which it did not enable him to
explain. Milton, whose poem is filled with allusions to Galileo and his
astronomy, has not suffered this beautiful phenomenon to pass unnoticed.
After describing the creation of the Sun, he adds:--

    Hither, as to their fountain, other stars
    Repairing, in their golden urns draw light,
    And hence the morning planet gilds her horns.[60]

Galileo also assured himself, at the same time, that the fixed stars did
not receive their light from the sun. This he ascertained by comparing
the vividness of their light, in all positions, with the feebleness of
that of the distant planets, and by observing the different degrees of
brightness with which all the planets shone at different distances from
the sun. The more remote planets did not, of course, afford equal
facilities with Venus for so decisive an observation; but Galileo
thought he observed, that when Mars was in quadratures, (or in the
quarters, the middle points of his path on either side,) his figure
varied slightly from a perfect circle. Galileo concludes the letter, in
which he announces these last observations to his pupil Castelli, with
the following expressions, shewing how justly he estimated the
opposition they encountered:--"You almost make me laugh by saying that
these clear observations are sufficient to convince the most obstinate:
it seems you have yet to learn that long ago the observations were
enough to convince those who are capable of reasoning, and those who
wish to learn the truth; but that to convince the obstinate, and those
who care for nothing beyond the vain applause of the stupid and
senseless vulgar, not even the testimony of the stars would suffice,
were they to descend on earth to speak for themselves. Let us then
endeavour to procure some knowledge for ourselves, and rest contented
with this sole satisfaction; but of advancing in popular opinion, or
gaining the assent of the book-philosophers, let us abandon both the
hope and the desire."


FOOTNOTES:

[56] Adone di Marini, Venetiis, 1623, Cant. x.

[57] Speculat. Lib Venetiis, 1585, Epistolæ.

[58] This opinion, with respect to the milky way, had been held by some
of the ancient astronomers. _See_ Manilius. Lib. i. v. 753.

  "_Anne magis densâ stellarum turba coronâ_
  "_Contexit flammas, et crasso lumine candet,_
  "_Et fulgore nitet collato clarior orbis._"

[59] Huyghens announced his discovery in this form: _a a a a a a a c c c
c c d e e e e e g h i i i i i i i l l l l m m n n n n n n n n n o o o o
p p q r r s t t t t t u u u u u_, which he afterwards recomposed into
the sentence. _Annulo cingitur, tenui, plano, nusquam cohærente, ad
eclipticam inclinato_. De Saturni Lunâ. Hagæ, 1656.

[60] B. vii. v. 364. Other passages may be examined in B. i. 286; iii.
565-590, 722-733; iv. 589; v. 261, 414; vii. 577; viii. 1-178.




CHAPTER IX.

    _Account of the Academia Lincea--Del Cimento--Royal Society._


GALILEO'S resignation of the mathematical professorship at Padua
occasioned much dissatisfaction to all those who were connected with
that university. Perhaps not fully appreciating his desire of returning
to his native country, and the importance to him and to the scientific
world in general, of the complete leisure which Cosmo secured to him at
Florence, (for by the terms of his diploma he was not even required to
reside at Pisa, nor to give any lectures, except on extraordinary
occasions, to sovereign princes and other strangers of distinction,) the
Venetians remembered only that they had offered him an honourable asylum
when almost driven from Pisa; that they had increased his salary to four
times the sum which any previous professor had enjoyed; and, finally, by
an almost unprecedented decree, that they had but just secured him in
his post during the remainder of his life. Many took such offence as to
refuse to have any further communication with him; and Sagredo, a
constant friend of Galileo, wrote him word that he had been threatened
with a similar desertion unless he should concur in the same peremptory
resolution, which threats, however, Sagredo, at the same time, intimates
his intention of braving.

Early in the year 1611, Galileo made his first appearance in Rome, where
he was received with marks of distinguished consideration, and where all
ranks were eager to share the pleasure of contemplating the new
discoveries. "Whether we consider cardinal, prince, or prelate, he found
an honourable reception from them all, and had their palaces as open and
free to him as the houses of his private friends."[61] Among other
distinctions he was solicited to become a member of the newly-formed
philosophical society, the once celebrated _Academia Lincea_, to which
he readily assented. The founder of this society was Federigo Cesi, the
Marchese di Monticelli, a young Roman nobleman, the devotion of whose
time and fortune to the interests of science has not been by any means
rewarded with a reputation commensurate with his deserts. If the energy
of his mind had been less worthily employed than in fostering the cause
of science and truth, and in extending the advantages of his birth and
fortune to as many as were willing to co-operate with him, the name of
Federigo Cesi might have appeared more prominently on the page of
history. Cesi had scarcely completed his 18th year, when, in 1603, he
formed the plan of a philosophical society, which in the first instance
consisted only of himself and three of his most intimate friends, Hecke,
a Flemish physician, Stelluti, and Anastasio de Filiis. Cesi's father,
the Duca d'Acquasparta, who was of an arbitrary and extravagant temper,
considered such pursuits and associates as derogatory to his son's rank;
he endeavoured to thwart the design by the most violent and
unjustifiable proceedings, in consequence of which, Cesi in the
beginning of 1605 privately quitted Rome, Hecke was obliged to leave
Italy altogether from fear of the Inquisition, which was excited against
him, and the academy was for a time virtually dissolved. The details of
these transactions are foreign to the present narrative: it will be
enough to mention that, in 1609, Cesi, who had never altogether
abandoned his scheme, found the opposition decaying which he at first
experienced, and with better success he renewed the plan which he had
sketched six years before. A few extracts from the Regulations will
serve to shew the spirit in which this distinguished society was
conceived:--

"The Lyncean Society desires for its academicians, philosophers eager
for real knowledge, who will give themselves to the study of nature, and
especially to mathematics; at the same time it will not neglect the
ornaments of elegant literature and philology, which like a graceful
garment adorn the whole body of science.--In the pious love of wisdom,
and to the praise of the most good and most high God, let the Lynceans
give their minds, first to observation and reflection, and afterwards to
writing and publishing.--It is not within the Lyncean plan to find
leisure for recitations and declamatory assemblies; the meetings will
neither be frequent nor full, and chiefly for transacting the necessary
business of the society: but those who wish to enjoy such exercises will
in no respect be hindered, provided they attend them as accessory
studies, decently and quietly, and without making promises and
professions of how much they are about to do. For there is ample
philosophical employment for every one by himself, particularly if pains
are taken in travelling and in the observation of natural phenomena, and
in the book of nature which every one has at home, that is to say, the
heavens and the earth; and enough may be learned from the habits of
constant correspondence with each other, and alternate offices of
counsel and assistance.--Let the first fruits of wisdom be love; and so
let the Lynceans love each other as if united by the strictest ties, nor
suffer any interruption of this sincere bond of love and faith,
emanating from the source of virtue and philosophy.--Let them add to
their names the title of Lyncean, which has been advisedly chosen as a
warning and constant stimulus, especially when they write on any
literary subject, also in their private letters to their associates, and
in general when any work comes from them wisely and well performed.--The
Lynceans will pass over in silence all political controversies and
quarrels of every kind, and wordy disputes, especially gratuitous ones,
which give occasion to deceit, unfriendliness, and hatred; like men who
desire peace, and seek to preserve their studies free from molestation,
and to avoid every sort of disturbance. And if any one by command of his
superiors, or from some other necessity, is reduced to handle such
matters, since they are foreign to physical and mathematical science,
and consequently alien to the object of the Academy, let them be printed
without the Lyncean name."[62]

The society which was eventually organized formed but a very trifling
part of the comprehensive scheme which Cesi originally proposed to
himself; it had been his wish to establish a scientific Order which
should have corresponding lodges in the principal towns of Europe, and
in other parts of the globe, each consisting of not more than five nor
less than three members, besides an unlimited number of Academicians not
restricted to any particular residence or regulations. The
mortifications and difficulties to which he was subjected from his
father's unprincipled behaviour, render it most extraordinary and
admirable that he should have ventured to undertake even so much as he
actually carried into execution. He promised to furnish to the members
of his society such assistance as they might require in the prosecution
of their respective researches, and also to defray the charges of
publishing such of their works as should be thought worthy of appearing
with the common sanction. Such liberal offers were not likely to meet
with an unfavourable reception: they were thankfully accepted by many
well qualified to carry his design into execution, and Cesi was soon
enabled formally to open his academy, the distinctive title of which he
borrowed from the Lynx, with reference to the piercing sight which that
animal has been supposed to possess. This quality seemed to him an
appropriate emblem of those which he desired to find in his
academicians, for the purpose of investigating the secrets of nature;
and although, at the present day, the name may appear to border on the
grotesque, it was conceived in the spirit of the age, and the fantastic
names of the numberless societies which were rapidly formed in various
parts of Italy far exceed whatever degree of quaintness may be thought
to belong to the Lyncean name. The Inflamed--the Transformed--the
Uneasy--the Humorists--the Fantastic--the Intricate--the Indolent--the
Senseless--the Undeceived--the Valiant--the Ætherial Societies are
selected from a vast number of similar institutions, the names of which,
now almost their sole remains, are collected by the industry of Morhof
and Tiraboschi.[63] The Humorists are named by Morhof as the only
Italian philosophical society anterior to the Lynceans; their founder
was Paolo Mancino, and the distinctive symbol which they adopted was
rain dropping from a cloud, with the motto _Redit agmine dulci_;--their
title is derived from the same metaphor. The object of their union
appears to have been similar to that of the Lynceans, but they at no
time attained to the celebrity to which Cesi's society rose from the
moment of its incorporation. Cesi took the presidency for his life, and
the celebrated Baptista Porta was appointed vice president at Naples.
Stelluti acted as the legal representative of the society, with the
title of procuratore. Of the other two original members Anastasio de
Filiis was dead, and although Hecke returned to Italy in 1614, and
rejoined the Academy, yet he was soon afterwards struck off the list in
consequence of his lapsing into insanity. Among the academicians we find
the names of Galileo, Fabio Colonna, Lucas Valerio, Guiducci, Welser,
Giovanni Fabro, Terrentio, Virginio Cesarini, Ciampoli, Molitor,
Cardinal Barberino, (nephew of Pope Urban VIII.) Stelliola, Salviati,
&c.

The principal monument still remaining of the zeal and industry to which
Cesi incited his academicians is the Phytobasanos, a compendium of the
natural history of Mexico, which must be considered a surprising
performance for the times in which it appeared. It was written by a
Spaniard named Hernandez; and Reccho, who often has the credit of the
whole work, made great additions to it. During fifty years the
manuscript had been neglected, when Cesi discovered it, and employed
Terrentio, Fabro, and Colonna, all Lynceans, to publish it enriched with
their notes and emendations. Cesi himself published several treatises,
two of which are extant; his _Tabulæ Phytosophicæ_, and a Dissertation
on Bees entitled _Apiarium_, the only known copy of which last is in the
library of the Vatican. His great work, _Theatrum Naturæ_, was never
printed; a circumstance which tends to shew that he did not assemble the
society round him for the purpose of ministering to his own vanity, but
postponed the publication of his own productions to the labours of his
coadjutors. This, and many other valuable works belonging to the academy
existed in manuscript till lately in the Albani Library at Rome. Cesi
collected, not a large, but an useful library for the use of the
academy, (which was afterwards augmented on the premature death of
Cesarini by the donation of his books); he filled a botanical garden
with the rarer specimens of plants, and arranged a museum of natural
curiosities; his palace at Rome was constantly open to the academicians;
his purse and his influence were employed with equal liberality in their
service.

Cesi's death, in 1632, put a sudden stop to the prosperity of the
society, a consequence which may be attributed to the munificence with
which he had from the first sustained it: no one could be found to fill
his place in the princely manner to which the academicians were
accustomed, and the society, after lingering some years under the
nominal patronage of Urban VIII., gradually decayed, till, by the death
of its principal members, and dispersion of the rest, it became entirely
extinct.[64] Bianchi, whose sketch of the academy was almost the only
one till the appearance of Odescalchi's history, made an attempt to
revive it in the succeeding century, but without any permanent effect. A
society under the same name has been formed since 1784, and is still
flourishing in Rome. Before leaving the subject it may be mentioned,
that one of the earliest notices that Bacon's works were known in Italy
is to be found in a letter to Cesi, dated 1625; in which Pozzo, who had
gone to Paris with Cardinal Barberino, mentions having seen them there
with great admiration, and suggests that Bacon would be a fit person to
be proposed as a member of their society. After Galileo's death, three
of his principal followers, Viviani, Torricelli, and Aggiunti formed the
plan of establishing a similar philosophical society, and though
Aggiunti and Torricelli died before the scheme could be realized,
Viviani pressed it forward, and, under the auspices of Ferdinand II.,
formed a society, which, in 1657, merged in the famous _Academia del
Cimento_, or Experimental Academy. This latter held its occasional
meetings at the palace of Ferdinand's brother, Leopold de' Medici: it
was composed chiefly, if not entirely, of Galileo's pupils and friends.
During the few years that this society lasted, one of the principal
objects of which was declared to be the repetition and developement of
Galileo's experiments, it kept up a correspondence with the principal
philosophers in every part of Europe, but when Leopold was, in 1666,
created a cardinal, it appears to have been dissolved, scarcely ten
years after its institution.[65] This digression may be excused in
favour of so interesting an establishment as the Academia Lincea, which
preceded by half a century the formation of the Royal Society of London,
and Académie Françoise of Paris.

These latter two are mentioned together, probably for the first time, by
Salusbury. The passage is curious in an historical point of view, and
worth extracting:--"In imitation of these societies, Paris and London
have erected theirs of _Les Beaux Esprits_, and of the _Virtuosi_: the
one by the countenance of the most eminent Cardinal Richelieu, the other
by the royal encouragement of his sacred Majesty that now is. The _Beaux
Esprits_ have published sundry volumes of their moral and physiological
conferences, with the laws and history of their fellowship; and I hope
the like in due time from our Royal Society; that so such as envie their
fame and felicity, and such as suspect their ability and candor, may be
silenced and disappointed in their detractions and expectations."[66]


FOOTNOTES:

[61] Salusbury, Math. Coll.

[62] Perhaps it was to deprecate the hostility of the Jesuits that, at
the close of these Regulations, the Lynceans are directed to address
their prayers, among other Saints, especially to Ignatius Loyola, as to
one who greatly favoured the interests of learning. Odescalchi, Memorie
dell'Acad. de' Lincei, Roma. 1806.

[63] Polyhistor Literarius, &c.--Storia della Letterat. Ital. The still
existing society of Chaff, more generally known by its Italian title,
Della Crusca, belongs to the same period.

[64] F. Colonnæ Phytobasanus Jano Planco Auctore. Florent, 1744.

[65] Nelli Saggio di Storia Literaria Fiorentina, Lucca, 1759.

[66] Salusbury's Math. Coll. vol. ii. London, 1664.




CHAPTER X.

    _Spots on the Sun--Essay on Floating Bodies--Scheiner--Change in
      Saturn._


GALILEO did not indulge the curiosity of his Roman friends by exhibiting
only the wonders already mentioned, which now began to lose the gloss of
novelty, but disclosed a new discovery, which appeared still more
extraordinary, and, to the opposite faction, more hateful than anything
of which he had yet spoken. This was the discovery, which he first made
in the month of March, 1611, of dark spots on the body of the sun. A
curious fact, and one which well serves to illustrate Galileo's
superiority in seeing things simply as they are, is, that these spots
had been observed and recorded centuries before he existed, but, for
want of careful observation, their true nature had been constantly
misapprehended. One of the most celebrated occasions was in the year 807
of our era, in which a dark spot is mentioned as visible on the face of
the sun during seven or eight days. It was then supposed to be
Mercury.[67] Kepler, whose astronomical knowledge would not suffer him
to overlook that it was impossible that Mercury could remain so long in
conjunction with the sun, preferred to solve the difficulty by supposing
that, in Aimoin's original account, the expression was not _octo dies_
(eight days), but _octoties_--a barbarous word, which he supposed to
have been written for _octies_ (eight times); and that the other
accounts (in which the number of days mentioned is different) copying
loosely from the first, had both mistaken the word, and misquoted the
time which they thought they found mentioned there. It is impossible to
look on this explanation as satisfactory, but Kepler, who at that time
did not dream of spots on the sun, was perfectly contented with it. In
1609, he himself observed upon the sun a black spot, which he in like
manner mistook for Mercury, and unluckily the day, being cloudy, did
not allow him to contemplate it sufficiently long to discover his
error, which the slowness of its apparent motion would soon have pointed
out.[68] He hastened to publish his supposed observation, but no sooner
was Galileo's discovery of the solar spots announced, than he, with that
candour which as much as his flighty disposition certainly characterized
him at all times, retracted his former opinion, and owned his belief
that he had been mistaken. In fact it is known from the more accurate
theory which we now possess of Mercury's motions, that it did not pass
over the sun's face at the time when Kepler thought he perceived it
there.

Galileo's observations were in their consequences to him particularly
unfortunate, as in the course of the controversy in which they engaged
him, he first became personally embroiled with the powerful party, whose
prevailing influence was one of the chief causes of his subsequent
misfortunes. Before we enter upon that discussion, it will be proper to
mention another famous treatise which Galileo produced soon after his
return from Rome to Florence, in 1612. This is, his Discourse on
Floating Bodies, which restored Archimedes' theory of hydrostatics, and
has, of course, met with the opposition which few of Galileo's works
failed to encounter. In the commencement, he thought it necessary to
apologize for writing on a subject so different from that which chiefly
occupied the public attention, and declared that he had been too closely
occupied in calculating the periods of the revolutions of Jupiter's
satellites to permit him to publish anything earlier. These periods he
had succeeded in determining during the preceding year, whilst at Rome,
and he now announced them to complete their circuits, the first in about
1 day, 18½ hours; the second in 3 days, 13 hours, 20 minutes; the third
in 7 days, 4 hours; and the outermost in 16 days, 18 hours. All these
numbers he gave merely as approximately true, and promised to continue
his observations, for the purpose of correcting the results. He then
adds an announcement of his recent discovery of the solar spots, "which,
as they change their situation, offer a strong argument, either that the
sun revolves on itself, or that, perhaps, other stars, like Venus and
Mercury, revolve about it, invisible at all other times, on account of
the small distance to which they are removed from him." To this he
afterwards subjoined, that, by continued observation, he had satisfied
himself that these solar spots were in actual contact with the surface
of the sun, where they are continually appearing and disappearing; that
their figures were very irregular, some being very dark, and others not
so black; that one would often divide into three or four, and, at other
times, two, three, or more would unite into one; besides which, that
they had all a common and regular motion, with which they revolved round
with the sun, which turned upon its axis in about the time of a lunar
month.

Having by these prefatory observations assuaged the public thirst for
astronomical novelties, he ventures to introduce the principal subject
of the treatise above mentioned. The question of floating bridges had
been discussed at one of the scientific parties, assembled at the house
of Galileo's friend Salviati, and the general opinion of the company
appearing to be that the floating or sinking of a body depended
principally upon its shape, Galileo undertook to convince them of their
error. If he had not preferred more direct arguments, he might merely
have told them that in this instance they were opposed to their
favourite Aristotle, whose words are very unequivocal on the point in
dispute. "Form is not the cause why a body moves downwards rather than
upwards, but it does affect the swiftness with which it moves;"[69]
which is exactly the distinction which those who called themselves
Aristotelians were unable to perceive, and to which the opinions of
Aristotle himself were not always true. Galileo states the discussion to
have immediately arisen from the assertion of some one in the company,
that condensation is the effect of cold, and ice was mentioned as an
instance. On this, Galileo observed, that ice is rather water rarefied
than condensed, the proof of which is, that ice always floats upon
water.[70] It was replied, that the reason of this phenomenon was, not
the superior lightness of the ice, but its incapacity, owing to its flat
shape, to penetrate and overcome the resistance of the water. Galileo
denied this, and asserted that ice of any shape would float upon water,
and that, if a flat piece of ice were forcibly taken to the bottom, it
would of itself rise again to the surface. Upon this assertion it
appears that the conversation became so clamorous, that Galileo thought
it pertinent to commence his Essay with the following observation on the
advantage of delivering scientific opinions in writing, "because in
conversational arguments, either one or other party, or perhaps both,
are apt to get overwarm, and to speak overloud, and either do not suffer
each other to be heard, or else, transported with the obstinacy of not
yielding, wander far away from the original proposition, and confound
both themselves and their auditors with the novelty and variety of their
assertions." After this gentle rebuke he proceeds with his argument, in
which he takes occasion to state the famous hydrostatical paradox, of
which the earliest notice is to be found in Stevin's works, a
contemporary Flemish engineer, and refers it to a principle on which we
shall enlarge in another chapter. He then explains the true theory of
buoyancy, and refutes the false reasoning on which the contrary opinions
were founded, with a variety of experiments.

The whole value and interest of experimental processes generally depends
on a variety of minute circumstances, the detail of which would be
particularly unsuited to a sketch like the present one. For those who
are desirous of becoming more familiar with Galileo's mode of conducting
an argument, it is fortunate that such a series of experiments exists as
that contained in this essay; experiments which, from their simplicity,
admit of being for the most part concisely enumerated, and at the same
time possess so much intrinsic beauty and characteristic power of
forcing conviction. They also present an admirable specimen of the
talent for which Galileo was so deservedly famous, of inventing
ingenious arguments in favour of his adversaries' absurd opinions before
he condescended to crush them, shewing that nothing but his love of
truth stood in the way of his being a more subtle sophist than any
amongst them. In addition to these reasons for giving these experiments
somewhat in detail, is the fact that all explanation of one of the
principal phenomena to which they allude is omitted in many more modern
treatises on Hydrostatics; and in some it is referred precisely to the
false doctrines here confuted.

The marrow of the dispute is included in Galileo's assertion, that "The
diversity of figure given to any solid cannot be in any way the cause of
its absolutely sinking or floating; so that if a solid, when formed for
example into a spherical figure, sinks or floats in the water, the same
body will sink or float in the same water, when put into any other form.
The breadth of the figure may indeed retard its velocity, as well of
ascent as descent, and more and more according as the said figure is
reduced to a greater breadth and thinness; but that it may be reduced to
such a form as absolutely to put an end to its motion in the same fluid,
I hold to be impossible. In this I have met with great contradictors
who, producing some experiments, and in particular a thin board of
ebony, and a ball of the same wood, and shewing that the ball in water
sinks to the bottom[71], and that the board if put lightly on the
surface floats, have held and confirmed themselves in their opinion with
the authority of Aristotle, that the cause of that rest is the breadth
of the figure, unable by its small weight to pierce and penetrate the
resistance of the water's thickness, which is readily overcome by the
other spherical figure."--For the purpose of these experiments, Galileo
recommends a substance such as wax, which may be easily moulded into any
shape, and with which, by the addition of a few filings of lead, a
substance may be readily made of any required specific gravity. He then
declares that if a ball of wax of the size of an orange, or bigger, be
made in this manner heavy enough to sink to the bottom, but so lightly
that if we take from it only one grain of lead it returns to the top;
and if the same wax be afterwards moulded into a broad and thin cake, or
into any other figure, regular or irregular, the addition of the same
grain of lead will always make it sink, and it will again rise when we
remove the lead from it.--"But methinks I hear some of the adversaries
raise a doubt upon my produced experiment: and, first, they offer to my
consideration that the figure, as a figure simply, and disjunct from the
matter, works no effect, but requires to be conjoined with the matter;
and, moreover, not with every matter, but with those only wherewith it
may be able to execute the desired operation. Just as we see by
experience that an acute and sharp angle is more apt to cut than an
obtuse; yet always provided that both one and the other are joined with
a matter fit to cut, as for instance, steel. Therefore a knife with a
fine and sharp edge cuts bread or wood with much ease, which it will not
do if the edge be blunt and thick; but if, instead of steel, any one
will take wax and mould it into a knife, undoubtedly he will never learn
the effects of sharp and blunt edges, because neither of them will cut;
the wax being unable, by reason of its flexibility, to overcome the
hardness of the wood and bread. And therefore, applying the like
discourse to our argument, they say that the difference of figure will
shew different effects with regard to floating and sinking, but not
conjoined with any kind of matter, but only with those matters which by
their weight are able to overcome the viscosity of the water (like the
ebony which they have selected); and he that will select cork or other
light wood to form solids of different figures, would in vain seek to
find out what operation figure has in sinking or floating, because all
would swim, and that not through any property of this or that figure,
but through the debility of the matter.

"When I begin to examine one by one all the particulars here produced, I
allow not only that figures, simply as such, do not operate in natural
things, but also that they are never separated from the corporeal
substance, nor have I ever alleged them to be stript of sensible matter:
and also I freely admit, that in our endeavours to examine the diversity
of accidents which depend upon the variety of figures, it is necessary
to apply them to matters which obstruct not the various operations of
those various figures. I admit and grant that I should do very ill if I
were to try the influence of a sharp edge with a knife of wax, applying
it to cut an oak, because no sharpness in wax is able to cut that very
hard wood. But yet, such an experiment of this knife would not be beside
the purpose to cut curded milk, or other very yielding matter; nay, in
such matters, the wax is more convenient than steel for finding the
difference depending on the acuteness of the angles, because milk is cut
indifferently with a razor, or a blunt knife. We must therefore have
regard not only to the hardness, solidity, or weight of the bodies
which, under different figures, are to divide some matters asunder; but
also, on the other hand, to the resistance of the matter to be
penetrated. And, since I have chosen a matter which does penetrate the
resistance of the water, and in all figures descends to the bottom, my
antagonists can charge me with no defect; nor (to revert to their
illustration) have I attempted to test the efficacy of acuteness by
cutting with matters unable to cut. I subjoin withal, that all caution,
distinction, and election of matter would be superfluous and
unnecessary, if the body to be cut should not at all resist the cutting:
if the knife were to be used in cutting a mist, or smoke, one of paper
would serve the purpose as well as one of Damascus steel; and I assert
that this is the case with water, and that there is not any solid of
such lightness or of such a figure, that being put on the water it will
not divide and penetrate its thickness; and if you will examine more
carefully your thin boards of wood, you will see that they have part of
their thickness under water; and, moreover, you will see that the
shavings of ebony, stone, or metal, when they float, have not only thus
broken the continuity of the water, but are with all their thickness
under the surface of it; and that more and more, according as the
floating substance is heavier, so that a thin floating plate of lead
will be lower than the surface of the surrounding water by at least
twelve times the thickness of the plate, and gold will dive below the
level of the water almost twenty times the thickness of the plate, as I
shall shew presently."

In order to illustrate more clearly the non-resistance of water to
penetration, Galileo then directs a cone to be made of wood or wax, and
asserts that when it floats, either with its base or point in the water,
the solid content of the part immersed will be the same, although the
point is, by its shape, better adapted to overcome the resistance of the
water to division, if that were the cause of the buoyancy. Or the
experiment may be varied by tempering the wax with filings of lead, till
it sinks in the water, when it will be found that in any figure the same
cork must be added to it to raise it to the surface.--"This silences not
my antagonists; but they say that all the discourse hitherto made by me
imports little to them, and that it serves their turn, that they have
demonstrated in one instance, and in such manner and figure as pleases
them best, namely, in a board and a ball of ebony, that one, when put
into the water, sinks to the bottom, and that the other stays to swim at
the top; and the matter being the same, and the two bodies differing in
nothing but in figure, they affirm that with all perspicuity they have
demonstrated and sensibly manifested what they undertook. Nevertheless I
believe, and think I can prove that this very experiment proves nothing
against my theory. And first it is false that the ball sinks, and the
board not; for the board will sink too, if you do to both the figures as
the words of our question require; that is, if you put them both _in_
the water; for to be in the water implies to be placed in the water, and
by Aristotle's own definition of place, to be placed imports to be
environed by the surface of the ambient body; but when my antagonists
shew the floating board of ebony, they put it not into the water, but
upon the water; where, being detained by a certain impediment (of which
more anon) it is surrounded, partly with water, partly with air, which
is contrary to our agreement, for that was that the bodies should be in
the water, and not part in the water, part in the air. I will not omit
another reason, founded also upon experience, and, if I deceive not
myself, conclusive against the notion that figure, and the resistance of
the water to penetration have anything to do with the buoyancy of
bodies. Choose a piece of wood or other matter, as for instance
walnut-wood, of which a ball rises from the bottom of the water to the
surface more slowly than a ball of ebony of the same size sinks, so that
clearly the ball of ebony divides the water more readily in sinking than
does the walnut in rising. Then take a board of walnut-tree equal to and
like the floating ebony one of my antagonists; and if it be true that
this latter floats by reason of the figure being unable to penetrate the
water, the other of walnut-tree, without all question, if thrust to the
bottom ought to stay there, as having the same impeding figure, and
being less apt to overcome the said resistance of the water. But if we
find by experience that not only the thin board, but every other figure
of the same walnut-tree will return to float, as unquestionably we
shall, then I must desire my opponents to forbear to attribute the
floating of the ebony to the figure of the board, since the resistance
of the water is the same in rising as in sinking, and the force of
ascension of the walnut-tree is less than the ebony's force for going to
the bottom.

"Now, let us return to the thin plate of gold or silver, or the thin
board of ebony, and let us lay it lightly upon the water, so that it may
stay there without sinking, and carefully observe the effect. It will
appear clearly that the plates are a considerable matter lower than the
surface of the water which rises up, and makes a kind of rampart round
them on every side, in the manner shewn in the annexed figure, in which
BDLF represents the surface of the water, and AEIO the surface of the
plate. But if it have already penetrated and overcome the continuity of
the water, and is of its own nature heavier than the water, why does it
not continue to sink, but stop and suspend itself in that little dimple
that its weight has made in the water? My answer is, because in sinking
till its surface is below the water which rises up in a bank round it,
it draws after and carries along with it the air above it, so that that
which in this case descends and is placed in the water, is not only the
board of ebony or plate of iron, but a compound of ebony and air, from
which composition results a solid no longer specifically heavier than
the water, as was the ebony or gold alone. But, Gentlemen, we want the
same matter; you are to alter nothing but the shape, and therefore have
the goodness to remove this air, which may be done simply by washing the
upper surface of the board, for the water having once got between the
board and air will run together, and the ebony will go to the bottom;
and if it does not, you have won the day. But methinks I hear some of my
antagonists cunningly opposing this, and telling me that they will not
on any account allow their board to be wetted, because the weight of the
water so added, by making it heavier than it was before, draws it to the
bottom, and that the addition of new weight is contrary to our
agreement, which was that the matter should be the same."

[Illustration]

"To this I answer first, that nobody can suppose bodies to be put into
the water without their being wet, nor do I wish to do more to the
board than you may do to the ball. Moreover, it is not true that the
board sinks on account of the weight of the water added in the washing;
for I will put ten or twenty drops on the floating board, and so long as
they stand separate it shall not sink; but if the board be taken out,
and all that water wiped off, and the whole surface bathed with one
single drop, and put it again upon the water, there is no question but
it will sink, the other water running to cover it, being no longer
hindered by the air. In the next place it is altogether false that water
can in any way increase the weight of bodies immersed in it, for water
has no weight in water, since it does not sink. Now, just as he who
should say that brass by its own nature sinks, but that when formed into
the shape of a kettle, it acquires from that figure a virtue of lying in
the water without sinking, would say what is false, because that is not
purely brass which then is put into the water, but a compound of brass
and air; so is it neither more nor less false, that a thin plate of
brass or ebony swims by virtue of its dilated and broad figure. Also I
cannot omit to tell my opponents, that this conceit of refusing to bathe
the surface of the board, might beget an opinion in a third person of a
poverty of arguments on their side, especially as the conversation began
about flakes of ice, in which it would be simple to require that the
surfaces should be kept dry; not to mention that such pieces of ice,
whether wet or dry, always float, and as my antagonists say, because of
their shape.

"Some may wonder that I affirm this power to be in the air of keeping
the plate of brass or silver above water, as if in a certain sense I
would attribute to the air a kind of magnetic virtue for sustaining
heavy bodies with which it is in contact. To satisfy all these doubts, I
have contrived the following experiment to demonstrate how truly the air
does support these solids; for I have found, when one of these bodies
which floats when placed lightly on the water, is thoroughly bathed and
sunk to the bottom, that by carrying down to it a little air without
otherwise touching it in the least, I am able to raise and carry it back
to the top, where it floats as before. To this effect I take a ball of
wax, and with a little lead make it just heavy enough to sink very
slowly to the bottom, taking care that its surface be quite smooth and
even. This, if put gently into the water, submerges almost entirely,
there remaining visible only a little of the very top, which, so long as
it is joined to the air, keeps the ball afloat; but if we take away the
contact of the air by wetting this top, the ball sinks to the bottom,
and remains there. Now to make it return to the surface by virtue of the
air which before sustained it, thrust into the water a glass, with the
mouth downwards, which will carry with it the air it contains; and move
this down towards the ball, until you see by the transparency of the
glass that the air has reached the top of it; then gently draw the glass
upwards, and you will see the ball rise, and afterwards stay on the top
of the water, if you carefully part the glass and water without too much
disturbing it.[72] There is therefore a certain affinity between the air
and other bodies, which holds them united, so that they separate not
without a kind of violence, just as between water and other bodies; for
in drawing them wholly out of the water, we see the water follow them,
and rise sensibly above the level before it quits them." Having
established this principle by this exceedingly ingenious and convincing
experiment, Galileo proceeds to shew from it what must be the dimensions
of a plate of any substance which will float as the wax does, assuming
in each case that we know the greatest height at which the rampart of
water will stand round it. In like manner he shows that a pyramidal or
conical figure may be made of any substance, such that by help of the
air, it shall rest upon the water without wetting more than its base;
and that we may so form a cone of any substance that it shall float if
placed gently on the surface, with its point downwards, whereas no care
or pains will enable it to float with its base downwards, owing to the
different proportions of air which in the two positions remain connected
with it. With this parting blow at his antagonist's theory we close our
extracts from this admirable essay.

The first elements of the theory of running waters were reserved for
Castelli, an intimate friend and pupil of Galileo. On the present
occasion, Castelli appeared as the ostensible author of a defence
against the attacks made by Vincenzio di Grazia and by Lodovico delle
Columbe (the author of the crystalline composition of the moon) on the
obnoxious theory. After destroying all the objections which they
produced, the writer tauntingly bids them remember, that he was merely
Galileo's pupil, and consider how much more effectually Galileo himself
would have confuted them, had he thought it worth while. It was not
known till several years after his death, that this Essay was in fact
written by Galileo himself.[73]

These compositions merely occupied the leisure time which he could
withhold from the controversy on the solar spots to which we have
already alluded. A German Jesuit named Christopher Scheiner, who was
professor of mathematics at Ingolstadt, in imitation of Galileo had
commenced a series of observations on them, but adopted the theory
which, as we have seen, Galileo had examined and rejected, that these
spots are planets circulating at some distance from the body of the sun.
The same opinion had been taken up by a French astronomer, who in honour
of the reigning family called them Borbonian stars. Scheiner promulgated
his notions in three letters, addressed to their common friend Welser,
under the quaint signature of "_Apelles latens post tabulam_." Galileo
replied to Scheiner's letters by three others, also addressed to Welser,
and although the dispute was carried on amid mutual professions of
respect and esteem, it laid the foundation of the total estrangement
which afterwards took place between the two authors. Galileo's part of
this controversy was published at Rome by the Lyncean Academy in 1613.
To the last of his letters, written in December, 1612, is annexed a
table of the expected positions of Jupiter's satellites during the
months of March and April of the following year, which, imperfect as it
necessarily was, cannot be looked upon without the greatest interest.

In the same letter it is mentioned that Saturn presented a novel
appearance, which, for an instant, almost induced Galileo to mistrust
the accuracy of his earlier observations. The lateral appendages of this
planet had disappeared, and the accompanying extract will show the
uneasiness which Galileo could not conceal at the sight of this
phenomenon, although it is admirable to see the contempt with which,
even in that trying moment, he expresses his consciousness that his
adversaries were unworthy of the triumph they appeared on the point of
celebrating.--"Looking on Saturn within these few days, I found it
solitary, without the assistance of its accustomed stars, and in short,
perfectly round and defined like Jupiter, and such it still remains. Now
what can be said of so strange a metamorphosis? are perhaps the two
smaller stars consumed, like the spots on the sun? have they suddenly
vanished and fled? or has Saturn devoured his own children? or was the
appearance indeed fraud and illusion, with which the glasses have for so
long a time mocked me, and so many others who have often observed with
me. Now perhaps the time is come to revive the withering hopes of those,
who, guided by more profound contemplations, have fathomed all the
fallacies of the new observations and recognised their impossibility! I
cannot resolve what to say in a chance so strange, so new, and so
unexpected; the shortness of the time, the unexampled occurrence, the
weakness of my intellect, and the terror of being mistaken, have greatly
confounded me." These first expressions of alarm are not to be wondered
at; however, he soon recovered courage, and ventured to foretel the
periods at which the lateral stars would again show themselves,
protesting at the same time, that he was in no respect to be understood
as classing this prediction among the results which depend on certain
principles and sound conclusions, but merely on some conjectures which
appeared to him probable. From one of the Dialogues on the System, we
learn that this conjecture was, that Saturn might revolve upon his axis,
but the period which he assumed is very different from the true one, as
might be expected from its being intended to account for a phenomenon of
which Galileo had not rightly apprehended the character.

He closed this letter with renewed professions of courtesy and
friendship towards Apelles, enjoining Welser not to communicate it
without adding his excuses, if he should be thought to dissent too
violently from his antagonist's ideas, declaring that his only object
was the discovery of truth, and that he had freely exposed his own
opinion, which he was still ready to change, so soon as his errors
should be made manifest to him; and that he would consider himself
under special obligation to any one who would be kind enough to discover
and correct them. These letters were written from the villa of his
friend Salviati at Selve near Florence, where he passed great part of
his time, particularly during his frequent indispositions, conceiving
that the air of Florence was prejudicial to him. Cesi was very anxious
for their appearance, since they were (in his own words) so hard a
morsel for the teeth of the Peripatetics, and he exhorted Galileo, in
the name of the society, "to continue to give them, and the nameless
Jesuit, something to gnaw."


FOOTNOTES:

[67] Aimoini Hist. Francorum. Parisiis. 1567.

[68] Mercurius in sole visus. 1609.

[69] De Coelo. lib. 4.

[70] For a discussion of this singular phenomenon, _see_ Treatise on
Heat, p. 12; and it is worth while to remark in passing, what an
admirable instance it affords of Galileo's instantaneous abandonment of
a theory so soon as it became inconsistent with experiment.

[71] Ebony is one of the few woods heavier than water. _See_ Treatise on
Hydrostatics.

[72] In making this very beautiful experiment, it is best to keep the
glass a few seconds in the water, to give time for the surface of the
ball to dry. It will also succeed with a light needle, if carefully
conducted.

[73] Nelli. Saggio di Stor. Liter. Fiorent.




CHAPTER XI.

    _Letter to Christina, Arch-Duchess of Tuscany--Caccini--Galileo
      revisits Rome--Inchoffer--Problem of Longitudes._


THE uncompromising boldness with which Galileo published and supported
his opinions, with little regard to the power and authority of those who
advocated the contrary doctrines, had raised against him a host of
enemies, who each had objections to him peculiar to themselves, but who
now began to perceive the policy of uniting their strength in the common
cause, to crush if possible so dangerous an innovator. All the
professors of the old opinions, who suddenly found the knowledge on
which their reputation was founded struck from under them, and who could
not reconcile themselves to their new situation of learners, were united
against him; and to this powerful cabal was now added the still greater
influence of the jesuits and pseudo-theological party, who fancied they
saw in the spirit of Galileo's writings the same inquisitive temper
which they had already found so inconvenient in Luther and his
adherents. The alarm became greater every day, inasmuch as Galileo had
succeeded in training round him a numerous band of followers who all
appeared imbued with the same dangerous spirit of innovation, and his
favourite scholars were successful candidates for professorships in many
of the most celebrated universities of Italy.

At the close of 1613, Galileo addressed a letter to his pupil, the Abbé
Castelli, in which he endeavoured to shew that there is as much
difficulty in reconciling the Ptolemaic as the Copernican system of the
world with the astronomical expressions contained in the Scriptures, and
asserted, that the object of the Scriptures not being to teach
astronomy, such expressions are there used as would be intelligible and
conformable to the vulgar belief, without regard to the true structure
of the universe; which argument he afterwards amplified in a letter
addressed to Christina, Grand Duchess of Tuscany, the mother of his
patron Cosmo. He discourses on this subject with the moderation and good
sense which so peculiarly characterized him. "I am," says he, "inclined
to believe, that the intention of the sacred Scriptures is to give to
mankind the information necessary for their salvation, and which,
surpassing all human knowledge, can by no other means be accredited than
by the mouth of the Holy Spirit. But I do not hold it necessary to
believe, that the same God who has endowed us with senses, with speech,
and intellect, intended that we should neglect the use of these, and
seek by other means for knowledge which they are sufficient to procure
us; especially in a science like astronomy, of which so little notice is
taken in the Scriptures, that none of the planets, except the sun and
moon, and, once or twice only, Venus under the name of Lucifer, are so
much as named there. This therefore being granted, methinks that in the
discussion of natural problems we ought not to begin at the authority of
texts of Scripture, but at sensible experiments and necessary
demonstrations: for, from the divine word, the sacred Scripture and
nature did both alike proceed, and I conceive that, concerning natural
effects, that which either sensible experience sets before our eyes, or
necessary demonstrations do prove unto us, ought not upon any account to
be called into question, much less condemned, upon the testimony of
Scriptural texts, which may under their words couch senses seemingly
contrary thereto.

"Again, to command the very professors of astronomy that they of
themselves see to the confuting of their own observations and
demonstrations, is to enjoin a thing beyond all possibility of doing;
for it is not only to command them not to see that which they do see,
and not to understand that which they do understand, but it is to order
them to seek for and to find the contrary of that which they happen to
meet with. I would entreat these wise and prudent fathers, that they
would with all diligence consider the difference that is between
opinionative and demonstrative doctrines: to the end that well weighing
in their minds with what force necessary inferences urge us, they might
the better assure themselves that it is not in the power of the
professors of demonstrative sciences to change their opinions at
pleasure, and adopt first one side and then another; and that there is a
great difference between commanding a mathematician or a philosopher,
and the disposing of a lawyer or a merchant; and that the demonstrated
conclusions touching the things of nature and of the heavens cannot be
changed with the same facility as the opinions are touching what is
lawful or not in a contract, bargain, or bill of exchange. Therefore,
first let these men apply themselves to examine the arguments of
Copernicus and others, and leave the condemning of them as erroneous and
heretical to whom it belongeth; yet let them not hope to find such rash
and precipitous determinations in the wary and holy fathers, or in the
absolute wisdom of him who cannot err, as those into which they suffer
themselves to be hurried by some particular affection or interest of
their own. In these and such other positions, which are not directly
articles of faith, certainly no man doubts but His Holiness hath always
an absolute power of admitting or condemning them, but it is not in the
power of any creature to make them to be true or false, otherwise than
of their own nature, and in fact they are." We have been more particular
in extracting these passages, because it has been advanced by a writer
of high reputation, that the treatment which Galileo subsequently
experienced was solely in consequence of his persisting in the endeavour
to prove that the Scriptures were reconcileable with the Copernican
theory[74], whereas we see here distinctly that, for the reasons we have
briefly stated, he regarded this as a matter altogether indifferent and
beside the question.

Galileo had not entered upon this discussion till driven to it by a most
indecent attack, made on him from the pulpit, by a Dominican friar named
Caccini, who thought it not unbecoming his habit or religion to play
upon the words of a Scriptural text for the purpose of attacking Galileo
and his partisans with more personality.[75] Galileo complained formally
of Caccini's conduct to Luigi Maraffi the general of the Dominicans, who
apologised amply to him, adding that he himself was to be pitied for
finding himself implicated in all the brutal conduct of thirty or forty
thousand monks.

In the mean time, the inquisitors at Rome had taken the alarm, and were
already, in 1615, busily employed in collecting evidence against
Galileo. Lorini, a brother Dominican of Caccini, had given them notice
of the letter to Castelli of which we have spoken, and the utmost
address was employed to get the original into their hands, which attempt
however was frustrated, as Castelli had returned it to the writer.
Caccini was sent for to Rome, settled there with the title of Master of
the Convent of St. Mary of Minerva, and employed to put the depositions
against Galileo into order. Galileo was not at this time fully aware of
the machinations against him, but suspecting something of their nature,
he solicited and obtained permission from Cosmo, towards the end of
1615, to make a journey to Rome, for the purpose of more directly
confronting his enemies in that city. There was a rumour at the time
that this visit was not voluntary, but that Galileo had been cited to
appear at Rome. A contemporary declares that he heard this from Galileo
himself: at any rate, in a letter which Galileo shortly afterwards wrote
to Picchena, the Grand Duke's secretary, he expresses himself well
satisfied with the results of this step, whether forced or not, and
Querenghi thus describes to the Cardinal d'Este the public effect of his
appearance: "Your Eminence would be delighted with Galileo if you heard
him holding forth, as he often does, in the midst of fifteen or twenty,
all violently attacking him, sometimes in one house, sometimes in
another. But he is armed after such fashion that he laughs all of them
to scorn--and even if the novelty of his opinions prevents entire
persuasion, at least he convicts of emptiness most of the arguments with
which his adversaries endeavour to overwhelm him. He was particularly
admirable on Monday last, in the house of Signor Frederico Ghisilieri;
and what especially pleased me was, that before replying to the contrary
arguments, he amplified and enforced them with new grounds of great
plausibility, so as to leave his adversaries in a more ridiculous plight
when he afterwards overturned them all."

Among the malicious stories which were put into circulation, it had been
said, that the Grand Duke had withdrawn his favour, which emboldened
many, who would not otherwise have ventured on such open opposition, to
declare against Galileo. His appearance at Rome, where he was lodged in
the palace of Cosmo's ambassador, and whence he kept up a close
correspondence with the Grand Duke's family, put an immediate stop to
rumours of this kind. In little more than a month he was apparently
triumphant, so far as regarded himself; but the question now began to be
agitated whether the whole system of Copernicus ought not to be
condemned as impious and heretical. Galileo again writes to Picchena,
"so far as concerns the clearing of my own character, I might return
home immediately; but although this new question regards me no more than
all those who for the last eighty years have supported these opinions
both in public and private, yet, as perhaps I may be of some assistance
in that part of the discussion which depends on the knowledge of truths
ascertained by means of the sciences which I profess, I, as a zealous
and Catholic Christian, neither can nor ought to withhold that
assistance which my knowledge affords; and this business keeps me
sufficiently employed." De Lambre, whose readiness to depreciate
Galileo's merit we have already noticed and lamented, sneeringly and
ungratefully remarks on this part of his life, that "it was scarcely
worth while to compromise his tranquillity and reputation, in order to
become the champion of a truth which could not fail every day to acquire
new partisans by the natural effect of the progress of enlightened
opinions." We need not stop to consider what the natural effects might
have been if none had at any time been found who thought their
tranquillity worthily offered up in such a cause.

It has been hinted by several, and is indeed probable, that Galileo's
stay at Rome rather injured the cause (so far as provoking the
inquisitorial censures could injure it) which it was his earnest desire
to serve, for we cannot often enough repeat the assertion, that it was
not the doctrine itself, so much as the free, unyielding manner in which
it was supported, which was originally obnoxious. Copernicus had been
allowed to dedicate his great work to Pope Paul III., and from the time
of its first appearance under that sanction in 1543, to the year 1616,
of which we are now writing, this theory was left in the hands of
mathematicians and philosophers, who alternately attacked and defended
it without receiving either support or molestation from ecclesiastical
decrees. But this was henceforward no longer the case, and a higher
degree of importance was given to the controversy from the religious
heresies which were asserted to be involved in the new opinions. We have
already given specimens of the so called philosophical arguments brought
against Copernicus; and the reader may be curious to know the form of
the theological ones. Those which we select are taken from a work, which
indeed did not come forth till the time of Galileo's third visit to
Rome, but it is relative to the matter now before us, as it professed to
be, and its author's party affected to consider it, a complete
refutation of the letters to Castelli and the Archduchess Christina.[76]

It was the work of a Jesuit, Melchior Inchoffer, and it was greatly
extolled by his companions, "as differing so entirely from the pruriency
of the Pythagorean writings." He quotes with approbation an author who,
first referring to the first verse of Genesis for an argument that the
earth was not created till after the heavens, observes that the whole
question is thus reduced to the examination of this purely geometrical
difficulty--In the formation of a sphere, does the centre or
circumference first come into existence? If the latter (which we presume
Melchior's friend found good reason for deciding upon), the consequence
is inevitable. The earth is in the centre of the universe.

It may not be unprofitable to contrast the extracts which we have given
from Galileo's letters on the same subject with the following passage,
which appears one of the most subtle and argumentative which is to be
found in Melchior's book. He _professes_ to be enumerating and refuting
the principal arguments which the Copernicans adduced for the motion of
the earth. "Fifth argument. Hell is in the centre of the earth, and in
it is a fire tormenting the damned; therefore it is absolutely necessary
that the earth is moveable. The antecedent is plain." (Inchoffer then
quotes a number of texts of Scripture on which, according to him, the
Copernicans relied in proof of this part of the argument.) "The
consequent is proved: because fire is the cause of motion, for which
reason Pythagoras, who, as Aristotle reports, puts the place of
punishment in the centre, perceived that the earth is animate and
endowed with action. I answer, even allowing that hell is in the centre
of the earth, and a fire in it, I deny the consequence: and for proof I
say, if the argument is worth any thing, it proves also that lime-kilns,
ovens, and fire-grates are animated and spontaneously moveable. I say,
_even allowing_ that hell is in the centre of the earth: for Gregory,
book 4, dial. chap. 42, says, that he dare not decide rashly on this
matter, although he thinks more probable the opinion of those who say
that it is under the earth. St. Thomas, in Opusc. 10, art. 31, says:
Where hell is, whether in the centre of the earth or at the surface,
does not in my opinion, relate to any article of faith; and it is
superfluous to be solicitous about such things, either in asserting or
denying them. And Opusc. 11, art. 24, he says, that it seems to him that
nothing should be rashly asserted on this matter, particularly as
Augustin thinks that nobody knows where it is; but I do not, says he,
think that it is in the centre of the earth. I should be loth, however,
that it should be hence inferred by _some people_ that hell is in the
earth, that we are ignorant where hell is, and therefore that the
situation of the earth is also unknown, and, in conclusion, that it
cannot therefore be the centre of the universe. The argument shall be
retorted in another fashion: for if the place of the earth is unknown,
it cannot be said to be in a great circle, so as to be moved round the
sun. Finally I say that in fact it is known where the earth is."

It is not impossible that some persons adopted the Copernican theory,
from an affectation of singularity and freethinking, without being able
to give very sound reasons for their change of opinion, of whom we have
an instance in Origanus, the astrological instructor of Wallenstein's
famous attendant Seni, who edited his work. His arguments in favour of
the earth's motion are quite on a level with those advanced on the
opposite side in favour of its immobility; but we have not found any
traces whatever of such absurdities as these having been urged by any of
the leaders of that party, and it is far more probable that they are the
creatures of Melchior's own imagination. At any rate it is worth
remarking how completely he disregards the real physical arguments,
which he ought, in justice to his cause, to have attempted to
controvert. His book was aimed at Galileo and his adherents, and it is
scarcely possible that he could seriously persuade himself that he was
stating and overturning arguments similar to those by which Galileo had
made so many converts to the opinions of Copernicus. Whatever may be our
judgment of his candour, we may at least feel assured that if this had
indeed been a fair specimen of Galileo's philosophy, he might to the end
of his life have taught that the earth moved round the sun, or if his
fancy led him to a different hypothesis, he might like the Abbé Baliani
have sent the earth spinning round the stationary moon, and like him
have remained unmolested by pontifical censures. It is true that Baliani
owned his opinion to be much shaken, on observing it to be opposed to
the decree of those in whose hands was placed the power of judging
articles of faith. But Galileo's uncompromising spirit of analytical
investigation, and the sober but invincible force of reasoning with
which he beat down every sophism opposed to him, the instruments with
which he worked, were more odious than the work itself, and the
condemnation which he had vainly hoped to avert was probably on his very
account accelerated.

Galileo, according to his own story, had in March 1616 a most gracious
audience of the pope, Paul V., which lasted for nearly an hour, at the
end of which his holiness assured him, that the Congregation were no
longer in a humour to listen lightly to calumnies against him, and that
so long as he occupied the papal chair, Galileo might think himself out
of all danger. But nevertheless he was not allowed to return home,
without receiving formal notice not to teach the opinions of
Copernicus, that the sun is in the centre of the system, and that the
earth moves about it, from that time forward, in any manner. That these
were the literal orders given to Galileo will be presently proved from
the recital of them in the famous decree against him, seventeen years
later. For the present, his letters which we have mentioned, as well as
one of a similar tendency by Foscarini, a Carmelite friar--a commentary
on the book of Joshua by a Spaniard named Diego Zuniga--Kepler's Epitome
of the Copernican Theory--and Copernicus's own work, were inserted in
the list of forbidden books, nor was it till four years afterwards, in
1620, that, on reconsideration, Copernicus was allowed to be read with
certain omissions and alterations then decided upon.

Galileo quitted Rome scarcely able to conceal his contempt and
indignation. Two years afterwards this spirit had but little subsided,
for in forwarding to the Archduke Leopold his Theory of the Tides, he
accompanied it with the following remarks:--"This theory occurred to me
when in Rome, whilst the theologians were debating on the prohibition of
Copernicus's book, and of the opinion maintained in it of the motion of
the earth, which I at that time believed; until it pleased those
gentlemen to suspend the book, and declare the opinion false and
repugnant to the Holy Scriptures. Now, as I know how well it becomes me
to obey and believe the decisions of my superiors, which proceed out of
more profound knowledge than the weakness of my intellect can attain to,
this theory which I send you, which is founded on the motion of the
earth, I now look upon as a fiction and a dream, and beg your highness
to receive it as such. But, as poets often learn to prize the creations
of their fancy, so, in like manner, do I set some value on this
absurdity of mine. It is true that when I sketched this little work, I
did hope that Copernicus would not, after 80 years, be convicted of
error, and I had intended to develope and amplify it farther, but a
voice from heaven suddenly awakened me, and at once annihilated all my
confused and entangled fancies."

It might have been predicted, from the tone of this letter alone, that
it would not be long before Galileo would again bring himself under the
censuring notice of the astronomical hierarchy, and indeed he had, so
early as 1610, collected some of the materials for the work which caused
the final explosion, and on which he now employed himself with as little
intermission as the weak state of his health permitted.

He had been before this time engaged in a correspondence with the court
of Spain, on the method of observing longitudes at sea, for the solution
of which important problem Philip III. had offered a considerable
reward, an example which has since been followed in our own and other
countries. Galileo had no sooner discovered Jupiter's satellites, than
he recognized the use which might be made of them for that purpose, and
devoted himself with peculiar assiduity to acquiring as perfect a
knowledge as possible of their revolutions. The reader will easily
understand how they were to be used, if their motion could be so well
ascertained as to enable Galileo at Florence to predict the exact times
at which any remarkable configurations would occur, as, for instance,
the times at which any one of them would be eclipsed by Jupiter. A
mariner who in the middle of the Atlantic should observe the same
eclipse, and compare the time of night at which he made the observation
(which he might know by setting his watch by the sun on the preceding
day) with the time mentioned in the predictions, would, from the
difference between the two, learn the difference between the hour at
Florence and the hour at the place where the ship at that time happened
to be. As the earth turns uniformly round through 360° of longitude in
24 hours, that is, through 15° in each hour, the hours, minutes, and
seconds of time which express this difference must be multiplied by 15,
and the respective products will give the degrees, minutes, and seconds
of longitude, by which the ship was then distant from Florence. This
statement is merely intended to give those who are unacquainted with
astronomy, a general idea of the manner in which it was proposed to use
these satellites. Our moon had already been occasionally employed in the
same way, but the comparative frequency of the eclipses of Jupiter's
moons, and the suddenness with which they disappear, gives a decided
advantage to the new method. Both methods were embarrassed by the
difficulty of observing the eclipses at sea. In addition to this, it was
requisite, in both methods, that the sailors should be provided with
accurate means of knowing the hour, wherever they might chance to be,
which was far from being the case, for although (in order not to
interrupt the explanation) we have above spoken of their _watches_, yet
the watches and clocks of that day were not such as could be relied on
sufficiently, during the interval which must necessarily occur between
the two observations. This consideration led Galileo to reflect on the
use which might be made of his pendulum for this purpose; and, with
respect to the other difficulty, he contrived a peculiar kind of
telescope, with which he flattered himself, somewhat prematurely, that
it would be as easy to observe on ship-board as on shore.

During his stay at Rome, in 1615, and the following year, he disclosed
some of these ideas to the Conte di Lemos, the viceroy of Naples, who
had been president of the council of the Spanish Indies, and was fully
aware of the importance of the matter. Galileo was in consequence
invited to communicate directly with the Duke of Lerma, the Spanish
minister, and instructions were accordingly sent by Cosmo, to the Conte
Orso d'Elci, his ambassador at Madrid, to conduct the business there.
Galileo entered warmly into the design, of which he had no other means
of verifying the practicability; for as he says in one of his letters to
Spain--"Your excellency may well believe that if this were an
undertaking which I could conclude by myself, I would never have gone
about begging favours from others; but in my study there are neither
seas, nor Indies, nor islands, nor ports, nor shoals, nor ships, for
which reason I am compelled to share the enterprise with great
personages, and to fatigue myself to procure the acceptance of that,
which ought with eagerness to be asked of me; but I console myself with
the reflection that I am not singular in this, but that it commonly
happens, with the exception of a little reputation, and that too often
obscured and blackened by envy, that the least part of the advantage
falls to the share of the inventors of things, which afterwards bring
great gain, honours, and riches to others; so that I will never cease on
my part to do every thing in my power, and I am ready to leave here all
my comforts, my country, my friends, and family, and to cross over into
Spain, to stay as long as I may be wanted in Seville, or Lisbon, or
wherever it may be convenient, to implant the knowledge of this method,
provided that due assistance and diligence be not wanting on the part of
those who are to receive it, and who should solicit and foster it." But
he could not, with all his enthusiasm, rouse the attention of the
Spanish court. The negotiation languished, and although occasionally
renewed during the next ten or twelve years, was never brought to a
satisfactory issue. Some explanation of this otherwise unaccountable
apathy of the Spanish court, with regard to the solution of a problem
which they had certainly much at heart, is given in Nelli's life of
Galileo; where it is asserted, on the authority of the Florentine
records, that Cosmo required privately from Spain, (in return for the
permission granted for Galileo to leave Florence, in pursuance of this
design,) the privilege of sending every year from Leghorn two
merchantmen, duty free, to the Spanish Indies.


FOOTNOTES:

[74] Ce philosophe (Galilée) ne fut point persecuté comme bon astronome,
mais comme mauvais théologien. C'est son entêtement à vouloir concilier
la Bible avec Copernic qui lui donna des juges. Mais vingt auteurs,
surtout parmi les protestans, ont écrit que Galilée fut persecuté et
imprisonné pour avoir soutenu que la terre tourne autour du soleil, que
ce système a été condanné par l'inquisition comme faux, erroné et
contraire à la Bible, &c.--Bergier, Encyclopédie Méthodique, Paris,
1790, Art. SCIENCES HUMAINES.

[75] Viri Galilæi, quid statis adspicientes in coelum. _Acts_ I. 11.

[76] Tractatus Syllepticus. Romæ, 1633. The title-page of this
remarkable production is decorated with an emblematical figure,
representing the earth included in a triangle; and in the three corners,
grasping the globe with their fore feet, are placed three bees, the arms
of Pope Urban VIII. who condemned Galileo and his writings. The motto is
"_His fixa quiescit_," "Fixed by these it is at rest."




CHAPTER XII.

    _Controversy on Comets--Saggiatore--Galileo's reception by Urban
      VIII--His family._


THE year 1618 was remarkable for the appearance of three comets, on
which almost every astronomer in Europe found something to say and
write. Galileo published some of his opinions with respect to them,
through the medium of Mario Guiducci. This astronomer delivered a
lecture before the Florentine academy, the heads of which he was
supposed to have received from Galileo, who, during the whole time of
the appearance of these comets, was confined to his bed by severe
illness. This essay was printed in Florence _at the sign of The Medicean
Stars_.[77] What principally deserves notice in it, is the opinion of
Galileo, that the distance of a comet cannot be safely determined by its
parallax, from which we learn that he inclined to believe that comets
are nothing but meteors occasionally appearing in the atmosphere, like
rainbows, parhelia, and similar phenomena. He points out the difference
in this respect between a fixed object, the distance of which may be
calculated from the difference of direction in which two observers (at a
known distance from each other) are obliged to turn themselves in order
to see it, and meteors like the rainbow, which are simultaneously formed
in different drops of water for each spectator, so that two observers
in different places are in fact contemplating different objects. He then
warns astronomers not to engage with too much warmth in a discussion on
the distance of comets before they assure themselves to which of these
two classes of phenomena they are to be referred. The remark is in
itself perfectly just, although the opinion which occasioned it is now
as certainly known to be erroneous, but it is questionable whether the
observations which, up to that time, had been made upon comets, were
sufficient, either in number or quality, to justify the censure which
has been cast on Galileo for his opinion. The theory, moreover, is
merely introduced as an hypothesis in Guiducci's essay. The same opinion
was for a short time embraced by Cassini, a celebrated Italian
astronomer, invited by Louis XIV. to the Observatory at Paris, when the
science was considerably more advanced, and Newton, in his _Principia_,
did not think it unworthy of him to show on what grounds it is
untenable.

Galileo was become the object of animosity in so many quarters that none
of his published opinions, whether correct or incorrect, ever wanted a
ready antagonist. The champion on the present occasion was again a
Jesuit; his name was Oratio Grassi, who published _The Astronomical and
Philosophical Balance_, under the disguised signature of Lotario Sarsi.

Galileo and his friends were anxious that his reply to Grassi should
appear as quickly as possible, but his health had become so precarious
and his frequent illnesses occasioned so many interruptions, that it was
not until the autumn of 1623 that Il Saggiatore (or The Assayer) as he
called his answer, was ready for publication. This was printed by the
Lyncean Academy, and as Cardinal Maffeo Barberino, who had just been
elected Pope, (with the title of Urban VIII.) had been closely connected
with that society, and was also a personal friend of Cesi and of
Galileo, it was thought a prudent precaution to dedicate the pamphlet to
him. This essay enjoys a peculiar reputation among Galileo's works, not
only for the matter contained in it, but also for the style in which it
is written; insomuch that Andrès[78], when eulogizing Galileo as one of
the earliest who adorned philosophical truths with the graces and
ornaments of language, expressly instances the Saggiatore, which is also
quoted by Frisi and Algarotti, as a perfect model of this sort of
composition. In the latter particular, it is unsafe to interfere with
the decisions of an Italian critic; but with respect to its substance,
this famous composition scarcely appears to deserve its preeminent
reputation. It is a prolix and rather tedious examination of Grassi's
Essay; nor do the arguments seem so satisfactory, nor the reasonings so
compact as is generally the case in Galileo's other writings. It does
however, like all his other works, contain many very remarkable
passages, and the celebrity of this production requires that we should
extract one or two of the most characteristic.

The first, though a very short one, will serve to shew the tone which
Galileo had taken with respect to the Copernican system since its
condemnation at Rome, in 1616. "In conclusion, since the motion
attributed to the earth, which I, as a pious and Catholic person,
consider most false, and not to exist, accommodates itself so well to
explain so many and such different phenomena, I shall not feel sure,
unless Sarsi descends to more distinct considerations than those which
he has yet produced, that, false as it is, it may not just as deludingly
correspond with the phenomena of comets."

Sarsi had quoted a story from Suidas in support of his argument that
motion always produces heat, how the Babylonians used to cook their eggs
by whirling them in a sling; to which Galileo replies: "I cannot refrain
from marvelling that Sarsi will persist in proving to me, by
authorities, that which at any moment I can bring to the test of
experiment. We examine witnesses in things which are doubtful, past, and
not permanent, but not in those things which are done in our own
presence. If discussing a difficult problem were like carrying a weight,
since several horses will carry more sacks of corn than one alone will,
I would agree that many reasoners avail more than one; but _discoursing_
is like _coursing_, and not like carrying, and one barb by himself will
run farther than a hundred Friesland horses. When Sarsi brings up such a
multitude of authors, it does not seem to me that he in the least degree
strengthens his own conclusions, but he ennobles the cause of Signor
Mario and myself, by shewing that we reason better than many men of
established reputation. If Sarsi insists that I believe, on Suidas'
credit, that the Babylonians cooked eggs by swiftly whirling them in a
sling, I will believe it; but I must needs say, that the cause of such
an effect is very remote from that to which it is attributed, and to
find the true cause I shall reason thus. If an effect does not follow
with us which followed with others at another time, it is because, in
our experiment, something is wanting which was the cause of the former
success; and if only one thing is wanting to us, that one thing is the
true cause. Now we have eggs, and slings, and strong men to whirl them,
and yet they will not become cooked; nay, if they were hot at first,
they more quickly become cold: and since nothing is wanting to us but to
be Babylonians, it follows that being Babylonians is the true cause why
the eggs became hard, and not the friction of the air, which is what I
wished to prove.--Is it possible that in travelling post, Sarsi has
never noticed what freshness is occasioned on the face by the continual
change of air? and if he has felt it, will he rather trust the relation
by others, of what was done two thousand years ago at Babylon, than what
he can at this moment verify in his own person? I at least will not be
so wilfully wrong, and so ungrateful to nature and to God, that having
been gifted with sense and language, I should voluntarily set less value
on such great endowments than on the fallacies of a fellow man, and
blindly and blunderingly believe whatever I hear, and barter the freedom
of my intellect for slavery to one as liable to error as myself."

Our final extract shall exhibit a sample of Galileo's metaphysics, in
which may be observed the germ of a theory very closely allied to that
which was afterwards developed by Locke and Berkeley.--"I have now only
to fulfil my promise of declaring my opinions on the proposition that
motion is the cause of heat, and to explain in what manner it appears to
me that it may be true. But I must first make some remarks on that which
we call heat, since I strongly suspect that a notion of it prevails
which is very remote from the truth; for it is believed that there is a
true accident, affection, and quality, really inherent in the substance
by which we feel ourselves heated. This much I have to say, that so soon
as I conceive a material or corporeal substance, I simultaneously feel
the necessity of conceiving that it has its boundaries, and is of some
shape or other; that, relatively to others, it is great or small; that
it is in this or that place, in this or that time; that it is in motion,
or at rest; that it touches, or does not touch another body; that it is
unique, rare, or common; nor can I, by any act of the imagination,
disjoin it from these qualities: but I do not find myself absolutely
compelled to apprehend it as necessarily accompanied by such conditions,
as that it must be white or red, bitter or sweet, sonorous or silent,
smelling sweetly or disagreeably; and if the senses had not pointed out
these qualities, it is probable that language and imagination alone
could never have arrived at them. Because, I am inclined to think that
these tastes, smells, colours, &c., with regard to the subject in which
they appear to reside, are nothing more than mere names, and exist only
in the sensitive body; insomuch that, when the living creature is
removed, all these qualities are carried off and annihilated; although
we have imposed particular names upon them, and different from those of
the other first and real accidents, and would fain persuade ourselves
that they are truly and in fact distinct. But I do not believe that
there exists any thing in external bodies for exciting tastes, smells,
and sounds, but size, shape, quantity, and motion, swift or slow; and if
ears, tongues, and noses were removed, I am of opinion that shape,
number, and motion would remain, but there would be an end of smells,
tastes, and sounds, which, abstractedly from the living creature, I take
to be mere words."

In the spring following the publication of the "Saggiatore," that is to
say, about the time of Easter, in 1624, Galileo went a third time to
Rome to compliment Urban on his elevation to the pontifical chair. He
was obliged to make this journey in a litter; and it appears from his
letters that for some years he had been seldom able to bear any other
mode of conveyance. In such a state of health it seems unlikely that he
would have quitted home on a mere visit of ceremony, which suspicion is
strengthened by the beginning of a letter from him to Prince Cesi, dated
in October, 1623, in which he says: "I have received the very courteous
and prudent advice of your excellency about the time and manner of my
going to Rome, and shall act upon it; and I will visit you at Acqua
Sparta, that I may be completely informed of the actual state of things
at Rome." However this may be, nothing could be more gratifying than his
public reception there. His stay in Rome did not exceed two months,
(from the beginning of April till June,) and during that time he was
admitted to six long and satisfactory interviews with the Pope, and on
his departure received the promise of a pension for his son Vincenzo,
and was himself presented with "a fine painting, two medals, one of gold
and the other of silver, and a good quantity of agnus dei." He had also
much communication with several of the cardinals, one of whom, Cardinal
Hohenzoller, told him that he had represented to the pope on the subject
of Copernicus, that "all the heretics were of that opinion, and
considered it as undoubted; and that it would be necessary to be very
circumspect in coming to any resolution: to which his holiness replied,
that the church had not condemned it, nor was it to be condemned as
heretical, but only as rash; adding, that there was no fear of any one
undertaking to prove that it must necessarily be true." Urban also
addressed a letter to Ferdinand, who had succeeded his father Cosmo as
Grand Duke of Tuscany, expressly for the purpose of recommending Galileo
to him. "For We find in him not only literary distinction, but also the
love of piety, and he is strong in those qualities by which pontifical
good-will is easily obtained. And now, when he has been brought to this
city to congratulate Us on Our elevation, We have very lovingly embraced
him;--nor can We suffer him to return to the country whither your
liberality recalls him without an ample provision of pontifical love.
And that you may know how dear he is to Us, We have willed to give him
this honourable testimonial of virtue and piety. And We further signify
that every benefit which you shall confer upon him, imitating, or even
surpassing your father's liberality, will conduce to Our gratification."
Honoured with these unequivocal marks of approbation, Galileo returned
to Florence.

His son Vincenzo is soon afterwards spoken of as being at Rome; and it
is not improbable that Galileo sent him thither on the appointment of
his friend and pupil, the Abbé Castelli, to be mathematician to the
pope. Vincenzo had been legitimated by an edict of Cosmo in 1619, and,
according to Nelli, married, in 1624, Sestilia, the daughter of Carlo
Bocchineri. There are no traces to be found of Vincenzo's mother after
1610, and perhaps she died about that time. Galileo's family by her
consisted of Vincenzo and two daughters, Julia and Polissena, who both
took the veil in the convent of Saint Matthew at Arcetri, under the
names of Sister Arcangiola and Sister Maria Celeste. The latter is said
to have possessed extraordinary talents. The date of Vincenzo's
marriage, as given by Nelli, appears somewhat inconsistent with the
correspondence between Galileo and Castelli, in which, so late as 1629,
Galileo is apparently writing of his son as a student under Castelli's
superintendence, and intimates the amount of pocket-money he can afford
to allow him, which he fixes at three crowns a month; adding, that "he
ought to be contented with as many crowns, as, at his age, I possessed
groats." Castelli had given but an unfavourable account of Vincenzo's
conduct, characterizing him as "dissolute, obstinate, and impudent;" in
consequence of which behaviour, Galileo seems to have thought that the
pension of sixty crowns, which had been granted by the pope, might be
turned to better account than by employing it on his son's education;
and accordingly in his reply he requested Castelli to dispose of it,
observing that the proceeds would be useful in assisting him to
discharge a great load of debt with which he found himself saddled on
account of his brother's family. Besides this pension, another of one
hundred crowns was in a few years granted by Urban to Galileo himself,
but it appears to have been very irregularly paid, if at all.

About the same time Galileo found himself menaced either with the
deprivation of his stipend as extraordinary professor at Pisa, or with
the loss of that leisure which, on his removal to Florence, he had been
so anxious to secure. In 1629, the question was agitated by the party
opposed to him, whether it were in the power of the grand duke to assign
a pension out of the funds of the University, arising out of
ecclesiastical dues, to one who neither lectured nor resided there. This
scruple had slept during nineteen years which had elapsed since
Galileo's establishment in Florence, but probably those who now raised
it reckoned upon finding in Ferdinand II., then scarcely of age, a less
firm supporter of Galileo than his father Cosmo had been. But the matter
did not proceed so far; for, after full deliberation, the prevalent
opinion of the theologians and jurists who were consulted appeared to be
in favour of this exercise of prerogative, and accordingly Galileo
retained his stipend and privileges.


FOOTNOTES:

[77] In Firenze nella Stamperia di Pietro Cecconcelli alle stelle
Medicee, 1619.

[78] Dell'Origine d'ogni Literatura: Parma, 1787.




CHAPTER XIII.

    _Publication of Galileo's 'System of the World'--His Condemnation
      and Abjuration._


IN the year 1630, Galileo brought to its conclusion his great work, "The
Dialogue on the Ptolemaic and Copernican Systems," and began to take the
necessary steps for procuring permission to print it. This was to be
obtained in the first instance from an officer at Rome, entitled the
master of the sacred palace; and after a little negotiation Galileo
found it would be necessary for him again to return thither, as his
enemies were still busy in thwarting his views and wishes. Niccolo
Riccardi, who at that time filled the office of master of the palace,
had been a pupil of Galileo, and was well disposed to facilitate his
plans; he pointed out, however, some expressions in the work which he
thought it necessary to erase, and, with the understanding that this
should be done, he returned the manuscript to Galileo with his
subscribed approbation. The unhealthy season was drawing near, and
Galileo, unwilling to face it, returned home, where he intended to
complete the index and dedication, and then to send it back to Rome to
be printed in that city, under the superintendence of Federigo Cesi.
This plan was disconcerted by the premature death of that accomplished
nobleman, in August 1630, in whom Galileo lost one of his steadiest and
most effective friends and protectors. This unfortunate event determined
Galileo to attempt to procure permission to print his book at Florence.
A contagious disorder had broken out in Tuscany with such severity as
almost to interrupt all communication between Florence and Rome, and
this was urged by Galileo as an additional reason for granting his
request. Riccardi at first seemed inclined to insist that the book
should be sent to him a second time, but at last contented himself with
inspecting the commencement and conclusion, and consented that (on its
receiving also a license from the inquisitor-general at Florence, and
from one or two others whose names appear on the title-page) it might be
printed where Galileo wished.

These protracted negotiations prevented the publication of the work till
late in 1632; it then appeared, with a dedication to Ferdinand, under
the following title:--"A Dialogue, by Galileo Galilei, Extraordinary
Mathematician of the University of Pisa, and Principal Philosopher and
Mathematician of the Most Serene Grand Duke of Tuscany; in which, in a
conversation of four days, are discussed the two principal Systems of
the World, the Ptolemaic and Copernican, indeterminately proposing the
Philosophical Arguments as well on one side as on the other." The
beginning of the introduction, which is addressed "To the discreet
Reader," is much too characteristic to be passed by without
notice.--"Some years ago, a salutary edict was promulgated at Rome,
which, in order to obviate the perilous scandals of the present age,
enjoined an opportune silence on the Pythagorean opinion of the earth's
motion. Some were not wanting, who rashly asserted that this decree
originated, not in a judicious examination, but in ill informed passion;
and complaints were heard that counsellors totally inexperienced in
astronomical observations ought not by hasty prohibitions to clip the
wings of speculative minds. My zeal could not keep silence when I heard
these rash lamentations, and I thought it proper, as being fully
informed with regard to that most prudent determination, to appear
publicly on the theatre of the world as a witness of the actual truth. I
happened at that time to be in Rome: I was admitted to the audiences,
and enjoyed the approbation of the most eminent prelates of that court,
nor did the publication of that decree occur without my receiving some
prior intimation of it.[79] Wherefore it is my intention in this present
work, to show to foreign nations that as much is known of this matter in
Italy, and particularly in Rome, as ultramontane diligence can ever have
formed any notion of, and collecting together all my own speculations on
the Copernican system, to give them to understand that the knowledge of
all these preceded the Roman censures, and that from this country
proceed not only dogmas for the salvation of the soul, but also
ingenious discoveries for the gratification of the understanding. With
this object, I have taken up in the Dialogue the Copernican side of the
question, treating it as a pure mathematical hypothesis; and
endeavouring in every artificial manner to represent it as having the
advantage, not over the opinion of the stability of the earth
absolutely, but according to the manner in which that opinion is
defended by some, who indeed profess to be Peripatetics, but retain only
the name, and are contented without improvement to worship shadows, not
philosophizing with their own reason, but only from the recollection of
four principles imperfectly understood."--This very flimsy veil could
scarcely blind any one as to Galileo's real views in composing this
work, nor does it seem probable that he framed it with any expectation
of appearing neutral in the discussion. It is more likely that he
flattered himself that, under the new government at Rome, he was not
likely to be molested on account of the personal prohibition which he
had received in 1616, "not to believe or teach the motion of the earth
in any manner," provided he kept himself within the letter of the limits
of the more public and general order, that the Copernican system was not
to be brought forward otherwise than as a mere mathematically
convenient, but in fact unreal supposition. So long as this decree
remained in force, a due regard to consistency would compel the Roman
Inquisitors to notice an unequivocal violation of it; and this is
probably what Urban had implied in the remark quoted by Hohenzoller to
Galileo.[80] There were not wanting circumstances which might compensate
for the loss of Cosmo and of Federigo Cesi; Cosmo had been succeeded by
his son, who, though he had not yet attained his father's energy, showed
himself as friendly as possible to Galileo. Cardinal Bellarmine, who had
been mainly instrumental in procuring the decree of 1616, was dead;
Urban on the contrary, who had been among the few Cardinals who then
opposed it as uncalled for and ill-advised, was now possessed of supreme
power, and his recent affability seemed to prove that the increased
difference in their stations had not caused him to forget their early
and long-continued intimacy. It is probable that Galileo would not have
found himself mistaken in this estimate of his position, but for an
unlucky circumstance, of which his enemies immediately saw the
importance, and which they were not slow in making available against
him. The dialogue of Galileo's work is conducted between three
personages;--Salviati and Sagredo, who were two noblemen, friends of
Galileo, and Simplicio, a name borrowed from a noted commentator upon
Aristotle, who wrote in the sixth century. Salviati is the principal
philosopher of the work; it is to him that the others apply for
solutions of their doubts and difficulties, and on him the principal
task falls of explaining the tenets of the Copernican theory. Sagredo is
only a half convert, but an acute and ingenious one; to him are allotted
the objections which seem to have some real difficulty in them, as well
as lively illustrations and digressions, which might have been thought
inconsistent with the gravity of Salviati's character. Simplicio, though
candid and modest, is of course a confirmed Ptolemaist and Aristotelian,
and is made to produce successively all the popular arguments of that
school in support of his master's system. Placed between the wit and the
philosopher, it may be guessed that his success is very indifferent, and
in fact he is alternately ridiculed and confuted at every turn. As
Galileo racked his memory and invention to leave unanswered no argument
which was or could be advanced against Copernicus, it unfortunately
happened, that he introduced some which Urban himself had urged upon him
in their former controversies on this subject; and Galileo's opponents
found means to make His Holiness believe that the character of Simplicio
had been sketched in personal derision of him. We do not think it
necessary to exonerate Galileo from this charge; the obvious folly of
such an useless piece of ingratitude speaks sufficiently for itself. But
self-love is easily irritated; and Urban, who aspired to a reputation
for literature and science, was peculiarly sensitive on this point. His
own expressions almost prove his belief that such had been Galileo's
design, and it seems to explain the otherwise inexplicable change which
took place in his conduct towards his old friend, on account of a book
which he had himself undertaken to examine, and of which he had
authorised the publication.

One of the earliest notices of what was approaching, is found in the
dispatches, dated August 24, 1632, from Ferdinand's minister, Andrea
Cioli, to Francesco Nicolini, the Tuscan ambassador at the court of
Rome.

"I have orders to signify to Your Excellency that His Highness remains
greatly astonished that a book, placed by the author himself in the
hands of the supreme authority in Rome, read and read again there most
attentively, and in which every thing, not only with the consent, but at
the request of the author, was amended, altered, added, or removed at
the will of his superiors, which was again subjected here to the same
examination, agreeably to orders from Rome, and which finally was
licensed both there and here, and here printed and published, should now
become an object of suspicion at the end of two years, and the author
and printer be prohibited from publishing any more."--In the sequel is
intimated Ferdinand's desire that the charges, of whatever nature they
might be, either against Galileo or his book, might be reduced to
writing and forwarded to Florence, that he might prepare for his
justification; but this reasonable demand was utterly disregarded. It
appears to have been owing to the mean subserviency of Cioli to the
court of Rome, that Ferdinand refrained from interfering more
strenuously to protect Galileo. Cioli's words are: "The Grand Duke is so
enraged with this business of Galileo, that I do not know what will be
done. I know, at least, that His Holiness shall have no reason to
complain of his ministers, or of their bad advice."[81]

A letter from Galileo's Venetian friend Micanzio, dated about a month
later, is in rather a bolder and less formal style:--"The efforts of
your enemies to get your book prohibited will occasion no loss either to
your reputation, or to the intelligent part of the world. As to
posterity, this is just one of the surest ways to hand the book down to
them. But what a wretched set this must be to whom every good thing, and
all that is founded in nature, necessarily appears hostile and odious!
The world is not restricted to a single corner; you will see the book
printed in more places and languages than one; and just for this reason,
I wish they would prohibit all good books. My disgust arises from seeing
myself deprived of what I most desire of this sort, I mean your other
dialogues; and if, from this cause, I fail in having the pleasure of
seeing them, I shall devote to a hundred thousand devils these unnatural
and godless hypocrites."

At the same time, Thomas Campanella, a monk, who had already
distinguished himself by an apology for Galileo (published in 1622),
wrote to him from Rome:--"I learn with the greatest disgust, that a
congregation of angry theologians is forming to condemn your Dialogues,
and that no single member of it has any knowledge of mathematics, or
familiarity with abstruse speculations. I should advise you to procure a
request from the Grand Duke that, among the Dominicans and Jesuits and
Theatins, and secular priests whom they are putting on this congregation
against your book, they should admit also Castelli and myself." It
appears, from subsequent letters both from Campanella and Castelli, that
the required letter was procured and sent to Rome, but it was not
thought prudent to irritate the opposite party by a request which it was
then clearly seen would have been made in vain. Not only were these
friends of Galileo not admitted to the congregation, but, upon some
pretext, Castelli was even sent away from Rome, as if Galileo's enemies
desired to have as few enlightened witnesses as possible of their
proceedings; and on the contrary, Scipio Chiaramonte, who had been long
known for one of the staunchest and most bigoted defenders of the old
system, and who, as Montucla says, seems to have spent a long life in
nothing but retarding, as far as he was able, the progress of discovery,
was summoned from Pisa to complete their number. From this period we
have a tolerably continuous account of the proceedings against Galileo
in the dispatches which Nicolini sent regularly to his court. It appears
from them that Nicolini had several interviews with the Pope, whom he
found highly incensed against Galileo, and in one of the earliest he
received an intimation to advise the Duke "not to engage himself in this
matter as he had done in the other business of Alidosi,[82] because he
would not get through it with honour." Finding Urban in this humour,
Nicolini thought it best to temporize, and to avoid the appearance of
any thing like direct opposition. On the 15th of September, probably as
soon as the first report on Galileo's book had been made, Nicolini
received a private notice from the Pope, "in especial token of the
esteem in which he held the Grand Duke," that he was unable to do less
than consign the work to the consideration of the Inquisition. Nicolini
was permitted to communicate this to the Grand Duke only, and both were
declared liable to "the usual censures" of the Inquisition in case of
divulging the secret.

The next step was to summon Galileo to Rome, and the only answer
returned to all Nicolini's representations of his advanced age of
seventy years, the very infirm state of his health, and the discomforts
which he must necessarily suffer in such a journey, and in keeping
quarantine, was that he might come at leisure, and that the quarantine
should be relaxed as much as possible in his favour, but that it was
indispensably necessary that he should be personally examined before the
Inquisition at Rome. Accordingly, on the 14th of February, 1633,
Nicolini announces Galileo's arrival, and that he had officially
notified his presence to the Assessor and Commissary of the Holy Office.
Cardinal Barberino, Urban's nephew, who seems on the whole to have acted
a friendly part towards Galileo, intimated to him that his most prudent
course would be to keep himself as much at home and as quiet as
possible, and to refuse to see any but his most intimate friends. With
this advice, which was repeated to him from several quarters, Galileo
thought it best to comply, and kept himself entirely secluded in
Nicolini's palace, where he was as usual maintained at the expense of
the Grand Duke. Nelli quotes two letters, which passed between
Ferdinand's minister Cioli and Nicolini, in which the former intimated
that Galileo's expenses were to be defrayed only during the first month
of his residence at Rome. Nicolini returned a spirited answer, that in
that case, after the time specified, he should continue to treat him as
before at his own private cost.

The permission to reside at the ambassador's palace whilst his cause was
pending, was granted and received as an extraordinary indulgence on the
part of the Inquisition, and indeed if we estimate the proceedings
throughout against Galileo by the usual practice of that detestable
tribunal, it will appear that he was treated with unusual consideration.
Even when it became necessary in the course of the inquiry to examine
him in person, which was in the beginning of April, although his removal
to the Holy Office was then insisted upon, yet he was not committed to
close or strictly solitary confinement. On the contrary, he was
honourably lodged in the apartments of the Fiscal of the Inquisition,
where he was allowed the attendance of his own servant, who was also
permitted to sleep in an adjoining room, and to come and go at pleasure.
His table was still furnished by Nicolini. But, notwithstanding the
distinction with which he was thus treated, Galileo was annoyed and
uneasy at being (though little more than nominally) within the walls of
the Inquisition. He became exceedingly anxious that the matter should be
brought to a conclusion, and a severe attack of his constitutional
complaints rendered him still more fretful and impatient. On the last
day of April, about ten days after his first examination, he was
unexpectedly permitted to return to Nicolini's house, although the
proceedings were yet far from being brought to a conclusion. Nicolini
attributes this favour to Cardinal Barberino, who, he says, liberated
Galileo on his own responsibility, in consideration of the enfeebled
state of his health.

In the society of Nicolini and his family, Galileo recovered something
of his courage and ordinary cheerfulness, although his return appears to
have been permitted on express condition of a strict seclusion; for at
the latter end of May, Nicolini was obliged to apply for permission that
Galileo should take that exercise in the open air which was necessary
for his health; on which occasion he was permitted to go into the public
gardens in a half-closed carriage.

On the evening of the 20th of June, rather more than four months after
Galileo's arrival in Rome, he was again summoned to the Holy Office,
whither he went the following morning; he was detained there during the
whole of that day, and on the next day was conducted in a penitential
dress[83] to the Convent of Minerva, where the Cardinals and Prelates,
his judges, were assembled for the purpose of passing judgment upon him,
by which this venerable old man was solemnly called upon to renounce and
abjure, as impious and heretical, the opinions which his whole existence
had been consecrated to form and strengthen. As we are not aware that
this remarkable record of intolerance and bigoted folly has ever been
printed entire in English, we subjoin a literal translation of the whole
sentence and abjuration.


_The Sentence of the Inquisition on Galileo._

    "We, the undersigned, by the Grace of God, Cardinals of the Holy
    Roman Church, Inquisitors General throughout the whole Christian
    Republic, Special Deputies of the Holy Apostolical Chair against
    heretical depravity,

    "Whereas you, Galileo, son of the late Vincenzo Galilei of Florence,
    aged seventy years, were denounced in 1615 to this Holy Office, for
    holding as true a false doctrine taught by many, namely, that the
    sun is immoveable in the centre of the world, and that the earth
    moves, and also with a diurnal motion; also, for having pupils whom
    you instructed in the same opinions; also, for maintaining a
    correspondence on the same with some German mathematicians; also for
    publishing certain letters on the solar spots, in which you
    developed the same doctrine as true; also, for answering the
    objections which were continually produced from the Holy Scriptures,
    by glozing the said Scriptures according to your own meaning; and
    whereas thereupon was produced the copy of a writing, in form of a
    letter, professedly written by you to a person formerly your pupil,
    in which, following the hypotheses of Copernicus, you include
    several propositions contrary to the true sense and authority of the
    Holy Scripture: therefore this holy tribunal being desirous of
    providing against the disorder and mischief which was thence
    proceeding and increasing to the detriment of the holy faith, by the
    desire of His Holiness, and of the Most Eminent Lords Cardinals of
    this supreme and universal Inquisition, the two propositions of the
    stability of the sun, and motion of the earth, were _qualified_ by
    the _Theological Qualifiers_ as follows:

    "_1st. The proposition that the Sun is in the centre of the world
    and immoveable from its place, is absurd, philosophically false, and
    formally heretical; because it is expressly contrary to the Holy
    Scripture._

    "_2dly. The proposition that the Earth is not the centre of the
    world, nor immoveable, but that it moves, and also with a diurnal
    motion, is also absurd, philosophically false, and, theologically
    considered, at least erroneous in faith._

    "But whereas being pleased at that time to deal mildly with you, it
    was decreed in the Holy Congregation, held before His Holiness on
    the 25th day of February, 1616, that His Eminence the Lord Cardinal
    Bellarmine should enjoin you to give up altogether the said false
    doctrine; if you should refuse, that you should be ordered by the
    Commissary of the Holy Office to relinquish it, not to teach it to
    others, nor to defend it, nor ever mention it, and in default of
    acquiescence that you should be imprisoned; and in execution of this
    decree, on the following day at the palace, in presence of His
    Eminence the said Lord Cardinal Bellarmine, after you had been
    mildly admonished by the said Lord Cardinal, you were commanded by
    the acting Commissary of the Holy Office, before a notary and
    witnesses, to relinquish altogether the said false opinion, and in
    future neither to defend nor teach it in any manner, neither
    verbally nor in writing, and upon your promising obedience you were
    dismissed.

    "And in order that so pernicious a doctrine might be altogether
    rooted out, nor insinuate itself farther to the heavy detriment of
    the Catholic truth, a decree emanated from the Holy Congregation of
    the Index[84] prohibiting the books which treat of this doctrine;
    and it was declared false, and altogether contrary to the Holy and
    Divine Scripture.

    "And whereas a book has since appeared, published at Florence last
    year, the title of which shewed that you were the author, which
    title is: _The Dialogue of Galileo Galilei, on the two principal
    systems of the world, the Ptolemaic and Copernican_; and whereas the
    Holy Congregation has heard that, in consequence of the printing of
    the said book, the false opinion of the earth's motion and stability
    of the sun is daily gaining ground; the said book has been taken
    into careful consideration, and in it has been detected a glaring
    violation of the said order, which had been intimated to you;
    inasmuch as in this book you have defended the said opinion,
    already and in your presence condemned; although in the said book
    you labour with many circumlocutions to induce the belief that it is
    left by you undecided, and in express terms probable: which is
    equally a very grave error, since an opinion can in no way be
    probable which has been already declared and finally determined
    contrary to the divine Scripture. Therefore by Our order you have
    been cited to this Holy Office, where, on your examination upon
    oath, you have acknowledged the said book as written and printed by
    you. You also confessed that you began to write the said book ten or
    twelve years ago, after the order aforesaid had been given. Also,
    that you demanded license to publish it, but without signifying to
    those who granted you this permission that you had been commanded
    not to hold, defend, or teach the said doctrine in any manner. You
    also confessed that the style of the said book was, in many places,
    so composed that the reader might think the arguments adduced on the
    false side to be so worded as more effectually to entangle the
    understanding than to be easily solved, alleging in excuse, that you
    have thus run into an error, foreign (as you say) to your intention,
    from writing in the form of a dialogue, and in consequence of the
    natural complacency which every one feels with regard to his own
    subtilties, and in showing himself more skilful than the generality
    of mankind in contriving, even in favour of false propositions,
    ingenious and apparently probable arguments.

    "And, upon a convenient time being given to you for making your
    defence, you produced a certificate in the hand-writing of His
    Eminence the Lord Cardinal Bellarmine, procured, as you said, by
    yourself, that you might defend yourself against the calumnies of
    your enemies, who reported that you had abjured your opinions, and
    had been punished by the Holy Office; in which certificate it is
    declared, that you had not abjured, nor had been punished, but
    merely that the declaration made by His Holiness, and promulgated by
    the Holy Congregation of the Index, had been announced to you, which
    declares that the opinion of the motion of the earth, and stability
    of the sun, is contrary to the Holy Scriptures, and, therefore,
    cannot be held or defended. Wherefore, since no mention is there
    made of two articles of the order, to wit, the order 'not to teach,'
    and 'in any manner,' you argued that we ought to believe that, in
    the lapse of fourteen or sixteen years, they had escaped your
    memory, and that this was also the reason why you were silent as to
    the order, when you sought permission to publish your book, and that
    this is said by you not to excuse your error, but that it may be
    attributed to vain-glorious ambition, rather than to malice. But
    this very certificate, produced on your behalf, has greatly
    aggravated your offence, since it is therein declared that the said
    opinion is contrary to the Holy Scripture, and yet you have dared to
    treat of it, to defend it, and to argue that it is probable; nor is
    there any extenuation in the licence artfully and cunningly extorted
    by you, since you did not intimate the command imposed upon you. But
    whereas it appeared to Us that you had not disclosed the whole truth
    with regard to your intentions, We thought it necessary to proceed
    to the rigorous examination of you, in which (without any prejudice
    to what you had confessed, and which is above detailed against you,
    with regard to your said intention) you answered like a good
    Catholic.

    "Therefore, having seen and maturely considered the merits of your
    cause, with your said confessions and excuses, and every thing else
    which ought to be seen and considered, We have come to the
    underwritten final sentence against you.

    "Invoking, therefore, the most holy name of Our Lord Jesus Christ,
    and of His Most Glorious Virgin Mother Mary, by this Our final
    sentence, which, sitting in council and judgment for the tribunal of
    the Reverend Masters of Sacred Theology, and Doctors of both Laws,
    Our Assessors, We put forth in this writing touching the matters and
    controversies before Us, between The Magnificent Charles Sincerus,
    Doctor of both Laws, Fiscal Proctor of this Holy Office of the one
    part, and you, Galileo Galilei, an examined and confessed criminal
    from this present writing now in progress as above of the other
    part, We pronounce, judge, and declare, that you, the said Galileo,
    by reason of these things which have been detailed in the course of
    this writing, and which, as above, you have confessed, have rendered
    yourself vehemently suspected by this Holy Office of heresy: that is
    to say, that you believe and hold the false doctrine, and contrary
    to the Holy and Divine Scriptures, namely, that the sun is the
    centre of the world, and that it does not move from east to west,
    and that the earth does move, and is not the centre of the world;
    also that an opinion can be held and supported as probable after it
    has been declared and finally decreed contrary to the Holy
    Scripture, and consequently that you have incurred all the censures
    and penalties enjoined and promulgated in the sacred canons, and
    other general and particular constitutions against delinquents of
    this description. From which it is Our pleasure that you be
    absolved, provided that, first, with a sincere heart and unfeigned
    faith, in Our presence, you abjure, curse, and detest the said
    errors and heresies, and every other error and heresy contrary to
    the Catholic and Apostolic Church of Rome, in the form now shown to
    you.

    "But, that your grievous and pernicious error and transgression may
    not go altogether unpunished, and that you may be made more cautious
    in future, and may be a warning to others to abstain from
    delinquencies of this sort, We decree that the book of the dialogues
    of Galileo Galilei be prohibited by a public edict, and We condemn
    you to the formal prison of this Holy Office for a period
    determinable at Our pleasure; and, by way of salutary penance, We
    order you, during the next three years, to recite once a week the
    seven penitential psalms, reserving to Ourselves the power of
    moderating, commuting, or taking off the whole or part of the said
    punishment and penance.

    "And so We say, pronounce, and by Our sentence declare, decree, and
    reserve, in this and in every other better form and manner, which
    lawfully We may and can use.

    "So We, the subscribing Cardinals, pronounce.

    Felix, Cardinal di Ascoli,
    Guido, Cardinal Bentivoglio,
    Desiderio, Cardinal di Cremona,
    Antonio, Cardinal S. Onofrio,
    Berlingero, Cardinal Gessi,
    Fabricio, Cardinal Verospi,
    Martino, Cardinal Ginetti."

We cannot suppose that Galileo, even broken down as he was with age and
infirmities, and overawed by the merciless tribunal to whose power he
was subjected, could without extreme reluctance thus formally give the
lie to his whole life, and call upon God to witness his renunciation of
the opinions which even his bigoted judges must have felt that he still
clung to in his heart.

We know indeed that his friends were unanimous in recommending an
unqualified acquiescence in whatever might be required, but some persons
have not been able to find an adequate explanation of his submission,
either in their exhortations, or in the mere dread of the alternative
which might await him in case of non-compliance. It has in short been
supposed, although the suspicion scarcely rests upon grounds
sufficiently strong to warrant the assertion, that Galileo did not
submit to this abjuration until forced to it, not merely by the
apprehension, but by the actual experience of personal violence. The
arguments on which this horrible idea appears to be mainly founded are
the two following: First, the Inquisitors declare in their sentence
that, not satisfied with Galileo's first confession, they judged it
necessary to proceed "to the rigorous examination of him, in which he
answered like a good Catholic."[85] It is pretended by those who are
more familiar with inquisitorial language than we can profess to be,
that the words _il rigoroso esame_, form the official phrase for the
application of the torture, and accordingly they interpret this passage
to mean, that the desired answers and submission had thus been extorted
from Galileo, which his judges had otherwise failed to get from him.
And, secondly, the partisans of this opinion bring forward in
corroboration of it, that Galileo immediately on his departure from
Rome, in addition to his old complaints, was found to be afflicted with
hernia, and this was a common consequence of the torture of the cord,
which they suppose to have been inflicted. It is right to mention that
no other trace can be found of this supposed torturing in all the
documents relative to the proceedings against Galileo, at least Venturi
was so assured by one who had inspected the originals at Paris.[86]

Although the arguments we have mentioned appear to us slight, yet
neither can we attach much importance to the contrast which the
favourers of the opposite opinion profess to consider so incredible
between the honourable manner in which Galileo was treated throughout
the rest of the inquiry, and the suspected harsh proceeding against him.
Whether Galileo should be lodged in a prison or a palace, was a matter
of far other importance to the Inquisitors and to their hold upon public
opinion, than the question whether or not he should be suffered to
exhibit a persevering resistance to the censures which they were
prepared to cast upon him. Nor need we shrink from the idea, as we might
from suspecting of some gross crime, on trivial grounds, one of hitherto
unblemished innocence and character. The question may be disencumbered
of all such scruples, since one atrocity more or less can do little
towards affecting our judgment of the unholy Office of the Inquisition.

Delambre, who could find so much to reprehend in Galileo's former
uncompromising boldness, is deeply penetrated with the insincerity of
his behaviour on the present occasion. He seems to have forgotten that a
tribunal which finds it convenient to carry on its inquiries in secret,
is always liable to the suspicion of putting words into the mouth of its
victims; and if it were worth while, there is sufficient internal
evidence that the language which Galileo is made to hold in his defence
and confession, is rather to be read as the composition of his judges
than his own. For instance, in one of the letters which we have
extracted[87], it may be seen that this obnoxious work was already in
forward preparation as early as 1610, and yet he is made to confess, and
the circumstance appears to be brought forward in aggravation of his
guilt, that he began to write it after the prohibition which he had
received in 1616.

The abjuration was drawn up in the following terms:--

    _The Abjuration of Galileo._

    "I Galileo Galilei, son of the late Vincenzo Galilei, of Florence,
    aged 70 years, being brought personally to judgment, and kneeling
    before you, Most Eminent and Most Reverend Lords Cardinals, General
    Inquisitors of the universal Christian republic against heretical
    depravity, having before my eyes the Holy Gospels, which I touch
    with my own hands, swear, that I have always believed, and now
    believe, and with the help of God will in future believe, every
    article which the Holy Catholic and Apostolic Church of Rome holds,
    teaches, and preaches. But because I had been enjoined by this Holy
    Office altogether to abandon the false opinion which maintains that
    the sun is the centre and immoveable, and forbidden to hold, defend,
    or teach, the said false doctrine in any manner, and after it had
    been signified to me that the said doctrine is repugnant with the
    Holy Scripture, I have written and printed a book, in which I treat
    of the same doctrine now condemned, and adduce reasons with great
    force in support of the same, without giving any solution, and
    therefore have been judged grievously suspected of heresy; that is
    to say, that I held and believed that the sun is the centre of the
    world and immoveable, and that the earth is not the centre and
    moveable. Willing, therefore, to remove from the minds of Your
    Eminences, and of every Catholic Christian, this vehement suspicion
    rightfully entertained towards me, with a sincere heart and
    unfeigned faith, I abjure, curse, and detest, the said errors and
    heresies, and generally every other error and sect contrary to the
    said Holy Church; and I swear, that I will never more in future say
    or assert anything verbally, or in writing, which may give rise to a
    similar suspicion of me: but if I shall know any heretic, or any one
    suspected of heresy, that I will denounce him to this Holy Office,
    or to the Inquisitor and Ordinary of the place in which I may be. I
    swear, moreover, and promise, that I will fulfil, and observe fully,
    all the penances which have been, or shall be laid on me by this
    Holy Office. But if it shall happen that I violate any of my said
    promises, oaths, and protestations, (which God avert!) I subject
    myself to all the pains and punishments, which have been decreed and
    promulgated by the sacred canons, and other general and particular
    constitutions, against delinquents of this description. So may God
    help me, and his Holy Gospels, which I touch with my own hands. I,
    the above-named Galileo Galilei, have abjured, sworn, promised, and
    bound myself, as above, and in witness thereof with my own hand have
    subscribed this present writing of my abjuration, which I have
    recited word for word. At Rome in the Convent of Minerva, 22d June,
    1633. I, Galileo Galilei, have abjured as above with my own hand."

It is said that Galileo, as he rose from his knees, stamped on the
ground, and whispered to one of his friends, _E pur si muove_--(It does
move though).

Copies of Galileo's sentence and abjuration were immediately promulgated
in every direction, and the professors at several universities received
directions to read them publicly. At Florence this ceremony took place
in the church of Sta. Croce, whither Guiducci, Aggiunti, and all others
who were known in that city as firm adherents to Galileo's opinions,
were specially summoned. The triumph of the "Paper Philosophers" was so
far complete, and the alarm occasioned by this proof of their dying
power extended even beyond Italy. "I have been told," writes Descartes
from Holland to Mersenne at Paris, "that Galileo's system was printed in
Italy last year, but that every copy has been burnt at Rome, and himself
condemned to some sort of penance, which has astonished me so much that
I have almost determined to burn all my papers, or at least never to let
them be seen by any one. I cannot collect that he, who is an Italian and
even a friend of the Pope, as I understand, has been criminated on any
other account than for having attempted to establish the motion of the
earth. I know that this opinion was formerly censured by some Cardinals,
but I thought I had since heard, that no objection was now made to its
being publicly taught, even at Rome."

The sentiments of all who felt themselves secured against the
apprehension of personal danger could take but one direction, for, as
Pascal well expressed it in one of his celebrated letters to the
Jesuits--"It is in vain that you have procured against Galileo a decree
from Rome condemning his opinion of the earth's motion. Assuredly, that
will never prove it to be at rest; and if we have unerring observations
proving that it turns round, not all mankind together can keep it from
turning, nor themselves from turning with it."

The assembly of doctors of the Sorbonne at Paris narrowly escaped from
passing a similar sentence upon the system of Copernicus. The question
was laid before them by Richelieu, and it appears that their opinion was
for a moment in favour of confirming the Roman decree. It is to be
wished that the name had been preserved of one of its members, who, by
his strong and philosophical representations, saved that celebrated body
from this disgrace.

Those who saw nothing in the punishment of Galileo but passion and
blinded superstition, took occasion to revert to the history of a
similar blunder of the Court of Rome in the middle of the eighth
century. A Bavarian bishop, named Virgil, eminent both as a man of
letters and politician, had asserted the existence of Antipodes, which
excited in the ignorant bigots of his time no less alarm than did the
motion of the earth in the seventeenth century. Pope Zachary, who was
scandalized at the idea of another earth, inhabited by another race of
men, and enlightened by another sun and moon (for this was the shape
which Virgil's system assumed in his eyes), sent out positive orders to
his legate in Bavaria. "With regard to Virgil, the philosopher, (I know
not whether to call him priest,) if he own these perverse opinions,
strip him of his priesthood, and drive him from the church and altars of
God." But Virgil had himself occasionally acted as legate, and was
moreover too necessary to his sovereign to be easily displaced. He
utterly disregarded these denunciations, and during twenty-five years
which elapsed before his death, retained his opinions, his bishopric of
Salzburg, and his political power. He was afterwards canonized.[88]

Even the most zealous advocates of the authority of Rome were
embarrassed in endeavouring to justify the treatment which Galileo
experienced. Tiraboschi has attempted to draw a somewhat subtle
distinction between the bulls of the Pope and the inquisitorial decrees
which were sanctioned and approved by him; he dwells on the reflection
that no one, even among the most zealous Catholics, has ever claimed
infallibility as an attribute of the Inquisition, and looks upon it as a
special mark of grace accorded to the Roman Catholic Church, that during
the whole period in which most theologians rejected the opinions of
Copernicus, as contrary to the Scriptures, the head of that Church was
never permitted to compromise his infallible character by formally
condemning it.[89]

Whatever may be the value of this consolation, it can hardly be
conceded, unless it be at the same time admitted that many scrupulous
members of the Church of Rome have been suffered to remain in singular
misapprehension of the nature and sanction of the authority to which
Galileo had yielded. The words of the bull of Sixtus V., by which the
Congregation of the Index was remodelled in 1588, are quoted by a
professor of the University of Louvain, a zealous antagonist of Galileo,
as follows: "They are to examine and expose the books which are
repugnant to the Catholic doctrines and Christian discipline, and after
reporting on them to us, they are to condemn them by our authority."[90]
Nor does it appear that the learned editors of what is commonly called
the Jesuit's edition of Newton's "Principia" were of opinion, that in
adopting the Copernican system they should transgress a mandate
emanating from any thing short of infallible wisdom. The remarkable
words which they were compelled to prefix to their book, show how
sensitive the court of Rome remained, even so late as 1742, with regard
to this rashly condemned theory. In their preface they say: "Newton in
this third book supposes the motion of the earth. We could not explain
the author's propositions otherwise than by making the same supposition.
We are therefore forced to sustain a character which is not our own; but
we profess to pay the obsequious reverence which is due to the decrees
pronounced by the supreme Pontiffs against the motion of the earth."[91]

This coy reluctance to admit what nobody any longer doubts has survived
to the present time; for Bailli informs us,[92] that the utmost
endeavours of Lalande, when at Rome, to obtain that Galileo's work
should be erased from the Index, were entirely ineffectual, in
consequence of the decree which had been fulminated against him; and in
fact both it, and the book of Copernicus, "Nisi Corrigatur," are still
to be seen on the forbidden list of 1828.

The condemnation of Galileo and his book was not thought sufficient.
Urban's indignation also vented itself upon those who had been
instrumental in obtaining the licence for him. The Inquisitor at
Florence was reprimanded; Riccardi, the master of the sacred palace, and
Ciampoli, Urban's secretary, were both dismissed from their situations.
Their punishment appears rather anomalous and inconsistent with the
proceedings against Galileo, in which it was assumed that his book was
not properly licensed; yet the others suffered on account of granting
that very licence, which he was accused of having surreptitiously
obtained from them, by concealing circumstances with which they were not
bound to be otherwise acquainted. Riccardi, in exculpation of his
conduct, produced a letter in the hand-writing of Ciampoli, in which was
contained that His Holiness, in whose presence the letter professed to
be written, ordered the licence to be given. Urban only replied that
this was a Ciampolism; that his secretary and Galileo had circumvented
him; that he had already dismissed Ciampoli, and that Riccardi must
prepare to follow him.

As soon as the ceremony of abjuration was concluded, Galileo was
consigned, pursuant to his sentence, to the prison of the Inquisition.
Probably it was never intended that he should long remain there, for at
the end of four days, he was reconducted on a very slight representation
of Nicolini to the ambassador's palace, there to await his further
destination. Florence was still suffering under the before-mentioned
contagion; and Sienna was at last fixed on as the place of his
relegation. He would have been shut up in some convent in that city, if
Nicolini had not recommended as a more suitable residence, the palace of
the Archbishop Piccolomini, whom he knew to be among Galileo's warmest
friends. Urban consented to the change, and Galileo finally left Rome
for Sienna in the early part of July.

Piccolomini received him with the utmost kindness, controlled of course
by the strict injunctions which were dispatched from Rome, not to suffer
him on any account to quit the confines of the palace. Galileo continued
at Sienna in this state of seclusion till December of the same year,
when the contagion having ceased in Tuscany, he applied for permission
to return to his villa at Arcetri. This was allowed, subject to the same
restrictions under which he had been residing with the archbishop.


FOOTNOTES:

[79] Delambre quotes this sentence from a passage which is so obviously
ironical throughout, as an instance of Galileo's mis-statement of
facts!--_Hist. de l'Astr. Mod._, vol, i. p. 666.

[80] Page 54.

[81] Galuzzi. Storia di Toscana. Firenze, 1822.

[82] Alidosi was a Florentine nobleman, whose estate Urban wished to
confiscate on a charge of heresy.--_Galuzzi._

[83] S'irrito il Papa, e lo fece abjurare, comparendo il pover uomo con
uno straccio di camicia indosso, che faceva compassione, MS. nella Bibl.
Magliab. Venturi.

[84] The Index is a list of books, the reading of which is prohibited to
Roman Catholics. This list, in the early periods of the Reformation, was
often consulted by the curious, who were enlarging their libraries; and
a story is current in England, that, to prevent this mischief, the Index
itself was inserted in its own forbidden catalogue. The origin of this
story is, that an Index was published in Spain, particularizing the
objectionable passages in such books as were only partially condemned;
and although compiled with the best intentions, this was found to be so
racy, that it became necessary to forbid the circulation of this edition
in subsequent lists.

[85] Giudicassimo esser necessario venir contro di te al rigoroso esame
nel quale rispondesti cattolicamente.

[86] The fate of these documents is curious; after being long preserved
at Rome, they were carried away in 1809, by order of Buonaparte, to
Paris, where they remained till his first abdication. Just before the
hundred days, the late king of France, wishing to inspect them, ordered
that they should be brought to his own apartments for that purpose. In
the hasty flight which soon afterwards followed, the manuscripts were
forgotten, and it is not known what became of them. A French
translation, begun by Napoleon's desire, was completed only down to the
30th of April, 1633, the date of Galileo's first return to Nicolini's
palace.

[87] Page 18.

[88] Annalium Bolorum, libri vii. Ingolstadii, 1554.

[89] La Chiesa non ha mai dichiarati eretici i sostenitori del Sistema
Copernicano, e questa troppo rigorosa censura non usci che dal tribunale
della Romana Inquisizione a cui niuno tra Cattolici ancor piu zelanti ha
mai attribuito it diritto dell'infallibilità. Anzi in cio ancora è d'
ammirarsi la providenza di Dio à favor della Chiesa, percioche in un
tempo in cui la maggior parte dei teologi fermamente credavano che il
Sistema Copernicano fosse all' autorità delle sacre Carte contrario, pur
non permise che dalla Chiesa si proferisse su cio un solenne
giudizio.--Stor. della Lett. Ital.

[90] Lib. Fromondi Antaristarchus, Antwerpiæ, 1631.

[91] Newtoni Principia, Coloniæ, 1760.

[92] Histoire de l'Astronomie Moderne.




CHAPTER XIV.

    _Extracts from the Dialogues on the System._


AFTER narrating the treatment to which Galileo was subject on account of
his admirable Dialogues, it will not be irrelevant to endeavour, by a
few extracts, to convey some idea of the style in which they are
written. It has been mentioned, that he is considered to surpass all
other Italian writers (unless we except Machiavelli) in the purity and
beauty of his language, and indeed his principal followers, who avowedly
imitated his style, make a distinguished group among the classical
authors of modern Italy. He professed to have formed himself from the
study of Ariosto, whose poems he passionately admired, insomuch that he
could repeat the greater part of them, as well as those of Berni and
Petrarca, all which he was in the frequent habit of quoting in
conversation. The fashion and almost universal practice of that day was
to write on philosophical subjects in Latin; and although Galileo wrote
very passably in that language, yet he generally preferred the use of
Italian, for which he gave his reasons in the following characteristic
manner:--

"I wrote in Italian because I wished every one to be able to read what I
wrote; and for the same cause I have written my last treatise in the
same language: the reason which has induced me is, that I see young men
brought together indiscriminately to study to become physicians,
philosophers, &c., and whilst many apply to such professions who are
most unfit for them, others who would be competent remain occupied
either with domestic business, or with other employments alien to
literature; who, although furnished, as Ruzzante might say, with a
_decent set of brains_, yet, not being able to understand things written
in _gibberish_, take it into their heads, that in these crabbed folios
there must be some grand _hocus pocus_ of logic and philosophy much too
high up for them to think of jumping at. I want them to know, that as
Nature has given eyes to them just as well as to philosophers for the
purpose of seeing her works, she has also given them brains for
examining and understanding them."

The general structure of the dialogues has been already described;[93]
we shall therefore premise no more than the judgment pronounced on them
by a highly gifted writer, to supply the deficiencies of our necessarily
imperfect analysis.

"One forms a very imperfect idea of Galileo, from considering the
discoveries and inventions, numerous and splendid as they are, of which
he was the undisputed author. It is by following his reasonings, and by
pursuing the train of his thoughts, in his own elegant, though somewhat
diffuse exposition of them, that we become acquainted with the fertility
of his genius--with the sagacity, penetration, and comprehensiveness of
his mind. The service which he rendered to real knowledge is to be
estimated, not only from the truths which he discovered, but from the
errors which he detected--not merely from the sound principles which he
established, but from the pernicious idols which he overthrew. The
dialogues on the system are written with such singular felicity, that
one reads them at the present day, when the truths contained in them are
known and admitted, with all the delight of novelty, and feels one's
self carried back to the period when the telescope was first directed to
the heavens, and when the earth's motion, with all its train of
consequences, was proved for the first time."[94]

The first Dialogue is opened by an attack upon the arguments by which
Aristotle pretended to determine _à priori_ the necessary motions
belonging to different parts of the world, and on his favourite
principle that particular motions belong naturally to particular
substances. Salviati (representing Galileo) then objects to the
Aristotelian distinctions between the corruptible elements and
incorruptible skies, instancing among other things the solar spots and
newly appearing stars, as arguments that the other heavenly bodies may
probably be subjected to changes similar to those which are continually
occurring on the earth, and that it is the great distance alone which
prevents their being observed. After a long discussion on this point,
Sagredo exclaims, "I see into the heart of Simplicio, and perceive that
he is much moved by the force of these too conclusive arguments; but
methinks I hear him say--'Oh, to whom must we betake ourselves to settle
our disputes if Aristotle be removed from the chair? What other author
have we to follow in our schools, our studies, and academies? What
philosopher has written on all the parts of Natural Philosophy, and so
methodically as not to have overlooked a single conclusion? Must we then
desolate this fabric, by which so many travellers have been sheltered?
Must we destroy this asylum, this Prytaneum wherein so many students
have found a convenient resting-place, where without being exposed to
the injuries of the weather, one may acquire an intimate knowledge of
nature, merely by turning over a few leaves? Shall we level this
bulwark, behind which we are safe from every hostile attack?' I pity him
no less than I do one who at great expense of time and treasure, and
with the labour of hundreds, has built up a very noble palace; and then,
because of insecure foundations, sees it ready to fall--unable to bear
that those walls be stripped that are adorned with so many beautiful
pictures, or to suffer those columns to fall that uphold the stately
galleries, or to see ruined the gilded roofs, the chimney-pieces, the
friezes, and marble cornices erected at so much cost, he goes about it
with girders and props, with shores and buttresses, to hinder its
destruction."

Salviati proceeds to point out the many points of similarity between the
earth and moon, and among others which we have already mentioned, the
following remark deserves especial notice:--

"Just as from the mutual and universal tendency of the parts of the
earth to form a whole, it follows that they all meet together with equal
inclination, and that they may unite as closely as possible, assume the
spherical form; why ought we not to believe that the moon, the sun, and
other mundane bodies are also of a round figure, from no other reason
than from a common instinct and natural concourse of all their component
parts; of which if by accident any one should be violently separated
from its whole, is it not reasonable to believe that spontaneously, and
of its natural instinct, it would return? It may be added that if any
centre of the universe may be assigned, to which the whole terrene globe
if thence removed would seek to return, we shall find most probable that
the sun is placed in it, as by the sequel you shall understand."

Many who are but superficially acquainted with the History of Astronomy,
are apt to suppose that Newton's great merit was in his being the first
to suppose an attractive force existing in and between the different
bodies composing the solar system. This idea is very erroneous; Newton's
discovery consisted in conceiving and proving the identity of the force
with which a stone falls, and that by which the moon falls, towards the
earth (on an assumption that this force becomes weaker in a certain
proportion as the distance increases at which it operates), and in
generalizing this idea, in applying it to all the visible creation, and
tracing the principle of universal gravitation with the assistance of a
most refined and beautiful geometry into many of its most remote
consequences. But the general notion of an attractive force between the
sun, moon, and planets, was very commonly entertained before Newton was
born, and may be traced back to Kepler, who was probably the first
modern philosopher who suggested it. The following extraordinary
passages from his "Astronomy" will shew the nature of his conceptions on
this subject:--

"The true doctrine of gravity is founded on these axioms: every
corporeal substance, so far forth as it is corporeal, has a natural
fitness for resting in every place where it may be situated by itself
beyond the sphere of influence of its cognate body. Gravity is a mutual
affection between cognate bodies towards union or conjunction (similar
in kind to the magnetic virtue), so that the earth attracts a stone much
rather than the stone seeks the earth. Heavy bodies (if in the first
place we put the earth in the centre of the world) are not carried to
the centre of the world in its quality of centre of the world, but as to
the centre of a cognate round body, namely the earth. So that
wheresoever the earth may be placed or whithersoever it may be carried
by its animal faculty, heavy bodies will always be carried towards it.
If the earth were not round heavy bodies would not tend from every side
in a straight line towards the centre of the earth, but to different
points from different sides. If two stones were placed in any part of
the world near each other and beyond the sphere of influence of a third
cognate body, these stones, like two magnetic needles, would come
together in the intermediate point, each approaching the other by a
space proportional to the comparative mass of the other. If the moon
and earth were not retained in their orbits by their animal force or
some other equivalent, the earth would mount to the moon by a
fifty-fourth part of their distance, and the moon fall towards the earth
through the other fifty-three parts, and would there meet, assuming
however that the substance of both is of the same density. If the earth
should cease to attract its waters to itself, all the waters of the sea
would be raised, and would flow to the body of the moon."[95]

He also conjectured that the irregularities in the moon's motion were
caused by the joint action of the sun and earth, and recognized the
mutual action of the sun and planets, when he declared the mass and
density of the sun to be so great that the united attraction of the
other planets cannot remove it from its place. Among these bold and
brilliant ideas, his temperament led him to introduce others which show
how unsafe it was to follow his guidance, and which account for, if they
do not altogether justify, the sarcastic remark of Ross, that "Kepler's
opinion that the planets are moved round by the sunne, and that this is
done by sending forth a magnetic virtue, and that the sun-beames are
like the teethe of a wheele taking hold of the planets, are senslesse
crotchets fitter for a wheeler or a miller than a philosopher."[96]
Roberval took up Kepler's notions, especially in the tract which he
falsely attributed to Aristarchus, and it is much to be regretted that
Roberval should deserve credit for anything connected with that impudent
fraud. The principle of universal gravitation, though not the varying
proportion, is distinctly assumed in it, as the following passages will
sufficiently prove: "In every single particle of the earth, and the
terrestrial elements, is a certain property or accident which we suppose
common to the whole system of the world, by virtue of which all its
parts are forced together, and reciprocally attract each other; and this
property is found in a greater or less degree in the different
particles, according to their density. If the earth be considered by
itself, its centres of magnitude and virtue, or gravity, as we usually
call it, will coincide, to which all its parts tend in a straight line,
as well by their own exertion or gravity, as by the reciprocal
attraction of all the rest." In a subsequent chapter, Roberval repeats
these passages nearly in the same words, applying them to the whole
solar system, adding, that "the force of this attraction is not to be
considered as residing in the centre itself, as some ignorant people
think, but in the whole system whose parts are equally disposed round
the centre."[97] This very curious work was reprinted in the third
volume of the _Reflexiones Physico-Mathematicæ_ of Mersenne, from whom
Roberval pretended to have received the Arabic manuscript, and who is
thus irretrievably implicated in the forgery.[98] The last remark,
denying the attractive force to be due to any property of the central
point, seems aimed at Aristotle, who, in a no less curious passage,
maintaining exactly the opposite opinion, says, "Hence, we may better
understand what the ancients have related, that like things are wont to
have a tendency to each other. For this is not absolutely true; for if
the earth were to be removed to the place now occupied by the moon, no
part of the earth would then have a tendency towards that place, but
would still fall towards the point which the earth's centre now
occupies."[99] Mersenne considered the consequences of the attractive
force of each particle of matter so far as to remark, that if a body
were supposed to fall towards the centre of the earth, it would be
retarded by the attraction of the part through which it had already
fallen.[100] Galileo had not altogether neglected to speculate on such a
supposition, as is plain from the following extract. It is taken from a
letter to Carcaville, dated from Arcetri, in 1637. "I will say farther,
that I have not absolutely and clearly satisfied myself that a heavy
body would arrive sooner at the centre of the earth, if it began to fall
from the distance only of a single yard, than another which should start
from the distance of a thousand miles. I do not affirm this, but I offer
it as a paradox."[101]

It is very difficult to offer any satisfactory comment upon this
passage; it may be sufficient to observe that this paradoxical result
was afterwards deduced by Newton, as one of the consequences of the
general law with which all nature is pervaded, but with which there is
no reason to believe that Galileo had any acquaintance; indeed the idea
is fully negatived by other passages in this same letter. This is one of
the many instances from which we may learn to be cautious how we invest
detached passages of the earlier mathematicians with a meaning which in
many cases their authors did not contemplate. The progressive
development of these ideas in the hands of Wallis, Huyghens, Hook, Wren,
and Newton, would lead us too far from our principal subject. There is
another passage in the third dialogue connected with this subject, which
it may be as well to notice in this place. "The parts of the earth have
such a propensity to its centre, that when it changes its place,
although they may be very distant from the globe at the time of the
change, yet must they follow. An example similar to this is the
perpetual sequence of the Medicean stars, although always separated from
Jupiter. The same may be said of the moon, obliged to follow the earth.
And this may serve for those simple ones who have difficulty in
comprehending how these two globes, not being chained together, nor
strung upon a pole, mutually follow each other, so that on the
acceleration or retardation of the one, the other also moves quicker or
slower."

The second Dialogue is appropriated chiefly to the discussion of the
diurnal motion of the earth; and the principal arguments urged by
Aristotle, Ptolemy, and others, are successively brought forward and
confuted. The opposers of the earth's diurnal motion maintained, that if
it were turning round, a stone dropped from the top of a tower would not
fall at its foot; but, by the rotation of the earth to the eastward
carrying away the tower with it, would be left at a great distance to
the westward; it was common to compare this effect to a stone dropped
from the mast-head of a ship, and without any regard to truth it was
boldly asserted that this would fall considerably nearer the stern than
the foot of the mast, if the ship were in rapid motion. The same
argument was presented in a variety of forms,--such as that a
cannon-ball shot perpendicularly upwards would not fall at the same
spot; that if fired to the eastward it would fly farther than to the
westward; that a mark to the east or west would never be hit, because of
the rising or sinking of the horizon during the flight of the ball; that
ladies' ringlets would all stand out to the westward,[102] with other
conceits of the like nature: to which the general reply is given, that
in all these cases the stone, or ball, or other body, participates
equally in the motion of the earth, which, therefore, so far as regards
the relative motion of its parts, may be disregarded. The manner in
which this is illustrated, appears in the following extract from the
dialogue:--"_Sagredo._ If the nib of a writing pen which was in the ship
during my voyage direct from Venice to Alexandria, had had the power of
leaving a visible mark of all its path, what trace, what mark, what line
would it have left?--_Simplicio._ It would have left a line stretched
out thither from Venice not perfectly straight, or to speak more
correctly, not perfectly extended in an exact circular arc, but here and
there more and less curved accordingly as the vessel had pitched more or
less; but this variation in some places of one or two yards to the right
or left, or up or down in a length of many hundred miles, would have
occasioned but slight alteration in the whole course of the line, so
that it would have been hardly sensible, and without any great error we
may speak of it as a perfectly circular arc.--_Sagred._ So that the true
and most exact motion of the point of the pen would also have been a
perfect arc of a circle if the motion of the vessel, abstracting from
the fluctuations of the waves, had been steady and gentle; and if I had
held this pen constantly in my hand, and had merely moved it an inch or
two one way or the other, what alteration would that have made in the
true and principal motion?--_Simpl._ Less than that which would be
occasioned in a line a thousand yards long, by varying here and there
from perfect straightness by the quantity of a flea's eye.--_Sagred._ If
then a painter on our quitting the port had begun to draw with this pen
on paper, and had continued his drawing till we got to Alexandria, he
would have been able by its motion, to produce an accurate
representation of many objects perfectly shadowed, and filled up on all
sides with landscapes, buildings, and animals, although all the true,
real, and essential motion of the point of his pen would have been no
other but a very long and very simple line; and as to the peculiar work
of the painter, he would have drawn it exactly the same if the ship had
stood still. Therefore, of the very protracted motion of the pen, there
remain no other traces than those marks drawn upon the paper, the reason
of this being that the great motion from Venice to Alexandria was common
to the paper, the pen, and everything that was in the ship; but the
trifling motion forwards and backwards, to the right and left,
communicated by the painter's fingers to the pen, and not to the paper,
from being peculiar to the pen, left its mark upon the paper, which as
to this motion was immoveable. Thus it is likewise true that in the
supposition of the earth's rotation, the motion of a falling stone is
really a long track of many hundreds and thousands of yards; and if it
could have delineated its course in the calm air, or on any other
surface, it would have left behind it a very long transversal line; but
that part of all this motion which is common to the stone, the tower,
and ourselves, is imperceptible by us and the same as if not existing,
and only that part remains to be observed of which neither we nor the
tower partake, which in short is the fall of the stone along the tower."

The mechanical doctrines introduced into this second dialogue will be
noticed on another occasion; we shall pass on to other extracts,
illustrative of the general character of Galileo's reasoning:--
"_Salviati._ I did not say that the earth has no principle, either
internal or external, of its motion of rotation, but I do say that I
know not which of the two it has, and that my ignorance has no power to
take its motion away; but if this author knows by what principle other
mundane bodies, of the motion of which we are certain, are turned round,
I say that what moves the Earth is something like that by which Mars and
Jupiter, and, as he believes, the starry sphere, are moved round; and if
he will satisfy me as to the cause of their motion, I bind myself to be
able to tell him what moves the earth. Nay more; I undertake to do the
same if he can teach me what it is which moves the parts of the earth
downwards.--_Simpl._ The cause of this effect is notorious, and every
one knows that it is Gravity.--_Salv._ You are out, Master Simplicio;
you should say that every one knows that it is called Gravity; but I do
not ask you the name but the nature of the thing, of which nature you do
not know one tittle more than you know of the nature of the moving cause
of the rotation of the stars, except it be the name which has been given
to the one, and made familiar and domestic, by the frequent experience
we have of it many thousand times in a day; but of the principle or
virtue by which a stone falls to the ground, we really know no more than
we know of the principle which carries it upwards when thrown into the
air, or which carries the moon round its orbit, except, as I have said,
the name of gravity which we have peculiarly and exclusively assigned to
it; whereas we speak of the other with a more generic term, and talk of
the virtue impressed, and call it either an assisting or an informing
intelligence, and are content to say that Nature is the cause of an
infinite number of other motions."

Simplicio is made to quote a passage from Scheiner's book of Conclusions
against Copernicus, to the following effect:--"'If the whole earth and
water were annihilated, no hail or rain would fall from the clouds, but
would only be naturally carried round in a circle, nor would any fire or
fiery thing ascend, since, according to the not improbable opinion of
these others, there is no fire in the upper regions.'--_Salv._ The
foresight of this philosopher is most admirable and praiseworthy, for he
is not content with providing for things that might happen during the
common course of nature, but persists in shewing his care for the
consequences of what he very well knows will never come to pass.
Nevertheless, for the sake of hearing some of his notable conceits, I
will grant that if the earth and water were annihilated there would be
no more hail or rain, nor would fiery matter ascend any more, but would
continue a motion of revolution. What is to follow? What conclusion is
the philosopher going to draw?--_Simpl._ This objection is in the very
next words--'Which nevertheless (says he) is contrary to experience and
reason.'--_Salv._ Now I must yield: since he has so great an advantage
over me as experience, with which I am quite unprovided. For hitherto I
have never happened to see the terrestrial earth and water annihilated,
so as to be able to observe what the hail and fire did in the confusion.
But does he tell us for our information at least what they did?--_Simp._
No, he does not say any thing more.--_Salv._ I would give something to
have a word or two with this person, to ask him whether, when this globe
vanished, it also carried away the common centre of gravity, as I fancy
it did, in which case I take it that the hail and water would remain
stupid and confounded amongst the clouds, without knowing what to do
with themselves.... And lastly, that I may give this philosopher a less
equivocal answer, I tell him that I know as much of what would follow
after the annihilation of the terrestrial globe, as he could have known
what was about to happen in and about it, before it was created."

Great part of the third Dialogue is taken up with discussions on the
parallax of the new stars of 1572 and 1604, in which Delambre notices
that Galileo does not employ logarithms in his calculations, although
their use had been known since Napier discovered them in 1616: the
dialogue then turns to the annual motion "first taken from the Sun and
conferred upon the Earth by Aristarchus Samius, and afterwards by
Copernicus." Salviati speaks of his contemporary philosophers with great
contempt--"If you had ever been worn out as I have been many and many a
time with hearing what sort of stuff is sufficient to make the obstinate
vulgar unpersuadable, I do not say to agree with, but even to listen to
these novelties, I believe your wonder at finding so few followers of
these opinions would greatly fall off. But little regard in my judgment
is to be had of those understandings who are convinced and immoveably
persuaded of the fixedness of the earth, by seeing that they are not
able to breakfast this morning at Constantinople, and sup in the evening
in Japan, and who feel satisfied that the earth, so heavy as it is,
cannot climb up above the sun, and then come tumbling in a breakneck
fashion down again!"[103] This remark serves to introduce several
specious arguments against the annual motion of the earth, which are
successively confuted, and it is shewn how readily the apparent stations
and retrogradations of the planets are accounted for on this
supposition.

The following is one of the frequently recurring passages in which
Galileo, whilst arguing in favour of the enormous distances at which the
theory of Copernicus necessarily placed the fixed stars, inveighs
against the arrogance with which men pretend to judge of matters removed
above their comprehension. "_Simpl._ All this is very well, and it is
not to be denied that the heavens may surpass in bigness the capacity of
our imaginations, as also that God might have created it yet a thousand
times larger than it really is, but we ought not to admit anything to be
created in vain, and useless in the universe. Now whilst we see this
beautiful arrangement of the planets, disposed round the earth at
distances proportioned to the effects they are to produce on us for our
benefit, to what purpose should a vast vacancy be afterwards interposed
between the orbit of Saturn and the starry spheres, containing not a
single star, and altogether useless and unprofitable? to what end? for
whose use and advantage?--_Salv._ Methinks we arrogate too much to
ourselves, Simplicio, when we will have it that the care of us alone is
the adequate and sufficient work and bound, beyond which the divine
wisdom and power does and disposes of nothing. I feel confident that
nothing is omitted by the Divine Providence of what concerns the
government of human affairs; but that there may not be other things in
the universe dependant upon His supreme wisdom, I cannot for myself, by
what my reason holds out to me, bring myself to believe. So that when I
am told of the uselessness of an immense space interposed between the
orbits of the planets and the fixed stars, empty and valueless, I reply
that there is temerity in attempting by feeble reason to judge the works
of God, and in calling vain and superfluous every part of the universe
which is of no use to us.--_Sagr._ Say rather, and I believe you would
say better, that we have no means of knowing what is of use to us; and I
hold it to be one of the greatest pieces of arrogance and folly that can
be in this world to say, because I know not of what use Jupiter or
Saturn are to me, that therefore these planets are superfluous; nay
more, that there are no such things in nature. To understand what effect
is worked upon us by this or that heavenly body (since you will have it
that all their use must have a reference to us), it would be necessary
to remove it for a while, and then the effect which I find no longer
produced in me, I may say that it depended upon that star. Besides, who
will dare say that the space which they call too vast and useless
between Saturn and the fixed stars is void of other bodies belonging to
the universe. Must it be so because we do not see them: then I suppose
the four Medicean planets, and the companions of Saturn, came into the
heavens when we first began to see them, and not before! and, by the
same rule, the other innumerable fixed stars did not exist before men
saw them. The nebulæ were till lately only white flakes, till with the
telescope we have made of them constellations of bright and beautiful
stars. Oh presumptuous! rather, Oh rash ignorance of man!"

After a discussion on Gilbert's Theory of Terrestrial Magnetism,
introduced by the parallelism of the earth's axis, and of which Galileo
praises very highly both the method and results, the dialogue proceeds
as follows:--"_Simpl._ It appears to me that Sig. Salviati, with a fine
circumlocution, has so clearly explained the cause of these effects,
that any common understanding, even though unacquainted with science,
may comprehend it: but we, confining ourselves to the terms of art,
reduce the cause of these and other similar natural phenomena to
sympathy, which is a certain agreement and mutual appetency arising
between things which have the same qualities, just as, on the other
hand, that disagreement and aversion, with which other things naturally
repel and abhor each other, we style antipathy.--_Sagr._ And thus with
these two words they are able to give a reason for the great number of
effects and accidents which we see, not without admiration, to be
produced in Nature. But it strikes me that this mode of philosophising
has a great sympathy with the style in which one of my friends used to
paint: on one part of the canvas he would write with chalk--there I will
have a fountain, with Diana and her nymphs; here some harriers; in this
corner I will have a huntsman, with a stag's head; the rest may be a
landscape of wood and mountain; and what remains to be done may be put
in by the colourman: and thus he flattered himself that he had painted
the story of Actæon, having contributed nothing to it beyond the names."

The fourth Dialogue is devoted entirely to an examination of the tides,
and is a development and extension of the treatise already mentioned to
have been sent to the Archduke Leopold, in 1618.[104] Galileo was
uncommonly partial to his theory of the tides, from which he thought to
derive a direct proof of the earth's motion in her orbit; and although
his theory was erroneous, it required a farther advance in the science
of motion than had been attained even at a much later period to point
out the insufficiency of it. It is well known that the problem of
explaining the cause of this alternate motion of the waters had been
considered from the earliest ages one of the most difficult that could
be proposed, and the solutions with which different inquirers were
obliged to rest contented, shew that it long deserved the name given to
it, of "the grave of human curiosity."[105] Riccioli has enumerated
several of the opinions which in turn had their favourers and
supporters. One party supposed the rise of the waters to be occasioned
by the influx of rivers into the sea; others compared the earth to a
large animal, of which the tides indicated the respiration; a third
theory supposed the existence of subterraneous fires, by which the sea
was periodically made to boil; others attributed the cause of a similar
change of temperature to the sun and moon.

There is an unfounded legend, that Aristotle drowned himself in despair
of being able to invent a plausible explanation of the extraordinary
tides in the Euripus. His curiosity on the subject does not appear to
have been so acute (judging from his writings) as this story would
imply. In one of his books he merely mentions a rumour, that there are
great elevations or swellings of the seas, which recur periodically,
according to the course of the moon. Lalande, in the fourth volume of
his Astronomy, has given an interesting account of the opinion of the
connection of the tides with the moon's motion. Pytheas of Marseilles, a
contemporary of Aristotle, was the first who has been recorded as
observing, that the full tides occur at full moon, and the ebbs at new
moon.[106] This is not quite correctly stated; for the tide of new moon
is known to be still higher than the rise at the full, but it is likely
enough, that the seeming inaccuracy should be attributed, not to
Pytheas, but to his biographer Plutarch, who, in many instances,
appears to have viewed the opinions of the old philosophers through the
mist of his own prejudices and imperfect information. The fact is, that,
on the same day when the tide rises highest, it also ebbs lowest; and
Pytheas, who, according to Pliny, had recorded a tide in Britain of
eighty cubits, could not have been ignorant of this. Posidonius, as
quoted by Strabo, maintained the existence of three periods of the tide,
daily, monthly, and annual, "in sympathy with the moon."[107] Pliny, in
his vast collection of natural observations, not unaptly styled the
Encyclopædia of the Antients, has the following curious passages:--"The
flow and ebb of the tide is very wonderful; it happens in a variety of
ways, but the cause is in the sun and moon."[108] He then very
accurately describes the course of the tide during a revolution of the
moon, and adds: "The flow takes place every day at a different hour;
being waited on by the star, which rises every day in a different place
from that of the day before, and with greedy draught drags the seas with
it."[109] "When the moon is in the north, and further removed from the
earth, the tides are more gentle than when digressing to the south, she
exerts her force with a closer effort."[110]

The College of Jesuits at Coimbra appears to deserve the credit of first
clearly pointing out the true relation between the tides and the moon,
which was also maintained a few years later by Antonio de Dominis and
Kepler. In the Society's commentary on Aristotle's book on Meteors,
after refuting the notion that the tides are caused by the light of the
sun and moon, they say, "It appears more probable to us, without any
rarefaction, of which there appears no need or indication, that the moon
raises the waters by some inherent power of impulsion, in the same
manner as a magnet moves iron; and according to its different aspects
and approaches to the sea, and the obtuse or acute angles of its
bearing, at one time to attract and raise the waters along the shore,
and then again to leave them to sink down by their own weight, and to
gather into a lower level."[111] The theory of Universal Gravitation
seems here within the grasp of these philosophers, but unfortunately it
did not occur to them that possibly the same attraction might be exerted
on the earth as well as the water, and that the tide was merely an
effect of the diminution of force, owing to the increase of distance,
with which the centre of the earth is attracted, as compared with that
exerted on its surface. This idea, so happily seized afterwards by
Newton, might at once have furnished them with a satisfactory
explanation of the tide, which is observed on the opposite side of the
earth as well as immediately under the moon. They might have seen that
in the latter case the centre of the earth is pulled away from the
water, just as in the former the water is pulled away from the centre of
the earth, the sensible effect to us being in both cases precisely the
same. For want of this generalization, the inferior tide as it is called
presented a formidable obstacle to this theory, and the most plausible
explanation that was given was, that this magnetic virtue radiated out
from the moon was reflected by the solid heavens, and concentrated again
as in a focus on the opposite side of the earth. The majority of modern
astronomers who did not admit the existence of any solid matter fit for
producing the effect assigned to it, found a reasonable difficulty in
acquiescing in this explanation. Galileo, who mentions the Archbishop of
Spalatro's book, treated the theory of attraction by the moon as absurd.
"This motion of the seas is local and sensible, made in an immense mass
of water, and cannot be brought to obey light, and warmth, and
predominancy of occult qualities, and such like vain fancies; all which
are so far from being the cause of the tide, that on the contrary the
tide is the cause of them, inasmuch as it gives rise to these ideas in
brains which are more apt for talkativeness and ostentation, than for
speculation and inquiry into the secrets of Nature; who, rather than see
themselves driven to pronounce these wise, ingenuous, and modest
words--_I do not know_,--will blurt out from their tongues and pens all
sorts of extravagancies."

Galileo's own theory is introduced by the following illustration, which
indeed probably suggested it, as he was in the habit of suffering no
natural phenomena, however trivial in appearance, to escape him. He felt
the advantage of this custom in being furnished on all occasions with a
stock of homely illustrations, to which the daily experience of his
hearers readily assented, and which he could shew to be identical in
principle with the phenomena under discussion. That he was mistaken in
applying his observations in the present instance cannot be urged
against the incalculable value of such a habit.

"We may explain and render sensible these effects by the example of one
of those barks which come continually from Lizza Fusina, with fresh
water for the use of the city of Venice. Let us suppose one of these
barks to come thence with moderate velocity along the canal, carrying
gently the water with which it is filled, and then, either by touching
the bottom, or from some other hindrance which is opposed to it, let it
be notably retarded; the water will not on that account lose like the
bark the impetus it has already acquired, but will forthwith run on
towards the prow where it will sensibly rise, and be depressed at the
stern. If on the contrary the said vessel in the middle of its steady
course shall receive a new and sensible increase of velocity, the
contained water before giving into it will persevere for some time in
its slowness, and will be left behind that is to say towards the stern
where consequently it will rise, and sink at the head.--Now, my masters,
that which the vessel does in respect of the water contained in it, and
that which the water does in respect of the vessel containing it, is the
same to a hair as what the Mediterranean vase does in respect of the
water which it contains, and that the waters do in respect of the
Mediterranean vase which contains them. We have now only to demonstrate
how, and in what manner it is true that the Mediterranean, and all other
gulfs, and in short all the parts of the earth move with a motion
sensibly not uniform, although no motion results thence to the whole
globe which is not perfectly uniform and regular."

This unequable motion is derived from a combination of the earth's
motion on her axis, and in her orbit, the consequence of which is that a
point turned from the sun is carried in the same direction by the annual
and diurnal velocities, whereas a point on the opposite side of the
globe is carried in opposite directions by the annual and diurnal
motions, so that in every twenty-four hours the absolute motion through
space of every point in the earth completes a cycle of varying
swiftness. Those readers who are unacquainted with the mathematical
theory of motion must be satisfied with the assurance that this specious
representation is fallacious, and that the oscillation of the water does
not in the least result from the causes here assigned to it: the
reasoning necessary to prove this is not elementary enough to be
introduced here with propriety.

Besides the principal daily oscillation of the water, there is a monthly
inequality in the rise and fall, of which the extremes are called the
spring and neap tides: the manner in which Galileo attempted to bring
his theory to bear upon these phenomena is exceedingly curious.

"It is a natural and necessary truth, that if a body be made to revolve,
the time of revolution will be greater in a greater circle than in a
less: this is universally allowed, and fully confirmed by experiments,
such for instance as these:--In wheel clocks, especially in large ones,
to regulate the going, the workmen fit up a bar capable of revolving
horizontally, and fasten two leaden weights to the ends of it; and if
the clock goes too slow, by merely approaching these weights somewhat
towards the centre of the bar, they make its vibrations more frequent,
at which time they are moving in smaller circles than before.[112]--Or,
if you fasten a weight to a cord which you pass round a pulley in the
ceiling, and whilst the weight is vibrating draw in the cord towards
you, the vibrations will become sensibly accelerated as the length of
the string diminishes. We may observe the same rule to hold among the
celestial motions of the planets, of which we have a ready instance in
the Medicean planets, which revolve in such short periods round Jupiter.
We may therefore safely conclude, that if the moon for instance shall
continue to be forced round by the same moving power, and were to move
in a smaller circle, it would shorten the time of its revolution. Now
this very thing happens in fact to the moon, which I have just advanced
on a supposition. Let us call to mind that we have already concluded
with Copernicus, that it is impossible to separate the moon from the
earth, round which without doubt it moves in a month: we must also
remember that the globe of the earth, accompanied always by the moon,
revolves in the great circle round the sun in a year, in which time the
moon revolves round the earth about thirteen times, whence it follows
that the moon is sometimes near the sun, that is to say between the
earth and sun, sometimes far from it, when she is on the outside of the
earth. Now if it be true that the power which moves the earth and the
moon round the sun remains of the same efficacy, and if it be true that
the same moveable, acted on by the same force, passes over similar arcs
of circles in a time which is least when the circle is smallest, we are
forced to the conclusion that at new moon, when in conjunction with the
sun, the moon passes over greater arcs of the orbit round the sun, than
when in opposition at full moon; and this inequality of the moon will be
shared by the earth also. So that exactly the same thing happens as in
the balance of the clocks; for the moon here represents the leaden
weight, which at one time is fixed at a greater distance from the centre
to make the vibrations slower, and at another time nearer to accelerate
them."

Wallis adopted and improved this theory in a paper which he inserted in
the Philosophical Transactions for 1666, in which he declares, that the
circular motion round the sun should be considered as taking place at a
point which is the centre of gravity of the earth and moon. "To the
first objection, that it appears not how two bodies that have no tie can
have one common centre of gravity, I shall only answer, that it is
harder to show how they have it, than that they have it."[113] As Wallis
was perfectly competent from the time at which he lived, and his
knowledge of the farthest advances of science in his time, to appreciate
the value of Galileo's writings, we shall conclude this chapter with the
judgment that he has passed upon them in the same paper. "Since Galileo,
and after him Torricelli and others have applied mechanical principles
to the solving of philosophical difficulties, natural philosophy is well
known to have been rendered more intelligible, and to have made a much
greater progress in less than a hundred years than before for many
ages."


FOOTNOTES:

[93] See page 56.

[94] Playfair's Dissertation, Supp. Encyc. Brit.

[95] Astronomia Nova. Pragæ. 1609.

[96] The new Planet no Planet, or the Earth no wandering Star, except in
the wandering heads of Galileans. London, 1646.

[97] Aristarchi Samii de Mundi Systemate. Parisiis 1644.

[98] See page 12.

[99] De Coelo, lib. iv. cap. 3.

[100] Reflexiones Physico-Mathematicæ, Parisiis, 1647.

[101] Venturi.

[102] Riccioli.

[103] The notions commonly entertained of 'up' and 'down,' as connected
with the observer's own situation, had long been a stumbling-block in
the way of the new doctrines. When Columbus held out the certainty of
arriving in India by sailing to the westward on account of the earth's
roundness, it was gravely objected, that it might be well enough to sail
down to India, but that the chief difficulty would consist in climbing
up back again.

[104] See page 50.

[105] Riccioli Almag. Nov.

[106] Plutarch, De placit. Philos. lib. iii. c. 17.

[107] [sympatheôs tê selênê]. Geographiæ, lib. iii.

[108] Historia Naturalis, lib. ii. c, 97.

[109] Ut ancillante sidere, trahenteque secum avido haustu maria.

[110] Eâdem Aquiloniâ, et à terris longius recedente, mitiores quam cum,
in Austros digressâ, propiore nisu vim suam exercet.

[111] Commentarii Collegii Conimbricensis. Coloniæ, 1603.

[112] See fig. 1. p. 96.

[113] Phil. Trans., No. 16, August 1666.




CHAPTER XV.

    _Galileo at Arcetri--Becomes Blind--Moon's Libration--Publication of
      the Dialogues on Motion._


WE have already alluded to the imperfect state of the knowledge
possessed with regard to Galileo's domestic life and personal habits;
there is reason however to think that unpublished materials exist from
which these outlines might be in part filled up. Venturi informs us that
he had seen in the collection from which he derived a great part of the
substance of his Memoirs of Galileo, about one hundred and twenty
manuscript letters, dated between the years 1623 and 1633, addressed to
him by his daughter Maria, who with her sister had attached herself to
the convent of St. Matthew, close to Galileo's usual place of residence.
It is difficult not to think that much interesting information might be
obtained from these, with respect to Galileo's domestic character. The
very few published extracts confirm our favourable impressions of it,
and convey a pleasing idea of this his favourite daughter. Even when, in
her affectionate eagerness to soothe her father's wounded feelings at
the close of his imprisonment in Rome, she dwells with delight upon her
hopes of being allowed to relieve him, by taking on herself the
penitential recitations which formed a part of his sentence, the
prevalent feeling excited in every one by the perusal must surely be
sympathy with the filial tenderness which it is impossible to
misunderstand.

The joy she had anticipated in again meeting her parent, and in
compensating to him by her attentive affection the insults of his
malignant enemies, was destined to be but of short duration. Almost in
the same month in which Galileo returned to Arcetri she was seized with
a fatal illness; and already in the beginning of April, 1634, we learn
her death from the fruitless condolence of his friends. He was deeply
and bitterly affected by this additional blow, which came upon him when
he was himself in a weak and declining state of health, and his answers
breathe a spirit of the most hopeless and gloomy despondency.

In a letter written in April to Bocchineri, his son's father-in-law, he
says: "The hernia has returned worse than at first: my pulse is
intermitting, accompanied with a palpitation of the heart; an
immeasurable sadness and melancholy; an entire loss of appetite; I am
hateful to myself; and in short I feel that I am called incessantly by
my dear daughter. In this state, I do not think it advisable that
Vincenzo should set out on his journey, and leave me, when every hour
something may occur, which would make it expedient that he should be
here." In this extremity of ill health, Galileo requested leave to go to
Florence for the advantage of medical assistance; but far from obtaining
permission, it was intimated that any additional importunities would be
noticed by depriving him of the partial liberty he was then allowed to
enjoy. After several years confinement at Arcetri, during the whole of
which time he suffered from continual indisposition, the inquisitor
Fariano wrote to him in 1638, that the Pope permitted his removal to
Florence, for the purpose of recovering his health; requiring him at the
same time to present himself at the Office of the Inquisition, where he
would learn the conditions on which this favour had been granted. These
were that he should neither quit his house nor receive his friends
there; and so closely was the letter of these instructions adhered to,
that he was obliged to obtain a special permission to go out to attend
mass during Passion week. The strictness with which all personal
intercourse with his friends was interrupted, is manifest from the
result of the following letter from the Duke of Tuscany's secretary of
state to Nicolini, his ambassador at Rome. "Signor Galileo Galilei, from
his great age and the illnesses which afflict him, is in a condition
soon to go to another world; and although in this the eternal memory of
his fame and value is already secured, yet his Highness is greatly
desirous that the world should sustain as little loss as possible by his
death; that his labours may not perish, but for the public good may be
brought to that perfection which he will not be able to give them. He
has in his thoughts many things worthy of him, which he cannot be
prevailed on to communicate to any but Father Benedetto Castelli, in
whom he has entire confidence. His Highness wishes therefore that you
should see Castelli, and induce him to procure leave to come to Florence
for a few months for this purpose, which his Highness has very much at
heart; and if he obtains permission, as his Highness hopes, you will
furnish him with money and every thing else he may require for his
journey." Castelli, it will be remembered, was at this time salaried by
the court of Rome. Nicolini answered that Castelli had been himself to
the Pope to ask leave to go to Florence. Urban immediately intimated his
suspicions that his design was to see Galileo, and upon Castelli's
stating that certainly it would be impossible for him to refrain from
attempting to see him, he received permission to visit him in the
company of an officer of the Inquisition. At the end of some months
Galileo was remanded to Arcetri, which he never again quitted.

In addition to his other infirmities, a disorder which some years before
had affected the sight of his right eye returned in 1636; in the course
of the ensuing year the other eye began to fail also, and in a few
months he became totally blind. It would be difficult to find any even
among those who are the most careless to make a proper use of the
invaluable blessing of sight, who could bear unmoved to be deprived of
it, but on Galileo the loss fell with peculiar and terrible severity; on
him who had boasted that he would never cease from using the senses
which God had given him, in declaring the glory of his works, and the
business of whose life had been the splendid fulfilment of that
undertaking. "The noblest eye is darkened," said Castelli, "which nature
ever made: an eye so privileged, and gifted with such rare qualities,
that it may with truth be said to have seen more than all of those who
are gone, and to have opened the eyes of all who are to come." His own
patience and resignation under this fatal calamity are truly wonderful;
and if occasionally a word of complaint escaped him, it was in the
chastened tone of the following expressions--"Alas! your dear friend and
servant Galileo has become totally and irreparably blind; so that this
heaven, this earth, this universe, which with wonderful observations I
had enlarged a hundred and thousand times beyond the belief of by-gone
ages, henceforward for me is shrunk into the narrow space which I myself
fill in it.--So it pleases God: it shall therefore please me also."
Hopes were at first entertained by Galileo's friends, that the
blindness was occasioned by cataracts, and that he might look forward to
relief from the operation of couching; but it very soon appeared that
the disorder was not in the humours of the eye, but in a cloudiness of
the cornea, the symptoms of which all external remedies failed to
alleviate.

As long as the power was left him, he had indefatigably continued his
astronomical observations. Just before his sight began to decay, he had
observed a new phenomenon in the moon, which is now known by the name of
the moon's libration, the nature of which we will shortly explain. A
remarkable circumstance connected with the moon's motion is, that the
same side is always visible from the earth, showing that the moon turns
once on her own axis in exactly the time of her monthly revolution.[114]
But Galileo, who was by this time familiar with the whole of the moon's
visible surface, observed that the above-mentioned effect does not
accurately take place, but that a small part on either side comes
alternately forward into sight, and then again recedes, according to the
moon's various positions in the heavens. He was not long in detecting
one of the causes of this apparent libratory or rocking motion. It is
partly occasioned by our distance as spectators from the centre of the
earth, which is also the centre of the moon's motion. In consequence of
this, as the moon rises in the sky we get an additional view of the
lower half, and lose sight of a small part of the upper half which was
visible to us while we were looking down upon her when low in the
horizon. The other cause is not quite so simple, nor is it so certain
that Galileo adverted to it: it is however readily intelligible even to
those who are unacquainted with astronomy, if they will receive as a
fact that the monthly motion of the moon is not uniform, but that she
moves quicker at one time than another, whilst the motion of rotation on
her own axis, like that of the earth, is perfectly uniform. A very
little reflection will show that the observed phenomenon will
necessarily follow. If the moon did not turn on her axis, every side of
her would be successively presented, in the course of a month, towards
the earth; it is the motion of rotation which tends to carry the newly
discovered parts out of sight.

Let us suppose the moon to be in that part of her orbit where she moves
with her average motion, and that she is moving towards the part where
she moves most quickly. If the motion in the orbit were to remain the
same all the way round, the motion of rotation would be just sufficient
at every point to bring round the same part of the moon directly in
front of the earth. But since, from the supposed point, the moon is
moving for some time round the earth with a motion continually growing
quicker, the motion of rotation is not sufficiently quick to carry out
of sight the entire part discovered by the motion of translation. We
therefore get a glimpse of a narrow strip on the side _from_ which the
moon is moving, which strip grows broader and broader, till she passes
the point where she moves most swiftly, and reaches the point of average
swiftness on the opposite side of her orbit. Her motion is now
continually growing slower, and therefore from this point the motion of
rotation is too swift, and carries too much out of sight, or in other
words, brings into sight a strip on the side _towards_ which the moon is
moving. This increases till she passes the point of least swiftness, and
arrives at the point from which we began to trace her course, and the
phenomena are repeated in the same order.

This interesting observation closes the long list of Galileo's
discoveries in the heavens. After his abjuration, he ostensibly withdrew
himself in a great measure from his astronomical pursuits, and employed
himself till 1636 principally with his Dialogues on Motion, the last
work of consequence that he published. In that year he entered into
correspondence with the Elzevirs, through his friend Micanzio, on the
project of printing a complete edition of his writings. Among the
letters which Micanzio wrote on the subject is one intimating that he
had enjoyed the gratification, in his quality of Theologian to the
Republic of Venice, of refusing his sanction to a work written against
Galileo and Copernicus. The temper however in which this refusal was
announced, contrasts singularly with that of the Roman Inquisitors. "A
book was brought to me which a Veronese Capuchin has been writing, and
wished to print, denying the motion of the earth. I was inclined to let
it go, to make the world laugh, for the ignorant beast entitles every
one of the twelve arguments which compose his book, 'An irrefragable and
undeniable demonstration,' and then adduces nothing but such childish
trash as every man of sense has long discarded. For instance, this poor
animal understands so much geometry and mathematics, that he brings
forward as a demonstration, that if the earth could move, having nothing
to support it, it must necessarily fall. He ought to have added that
then we should catch all the quails. But when I saw that he speaks
indecently of you, and has had the impudence to put down an account of
what passed lately, saying that he is in possession of the whole of your
process and sentence, I desired the man who brought it to me to go and
be hanged. But you know the ingenuity of impertinence; I suspect he will
succeed elsewhere, because he is so enamoured of his absurdities, that
he believes them more firmly than his Bible."

After Galileo's condemnation at Rome, he had been placed by the
Inquisition in the list of authors the whole of whose writings, '_edita
et edenda_,' were strictly forbidden. Micanzio could not even obtain
permission to reprint the Essay on Floating Bodies, in spite of his
protestations that it did not in any way relate to the Copernican
theory. This was the greatest stigma with which the Inquisition were in
the habit of branding obnoxious authors; and, in consequence of it, when
Galileo had completed his Dialogues on Motion, he found great difficulty
in contriving their publication, the nature of which may be learned from
the account which Pieroni sent to Galileo of his endeavours to print
them in Germany. He first took the manuscript to Vienna, but found that
every book printed there must receive the approbation of the Jesuits;
and Galileo's old antagonist, Scheiner, happening to be in that city,
Pieroni feared lest he should interfere to prevent the publication
altogether, if the knowledge of it should reach him. Through the
intervention of Cardinal Dietrichstein, he therefore got permission to
have it printed at Olmutz, and that it should be approved by a
Dominican, so as to keep the whole business a secret from Scheiner and
his party; but during this negociation the Cardinal suddenly died, and
Pieroni being besides dissatisfied with the Olmutz type, carried back
the manuscript to Vienna, from which he heard that Scheiner had gone
into Silesia. A new approbation was there procured, and the work was
just on the point of being sent to press, when the dreaded Scheiner
re-appeared in Vienna, on which Pieroni again thought it advisable to
suspend the impression till his departure. In the mean time his own duty
as a military architect in the Emperor's service carried him to Prague,
where Cardinal Harrach, on a former occasion, had offered him the use of
the newly-erected University press. But Harrach happened not to be at
Prague, and this plan like the rest became abortive. In the meantime
Galileo, wearied with these delays, had engaged with Louis Elzevir, who
undertook to print the Dialogues at Amsterdam.

It is abundantly evident from Galileo's correspondence that this edition
was printed with his full concurrence, although, in order to obviate
further annoyance, he pretended that it was pirated from a manuscript
copy which he sent into France to the Comte de Noailles, to whom the
work is dedicated. The same dissimulation had been previously thought
necessary, on occasion of the Latin translation of "The Dialogues on the
System," by Bernegger, which Galileo expressly requested through his
friend Deodati, and of which he more than once privately signified his
approbation, presenting the translator with a valuable telescope,
although he publicly protested against its appearance. The story which
Bernegger introduced in his preface, tending to exculpate Galileo from
any share in the publication, is by his own confession a mere fiction.
Noailles had been ambassador at Rome, and, by his conduct there, well
deserved the compliment which Galileo paid him on the present occasion.

As an introduction to the account of this work, which Galileo considered
the best he had ever produced, it will become necessary to premise a
slight sketch of the nature of the mechanical philosophy which he found
prevailing, nearly as it had been delivered by Aristotle, with the same
view with which we introduced specimens of the astronomical opinions
current when Galileo began to write on that subject: they serve to show
the nature and objects of the reasoning which he had to oppose; and,
without some exposition of them, the aim and value of many of his
arguments would be imperfectly understood and appreciated.


FOOTNOTES:

[114] Frisi says that Galileo did not perceive this conclusion (Elogio
del Galileo); but see The Dial. on the System, Dial. 1. pp. 61, 62, 85.
Edit. 1744. Plutarch says, (De Placitis Philos. lib. ii. c. 28,) that
the Pythagoreans believed the moon to have inhabitants fifteen times as
large as men, and that their day is fifteen times as long as ours. It
seems probable, that the former of these opinions was engrafted on the
latter, which is true, and implies a perception of the fact in the text.




CHAPTER XVI.

    _State of the Science of Motion before Galileo._


IT is generally difficult to trace any branch of human knowledge up to
its origin, and more especially when, as in the case of mechanics, it is
very closely connected with the immediate wants of mankind. Little has
been told to us when we are informed that so soon as a man might wish to
remove a heavy stone, "he would be led, by natural instinct, to slide
under it the end of some long instrument, and that the same instinct
would teach him either to raise the further end, or to press it
downwards, so as to turn round upon some support placed as near to the
stone as possible."[115]

Montucla's history would have lost nothing in value, if, omitting "this
philosophical view of the birth of the art," he had contented himself
with his previous remark, that there can be little doubt that men were
familiar with the use of mechanical contrivances long before the idea
occurred of enumerating or describing them, or even of examining very
closely the nature and limits of the aid they are capable of affording.
The most careless observer indeed could scarcely overlook that the
weights heaved up with a lever, or rolled along a slope into their
intended places, reached them more slowly than those which the workmen
could lift directly in their hands; but it probably needed a much longer
time to enable them to see the exact relation which, in these and all
other machines, exists between the increase of the power to move, and
the decreasing swiftness of the thing moved.

In the preface to Galileo's Treatise on Mechanical Science, published in
1592, he is at some pains to set in a clear light the real advantages
belonging to the use of machines, "which (says he) I have thought it
necessary to do, because, if I mistake not, I see almost all mechanics
deceiving themselves in the belief that, by the help of a machine, they
can raise a greater weight than they are able to lift by the exertion of
the same force without it.--Now if we take any determinate weight, and
any force, and any distance whatever, it is beyond doubt that we can
move the weight to that distance by means of that force; because even
although the force may be exceedingly small, if we divide the weight
into a number of fragments, each of which is not too much for our force,
and carry these pieces one by one, at length we shall have removed the
whole weight; nor can we reasonably say at the end of our work, that
this great weight has been moved and carried away by a force less than
itself, unless we add that the force has passed several times over the
space through which the whole weight has gone but once. From which it
appears that the velocity of the force (understanding by velocity the
space gone through in a given time) has been as many times greater than
that of the weight, as the weight is greater than the force: nor can we
on that account say that a great force is overcome by a small one,
contrary to nature: then only might we say that nature is overcome when
a small force moves a great weight as swiftly as itself, which we assert
to be absolutely impossible with any machine either already or hereafter
to be contrived. But since it may occasionally happen that we have but a
small force, and want to move a great weight without dividing it into
pieces, then we must have recourse to a machine by means of which we
shall remove the given weight, with the given force, through the
required space. But nevertheless the force as before will have to travel
over that very same space as many times repeated as the weight surpasses
its power, so that, at the end of our work, we shall find that we have
derived no other benefit from our machine than that we have carried away
the same weight altogether, which if divided into pieces we could have
carried without the machine, by the same force, through the same space,
in the same time. This is one of the advantages of a machine, because it
often happens that we have a lack of force but abundance of time, and
that we wish to move great weights all at once."

This compensation of force and time has been fancifully personified by
saying that Nature cannot be cheated, and in scientific treatises on
mechanics, is called the "principle of virtual velocities," consisting
in the theorem that two weights will balance each other on any machine,
no matter how complicated or intricate the connecting contrivances may
be, when one weight bears to the other the same proportion that the
space through which the latter would be raised bears to that through
which the former would sink, in the first instant of their motion, if
the machine were stirred by a third force. The whole theory of machines
consists merely in generalizing and following out this principle into
its consequences; combined, when the machines are in a state of motion,
with another principle equally elementary, but to which our present
subject does not lead us to allude more particularly.

The credit of making known the principle of virtual velocities is
universally given to Galileo; and so far deservedly, that he undoubtedly
perceived the importance of it, and by introducing it everywhere into
his writings succeeded in recommending it to others; so that five and
twenty years after his death, Borelli, who had been one of Galileo's
pupils, calls it "that mechanical principle with which everybody is so
familiar[116]," and from that time to the present it has continued to be
taught as an elementary truth in most systems of mechanics. But although
Galileo had the merit in this, as in so many other cases, of
familiarizing and reconciling the world to the reception of truth, there
are remarkable traces before his time of the employment of this same
principle, some of which have been strangely disregarded. Lagrange
asserts[117] that the ancients were entirely ignorant of the principle
of virtual velocities, although Galileo, to whom he refers it,
distinctly mentions that he himself found it in the writings of
Aristotle. Montucla quotes a passage from Aristotle's Physics, in which
the law is stated generally, but adds that he did not perceive its
immediate application to the lever, and other machines. The passage to
which Galileo alludes is in Aristotle's Mechanics, where, in discussing
the properties of the lever, he says expressly, "the same force will
raise a greater weight, in proportion as the force is applied at a
greater distance from the fulcrum, and the reason, as I have already
said, is because it describes a greater circle; and a weight which is
farther removed from the centre is made to move through a greater
space."[118]

It is true, that in the last mentioned treatise, Aristotle has given
other reasons which belong to a very different kind of philosophy, and
which may lead us to doubt whether he fully saw the force of the one we
have just quoted. It appeared to him not wonderful that so many
mechanical paradoxes (as he called them) should be connected with
circular motion, since the circle itself seemed of so paradoxical a
nature. "For, in the first place, it is made up of an immoveable centre,
and a moveable radius, qualities which are contrary to each other. 2dly.
Its circumference is both convex and concave. 3dly. The motion by which
it is described is both forward and backward, for the describing radius
comes back to the place from which it started. 4thly. The radius is
_one_; but every point of it moves in describing the circle with a
different degree of swiftness."

Perhaps Aristotle may have borrowed the idea of virtual velocities,
contrasting so strongly with his other physical notions, from some older
writer; possibly from Archytas, who, we are told, was the first to
reduce the science of mechanics to methodical order;[119] and who by the
testimony of his countrymen was gifted with extraordinary talents,
although none of his works have come down to us. The other principles
and maxims of Aristotle's mechanical philosophy, which we shall have
occasion to cite, are scattered through his books on Mechanics, on the
Heavens, and in his Physical Lectures, and will therefore follow rather
unconnectedly, though we have endeavoured to arrange them with as much
regularity as possible.

After defining a body to be that which is divisible in every direction,
Aristotle proceeds to inquire how it happens that a body has only the
three dimensions of length, breadth, and thickness; and seems to think
he has given a reason in saying that, when we speak of two things, we do
not say "all," but "both," and three is the first number of which we say
"all."[120] When he comes to speak of motion, he says, "If motion is not
understood, we cannot but remain ignorant of Nature. Motion appears to
be of the nature of continuous quantities, and in continuous quantity
infinity first makes its appearance; so as to furnish some with a
definition who say that continuous quantity is that which is infinitely
divisible.--Moreover, unless there be time, space, and a vacuum, it is
impossible that there should be motion."[121]--Few propositions of
Aristotle's physical philosophy are more notorious than his assertion
that nature abhors a vacuum, on which account this last passage is the
more remarkable, as he certainly did not go so far as to deny the
existence of motion, and therefore asserts here the necessity of that of
which he afterwards attempts to show the absurdity.--"Motion is the
energy of what exists in power so far forth as so existing. It is that
act of a moveable which belongs to its power of moving."[122] After
struggling through such passages as the preceding we come at last to a
resting-place.--"It is difficult to understand what motion is."--When
the same question was once proposed to another Greek philosopher, he
walked away, saying, "I cannot tell you, but I will show you;" an answer
intrinsically worth more than all the subtleties of Aristotle, who was
not humble-minded enough to discover that he was tasking his genius
beyond the limits marked out for human comprehension.

He labours in the same manner and with the same success to vary the idea
of space. He begins the next book with declaring, that "those who say
there is a vacuum assert the existence of space; for a vacuum is space,
in which there is no substance;" and after a long and tedious reasoning
concludes that, "not only what space is, but also whether there be such
a thing, cannot but be doubted."[123] Of time he is content to say
merely, that "it is clear that time is not motion, but that without
motion there would be no time;"[124] and there is perhaps little fault
to be found with this remark, understanding motion in the general sense
in which Aristotle here applies it, of every description of change.

Proceeding after these remarks on the nature of motion in general to the
motion of bodies, we are told that "all local motion is either straight,
circular, or compounded of these two; for these two are the only simple
sorts of motion. Bodies are divided into simple and concrete; simple
bodies are those which have naturally a principle of motion, as fire and
earth, and their kinds. By simple motion is meant the motion of a simple
body."[125] By these expressions Aristotle did not mean that a simple
body cannot have what he calls a compound motion, but in that case he
called the motion violent or unnatural; this division of motion into
natural and violent runs through the whole of the mechanical philosophy
founded upon his principles. "Circular motion is the only one which can
be endless;"[126] the reason of which is given in another place: for
"that cannot be doing, which cannot be done; and therefore it cannot be
that a body should be moving towards a point (_i.e._ the end of an
infinite straight line) whither no motion is sufficient to bring
it."[127] Bacon seems to have had these passages in view when he
indulged in the reflections which we have quoted in page 14. "There are
four kinds of motion of one thing by another: Drawing, Pushing,
Carrying, Rolling. Of these, Carrying and Rolling may be referred to
Drawing and Pushing.[128]--The prime mover and the thing moved are
always in contact."

The principle of the composition of motions is stated very plainly:
"when a moveable is urged in two directions with motions bearing an
indefinitely small ratio to each other, it moves necessarily in a
straight line, which is the diameter of the figure formed by drawing the
two lines of direction in that ratio;"[129] and adds, in a singularly
curious passage, "but when it is urged for any time with two motions
which have an indefinitely small ratio one to another, the motion cannot
be straight, so that a body describes a curve, when it is urged by two
motions bearing an indefinitely small ratio one to another, and lasting
an indefinitely small time."[130]

He seemed on the point of discovering some of the real laws of motion,
when he was led to ask--"Why are bodies in motion more easily moved than
those which are at rest?--And why does the motion cease of things cast
into the air? Is it that the force has ceased which sent them forth, or
is there a struggle against the motion, or is it through the disposition
to fall, does it become stronger than the projectile force, or is it
foolish to entertain doubts on this question, when the body has quitted
the principle of its motion?" A commentator at the close of the
sixteenth century says on this passage: "They fall because every thing
recurs to its nature; for if you throw a stone a thousand times into the
air, it will never accustom itself to move upwards." Perhaps we shall
now find it difficult not to smile at the idea we may form of this
luckless experimentalist, teaching stones to fly; yet it may be useful
to remember that it is only because we have already collected an opinion
from the results of a vast number of observations in the daily
experience of life, that our ridicule would not be altogether misplaced,
and that we are totally unable to determine by any kind of reasoning,
unaccompanied by experiment, whether a stone thrown into the air would
fall again to the earth, or move for ever upwards, or in any other
conceivable manner and direction.

The opinion which Aristotle held, that motion must be caused by
something in contact with the body moved, led him to his famous theory
that falling bodies are accelerated by the air through which they pass.
We will show how it was attempted to explain this process when we come
to speak of more modern authors. He classed natural bodies into heavy
and light, remarking at the same time that it is clear that there are
some bodies possessing neither gravity nor levity."[131] By light bodies
he understood those which have a natural tendency to move from the
earth, observing that "that which is lighter is not always light."[132]
He maintained that the heavenly bodies were altogether devoid of
gravity; and we have already had occasion to mention his assertion, that
a large body falls faster than a small one in proportion to its
weight.[133] With this opinion may be classed another great mistake, in
maintaining that the same bodies fall through different mediums, as air
or water, with velocities reciprocally proportional to their densities.
By a singular inversion of experimental science, Cardan, relying on this
assertion, proposed in the sixteenth century to determine the densities
of air and water by observing the different times taken by a stone in
falling through them.[134] Galileo inquired afterwards why the
experiment should not be made with a cork, which pertinent question put
an end to the theory.

There are curious traces still preserved in the poem of Lucretius of a
mechanical philosophy, of which the credit is in general given to
Democritus, where many principles are inculcated strongly at variance
with Aristotle's notions. We find absolute levity denied, and not only
the assertion that in a vacuum all things would fall, but that they
would fall with the same velocity; and the inequalities which we observe
are attributed to the right cause, the impediment of the air, although
the error remains of believing the velocity of bodies falling through
the air to be proportional to their weight.[135] Such specimens of this
earlier philosophy may well indispose us towards Aristotle, who was as
successful in the science of motion as he was in astronomy in
suppressing the knowledge of a theory so much sounder than that which he
imposed so long upon the credulity of his blinded admirers.

An agreeable contrast to Aristotle's mystical sayings and fruitless
syllogisms is presented in Archimedes' book on Equilibrium, in which he
demonstrates very satisfactorily, though with greater cumbrousness of
apparatus than is now thought necessary, the principal properties of the
lever. This and the Treatise on the Equilibrium of Floating Bodies are
the only mechanical works which have reached us of this writer, who was
by common consent one of the most accomplished mathematicians of
antiquity. Ptolemy the astronomer wrote also a Treatise on Mechanics,
now lost, which probably contained much that would be interesting in the
history of mechanics; for Pappus says, in the Preface to the Eighth Book
of his Mathematical Collections: "There is no occasion for me to explain
what is meant by a heavy, and what by a light body, and why bodies are
carried up and down, and in what sense these very words 'up' and 'down'
are to be taken, and by what limits they are bounded; for all this is
declared in Ptolemy's Mechanics."[136] This book of Ptolemy's appears to
have been also known by Eutocius, a commentator of Archimedes, who lived
about the end of the fifth century of our era; he intimates that the
doctrines contained in it are grounded upon Aristotle's; if so, its loss
is less to be lamented. Pappus's own book deserves attention for the
enumeration which he makes of the mechanical powers, namely, the wheel
and axle, the lever, pullies, the wedge and the screw. He gives the
credit to Hero and Philo of having shown, in works which have not
reached us, that the theory of all these machines is the same. In Pappus
we also find the first attempt to discover the force necessary to
support a given weight on an inclined plane. This in fact is involved in
the theory of the screw; and the same vicious reasoning which Pappus
employs on this occasion was probably found in those treatises which he
quotes with so much approbation. Numerous as are the faults of his
pretended demonstration, it was received undoubtingly for a long period.

[Illustration: Chain.]

The credit of first giving the true theory of equilibrium on the
inclined plane is usually ascribed to Stevin, although, as we shall
presently show, with very little reason. Stevin supposed a chain to be
placed over two inclined planes, and to hang down in the manner
represented in the figure. He then urged that the chain would be in
equilibrium; for otherwise, it would incessantly continue in motion, if
there were any cause why it should begin to move. This being conceded,
he remarks further, that the parts AD and BD are also in equilibrium,
being exactly similar to each other; and therefore if they are taken
away, the remaining parts AC and BC will also be in equilibrium. The
weights of these parts are proportional to the lengths AC and BC; and
hence Stevin concluded that two weights would balance on two inclined
planes, which are to each other as the lengths of the planes included
between the same parallels to the horizon.[137] This conclusion is the
correct one, and there is certainly great ingenuity in this contrivance
to facilitate the demonstration; it must not however be mistaken for an
_à priori_ proof, as it sometimes seems to have been: we should remember
that the experiments which led to the principle of virtual velocities
are also necessary to show the absurdity of supposing a perpetual
motion, which is made the foundation of this theorem. That principle had
been applied directly to determine the same proportion in a work written
long before, where it has remained singularly concealed from the notice
of most who have written on this subject. The book bears the name of
Jordanus, who lived at Namur in the thirteenth century; but Commandine,
who refers to it in his Commentary on Pappus, considers it as the work
of an earlier period. The author takes the principle of virtual
velocities for the groundwork of his explanations, both of the lever and
inclined plane; the latter will not occupy much space, and in an
historical point of view is too curious to be omitted.

"_Quæst. 10._--If two weights descend by paths of different
obliquities, and the proportion be the same of the weights and the
inclinations taken in the same order, they will have the same descending
force. By the inclinations, I do not mean the angles, but the paths up
to the point in which both meet the same perpendicular.[138] Let,
therefore, _e_ be the weight upon _dc_, and _h_ upon _da_, and let _e_
be to _h_ as _dc_ to _da_. I say these weights, in this situation, are
equally effective. Take _dk_ equally inclined with _dc_, and upon it a
weight equal to _e_, which call 6. If possible let _e_ descend to _l_,
so as to raise _h_ to _m_, and take 6_n_ equal to _hm_ or _el_, and draw
the horizontal and perpendicular lines as in the figure.

[Illustration]

  Then _nz_:_n_6 :: _db_:_dk_
  and _mh_:_mx_ :: _da_:_db_

therefore _nz_:_mx_ :: _da_:_dk_ :: _h_:6, _and therefore since er is
not able to raise_ 6 _to n, neither will it be able to raise h to m_;
therefore they will remain as they are."[139] The passage in Italics
tacitly assumes the principle in question. Tartalea, who edited
Jordanus's book in 1565, has copied this theorem _verbatim_ into one of
his own treatises, and from that time it appears to have attracted no
further attention. The rest of the book is of an inferior description.
We find Aristotle's doctrine repeated, that the velocity of a falling
body is proportional to its weight; that the weight of a heavy body
changes with its form; and other similar opinions. The manner in which
falling bodies are accelerated by the air is given in detail. "By its
first motion the heavy body will drag after it what is behind, and move
what is just below it; and these when put in motion move what is next to
them, so that by being set in motion they less impede the falling body.
In this manner it has the effect of being heavier, and impels still more
those which give way before it, until at last they are no longer
impelled, but begin to drag. And thus it happens that its gravity is
increased by their attraction, and their motion by its gravity, whence
we see that its velocity is continually multiplied."

In this short review of the state of mechanical science before Galileo,
the name of Guido Ubaldi ought not to be omitted, although his works
contain little or nothing original. We have already mentioned Benedetti
as having successfully attacked some of Aristotle's statical doctrines,
but it is to be noticed that the laws of motion were little if at all
examined by any of these writers. There are a few theorems connected
with this latter subject in Cardan's extraordinary book "On
Proportions," but for the most part false and contradictory. In the
seventy-first proposition of his fifth book, he examines the force of
the screw in supporting a given weight, and determines it accurately on
the principle of virtual velocities; namely, that the power applied at
the end of the horizontal lever must make a complete circuit at that
distance from the centre, whilst the weight rises through the
perpendicular height of the thread. The very next proposition in the
same page is to find the same relation between the power and weight on
an inclined plane; and although the identity of principle in these two
mechanical aids was well known, yet Cardan declares the necessary
sustaining force to vary as the angle of inclination of the plane, for
no better reason than that such an expression will properly represent it
at the two limiting angles of inclination, since the force is nothing
when the plane is horizontal, and equal to the weight when
perpendicular. This again shows how cautious we should be in attributing
the full knowledge of general principles to these early writers, on
account of occasional indications of their having employed them.


FOOTNOTES:

[115] Histoire des Mathématiques, vol. i. p. 97.

[116] De vi Percussionis, Bononiæ, 1667.

[117] Mec. Analyt.

[118] Mechanica.

[119] Diog. Laert. In vit. Archyt.

[120] De Coelo, lib. i. c. 1.

[121] Phys. lib. i. c. 3.

[122] Lib. iii. c. 2. The Aristotelians distinguished between things as
existing in act or energy ([energeia]) and things in capacity or power
([dynamis]). For the advantage of those who may think the distinction
worth attending to, we give an illustration of Aristotle's meaning, from
a very acute and learned commentator:--"It (motion) is something more
than dead capacity; something less than perfect actuality; capacity
roused, and striving to quit its latent character; not the capable
brass, nor yet the actual statue, but the capacity in energy; that is to
say, the brass in fusion while it is becoming the statue and is not yet
become."--"The bow moves not because it may be bent, nor because it is
bent; but the motion lies between; lies in an imperfect and obscure
union of the two together; is the actuality (if I may so say) even of
capacity itself: imperfect and obscure, because such is capacity to
which it belongs."--Harris, Philosophical Arrangements.

[123] Lib. iv. c. 1.

[124] Lib. iv. c. 11.

[125] De Coelo, lib. i. c. 2.

[126] Phys. lib. vii. c. 8.

[127] De Coelo, lib. i. c. 6.

[128] Phys. lib. vii. c. 2.

[129] Mechanica.

[130] [Ean de en mêdeni logô pherêtai duo phoras kata mêdena chronon,
adynaton eutheian einai tên phoran. Ean gar tina logon enechthê en
chronô tini touton anagkê ton chronon eutheian einai phoran dia ta
proeirêmena, hôste peripheres ginetai duo pheromenon phoras en mêdeni
logô mêdena chronon.]--_i.e._ v = ds/dt

[131] De Coelo, lib. i. c. 3.

[132] Lib. iv. c. 2.

[133] Phys., lib. iv. c. 8.

[134] De Proport. Basileæ, 1570.

[135]

    "Nunc locus est, ut opinor, in his illud quoque rebus
    Confirmare tibi, nullam rem posse suâ vi
    Corpoream sursum ferri, sursumque meare.--
    Nec quom subsiliunt ignes ad tecta domorum,
    Et celeri flammâ degustant tigna trabeisque
    Sponte suâ facere id sine vi subicente putandum est.
    --Nonne vides etiam quantâ vi tigna trabeisque
    Respuat humor aquæ? Nam quod magi' mersimus altum
    Directâ et magnâ vi multi pressimus ægre:--
    Tam cupide sursum revomit magis atque remittit
    Plus ut parte foras emergant, exsiliantque:
    --Nec tamen hæc, quantu'st in sedubitamus, opinor,
    Quinvacuum per inane deorsum cuncta ferantur,
    Sic igitur debent flammæ quoque posse per auras
    Aeris expressæ sursum subsidere, quamquam
    Pondera quantum in se est deorsum deducere pugnent.
    --Quod si forte aliquis credit Graviora potesse
    Corpora, quo citius rectum per Inane feruntur,
    --Avius a verâ longe ratione recedit.
    Nam per Aquas quæcunque cadunt atque Aera deorsum
    Hæc pro ponderibus casus celerare necesse 'st
    Propterea quia corpus Aquæ, naturaque tenuis
    Aeris haud possunt æque rem quamque morari:
    Sed citius cedunt Gravioribus exsuperata.
    At contra nulli de nullâ parte, neque ullo
    Tempore Inane potest Vacuum subsistere reii
    Quin, sua quod natura petit, considere pergat:
    Omnia quâ propter debent per Inane quietum
    Æque ponderibus non æquis concita ferri."

                                   De Rerum Natura, lib. ii, v. 184-239.

[136] Math. Coll. Pisani, 1662.

[137] Oeuvres Mathématiques. Leyde, 1634.

[138] This is not a literal translation, but by what follows, is
evidently the Author's meaning. His words are, "Proportionem igitur
declinationum dico non angulorum, sed linearum usque ad æquidistantem
resecationem in quâ æqualiter sumunt de directo."

[139] Opusculum De Ponderositate. Venetiis, 1565.




CHAPTER XVII.

    _Galileo's theory of Motion--Extracts from the Dialogues._


DURING Galileo's residence at Sienna, when his recent persecution had
rendered astronomy an ungrateful, and indeed an unsafe occupation for
his ever active mind, he returned with increased pleasure to the
favourite employment of his earlier years, an inquiry into the laws and
phenomena of motion. His manuscript treatises on motion, written about
1590, which are mentioned by Venturi to be in the Ducal library at
Florence, seem, from the published titles of the chapters, to consist
principally of objections to the theory of Aristotle; a few only appear
to enter on a new field of speculation. The 11th, 13th, and 17th
chapters relate to the motion of bodies on variously inclined planes,
and of projectiles. The title of the 14th implies a new theory of
accelerated motion, and the assertion in that of the 16th, that a body
falling naturally for however great a time would never acquire more than
an assignable degree of velocity, shows that at this early period
Galileo had formed just and accurate notions of the action of a
resisting medium. It is hazardous to conjecture how much he might have
then acquired of what we should now call more elementary knowledge; a
safer course will be to trace his progress through existing documents in
their chronological order. In 1602 we find Galileo apologizing in a
letter addressed to his early patron the Marchese Guido Ubaldi, for
pressing again upon his attention the isochronism of the pendulum, which
Ubaldi had rejected as false and impossible. It may not be superfluous
to observe that Galileo's results are not quite accurate, for there is a
perceptible increase in the time occupied by the oscillations in larger
arcs; it is therefore probable that he was induced to speak so
confidently of their perfect equality, from attributing the increase of
time which he could not avoid remarking to the increased resistance of
the air during the larger vibrations. The analytical methods then known
would not permit him to discover the curious fact, that the time of a
total vibration is not sensibly altered by this cause, except so far as
it diminishes the extent of the swing, and thus in fact, (paradoxical as
it may sound) renders each oscillation successively more rapid, though
in a very small degree. He does indeed make the same remark, that the
resistance of the air will not affect the time of the oscillation, but
that assertion was a consequence of his erroneous belief that the time
of vibration in all arcs is the same. Had he been aware of the
variation, there is no reason to think that he could have perceived that
this result is not affected by it. In this letter is the first mention
of the theorem, that the times of fall down all the chords drawn from
the lowest point of a circle are equal; and another, from which Galileo
afterwards deduced the curious result, that it takes less time to fall
down the curve than down the chord, notwithstanding the latter is the
direct and shortest course. In conclusion he says, "Up to this point I
can go without exceeding the limits of mechanics, but I have not yet
been able to demonstrate that all arcs are passed in the same time,
which is what I am seeking." In 1604 he addressed the following letter
to Sarpi, suggesting the false theory sometimes called Baliani's, who
took it from Galileo.

[Illustration:

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"Returning to the subject of motion, in which I was entirely without a
fixed principle, from which to deduce the phenomena I have observed, I
have hit upon a proposition, which seems natural and likely enough; and
if I take it for granted, I can show that the spaces passed in natural
motion are in the double proportion of the times, and consequently that
the spaces passed in equal times are as the odd numbers beginning from
unity, and the rest. The principle is this, that the swiftness of the
moveable increases in the proportion of its distance from the point
whence it began to move; as for instance,--if a heavy body drop from A
towards D, by the line ABCD, I suppose the degree of velocity which it
has at B to bear to the velocity at C the ratio of AB to AC. I shall be
very glad if your Reverence will consider this, and tell me your opinion
of it. If we admit this principle, not only, as I have said, shall we
demonstrate the other conclusions, but we have it in our power to show
that a body falling naturally, and another projected upwards, pass
through the same degrees of velocity. For if the projectile be cast up
from D to A, it is clear that at D it has force enough to reach A, and
no farther; and when it has reached C and B, it is equally clear that it
is still joined to a degree of force capable of carrying it to A: thus
it is manifest that the forces at D, C and B decrease in the proportion
of AB, AC, and AD; so that if, in falling, the degrees of velocity
observe the same proportion, that is true which I have hitherto
maintained and believed."

We have no means of knowing how early Galileo discovered the fallacy of
this reasoning. In his Dialogues on Motion, which contain the correct
theory, he has put this erroneous supposition in the mouth of Sagredo,
on which Salviati remarks, "Your discourse has so much likelihood in it,
that our author himself did not deny to me when I proposed it to him,
that he also had been for some time in the same mistake. But that which
I afterwards extremely wondered at, was to see discovered in four plain
words, not only the falsity, but the impossibility of a supposition
carrying with it so much of seeming truth, that although I proposed it
to many, I never met with any one but did freely admit it to be so; and
yet it is as false and impossible as that motion is made in an instant:
for if the velocities are as the spaces passed, those spaces will be
passed in equal times, and consequently all motion must be
instantaneous." The following manner of putting this reasoning will
perhaps make the conclusion clearer. The velocity at any point is the
space that would be passed in the next moment of time, if the motion be
supposed to continue the same as at that point. At the beginning of the
time, when the body is at rest, the motion is none; and therefore, on
this theory, the space passed in the next moment is none, and thus it
will be seen that the body cannot begin to move according to the
supposed law.

A curious fact, noticed by Guido Grandi in his commentary on Galileo's
Dialogues on Motion, is that this false law of acceleration is precisely
that which would make a circular arc the shortest line of descent
between two given points; and although in general Galileo only declared
that the fall down the arc is made in less time than down the chord (in
which he is quite correct), yet in some places he seems to assert that
the circular arc is absolutely the shortest line of descent, which is
not true. It has been thought possible that the law, which on reflection
he perceived to be impossible, might have originally recommended itself
to him from his perception that it satisfied his prejudice in this
respect.

John Bernouilli, one of the first mathematicians in Europe at the
beginning of the last century, has given us a proof that such a reason
might impose even on a strong understanding, in the following argument
urged by him in favour of Galileo's second and correct theory, that the
spaces vary as the squares of the times. He had been investigating the
curve of swiftest descent, and found it to be a cycloid, the same curve
in which Huyghens had already proved that all oscillations are made in
accurately equal times. "I think it," says he, "worthy of remark that
this identity only occurs on Galileo's supposition, so that this alone
might lead us to presume it to be the real law of nature. For nature,
which always does everything in the very simplest manner, thus makes one
line do double work, whereas on any other supposition, we must have had
two lines, one for equal oscillations, the other for the shortest
descent."[140]

Venturi mentions a letter addressed to Galileo in May 1609 by Luca
Valerio, thanking him for his experiments on the descent of bodies on
inclined planes. His method of making these experiments is detailed in
the Dialogues on Motion:--"In a rule, or rather plank of wood, about
twelve yards long, half a yard broad one way, and three inches the
other, we made upon the narrow side or edge a groove of little more than
an inch wide: we cut it very straight, and, to make it very smooth and
sleek, we glued upon it a piece of vellum, polished and smoothed as
exactly as possible, and in that we let fall a very hard, round, and
smooth brass ball, raising one of the ends of the plank a yard or two at
pleasure above the horizontal plane. We observed, in the manner that I
shall tell you presently, the time which it spent in running down, and
repeated the same observation again and again to assure ourselves of the
time, in which we never found any difference, no, not so much as the
tenth part of one beat of the pulse. Having made and settled this
experiment, we let the same ball descend through a fourth part only of
the length of the groove, and found the measured time to be exactly half
the former. Continuing our experiments with other portions of the
length, comparing the fall through the whole with the fall through half,
two-thirds, three-fourths, in short, with the fall through any part, we
found by many hundred experiments that the spaces passed over were as
the squares of the times, and that this was the case in all inclinations
of the plank; during which, we also remarked that the times of descent,
on different inclinations, observe accurately the proportion assigned to
them farther on, and demonstrated by our author. As to the estimation of
the time, we hung up a great bucket full of water, which by a very small
hole pierced in the bottom squirted out a fine thread of water, which we
caught in a small glass during the whole time of the different descents:
then weighing from time to time, in an exact pair of scales, the
quantity of water caught in this way, the differences and proportions of
their weights gave the differences and proportions of the times; and
this with such exactness that, as I said before, although the
experiments were repeated again and again, they never differed in any
degree worth noticing." In order to get rid of the friction, Galileo
afterwards substituted experiments with the pendulum; but with all his
care he erred very widely in his determination of the space through
which a body would fall in 1´´, if the resistance of the air and all
other impediments were removed. He fixed it at 4 _braccia_: Mersenne has
engraved the length of the '_braccia_' used by Galileo, in his "Harmonie
Universelle," from which it appears to be about 23½ English inches, so
that Galileo's result is rather less than eight feet. Mersenne's own
result from direct observation was thirteen feet: he also made
experiments in St. Peter's at Rome, with a pendulum 325 feet long, the
vibrations of which were made in 10´´; from this the fall in 1´´ might
have been deduced rather more than sixteen feet, which is very close to
the truth.

From another letter also written in the early part of 1609, we learn
that Galileo was then busied with examining the strength and resistance
"of beams of different sizes and forms, and how much weaker they are in
the middle than at the ends, and how much greater weight they can
support laid along their whole length, than if sustained on a single
point, and of what form they should be so as to be equally strong
throughout." He was also speculating on the motion of projectiles, and
had satisfied himself that their motion in a vertical direction is
unaffected by their horizontal velocity; a conclusion which, combined
with his other experiments, led him afterwards to determine the path of
a projectile in a non-resisting medium to be parabolical.

Tartalea is supposed to have been the first to remark that no bullet
moves in a horizontal line; but his theory beyond this point was very
erroneous, for he supposed the bullet's path through the air to be made
up of an ascending and descending straight line, connected in the middle
by a circular arc.

Thomas Digges, in his treatise on the Newe Science of Great Artillerie,
came much nearer the truth; for he remarked[141], that "The bullet
violentlye throwne out of the peece by the furie of the poulder hath two
motions: the one violent, which endeuoreth to carry the bullet right out
in his line diagonall, according to the direction of the peece's axis,
from whence the violent motion proceedeth; the other naturall in the
bullet itselfe, which endeuoreth still to carrye the same directlye
downeward by a right line perpendiculare to the horizon, and which dooth
though insensiblye euen from the beginning by little and little drawe it
from that direct and diagonall course." And a little farther he observes
that "These middle curve arkes of the bullet's circuite, compounded of
the violent and naturall motions of the bullet, albeit they be indeed
mere helicall, yet have they a very great resemblance of the Arkes
Conical. And in randons above 45° they doe much resemble the Hyperbole,
and in all vnder the Ellepsis. But exactlye they neuer accorde, being
indeed Spirall mixte and Helicall."

Perhaps Digges deserves no greater credit from this latter passage than
the praise of a sharp and accurate eye, for he does not appear to have
founded this determination of the form of the curve on any theory of the
direct fall of bodies; but Galileo's arrival at the same result was
preceded, as we have seen, by a careful examination of the simplest
phenomena into which this compound motion may be resolved. But it is
time to proceed to the analysis of his "Dialogues on Motion," these
preliminary remarks on their subject matter having been merely intended
to show how long before their publication Galileo was in possession of
the principal theories contained in them.

Descartes, in one of his letters to Mersenne, insinuates that Galileo
had taken many things in these Dialogues from him: the two which he
especially instances are the isochronism of the pendulum, and the law of
the spaces varying as the squares of the times.[142] Descartes was born
in 1596: we have shown that Galileo observed the isochronism of the
pendulum in 1583, and knew the law of the spaces in 1604, although he
was then attempting to deduce it from an erroneous principle. As
Descartes on more than one occasion has been made to usurp the credit
due to Galileo, (in no instance more glaringly so than when he has been
absurdly styled the forerunner of Newton,) it will not be misplaced to
mention a few of his opinions on these subjects, recorded in his letters
to Mersenne in the collection of his letters just cited:--"I am
astonished at what you tell me of having found by experiment that bodies
thrown up in the air take neither more nor less time to rise than to
fall again; and you will excuse me if I say that I look upon the
experiment as a very difficult one to make accurately. This proportion
of increase according to the odd numbers 1, 3, 5, 7, &c., which is in
Galileo, and which I think I wrote to you some time back, cannot be
true, as I believe I intimated at the same time, unless we make two or
three suppositions which are entirely false. One is Galileo's opinion,
that motion increases gradually from the slowest degree; and the other
is, that the air makes no resistance." In a later letter to the same
person he says, apparently with some uneasiness, "I have been revising
my notes on Galileo, in which I have not said expressly, that falling
bodies do not pass through every degree of slowness, but I said that
this cannot be determined without knowing what weight is; _which comes
to the same thing_. As to your example, I grant that it proves that
every degree of velocity is infinitely divisible, but not that a falling
body actually passes through all these divisions.--It is certain that a
stone is not equally disposed to receive a new motion or increase of
velocity, when it is already moving very quickly, and when it is moving
slowly. But I believe that I am now able to determine in what proportion
the velocity of a stone increases, not when falling in a vacuum, but in
this substantial atmosphere.--However I have now got my mind full of
other things, and I cannot amuse myself with hunting this out, _nor is
it a matter of much utility_." He afterwards returns once more to the
same subject:--"As to what Galileo says, that falling bodies pass
through every degree of velocity, I do not believe that it generally
happens, but I allow it is not impossible that it may happen
occasionally." After this the reader will know what value to attach to
the following assertion by the same Descartes:--"I see nothing in
Galileo's books to envy him, and hardly any thing which I would own as
mine;" and then may judge how far Salusbury's blunt declaration is borne
out, "Where or when did any one appear that durst enter the lists with
our Galileus? save only one bold and unfortunate Frenchman, who yet no
sooner came within the ring but he was hissed out again."[143]

The principal merit of Descartes must undoubtedly be derived from the
great advances he made in what are generally termed Abstract or Pure
Mathematics; nor was he slow to point out to Mersenne and his other
friends the acknowledged inferiority of Galileo to himself in this
respect. We have not sufficient proof that this difference would have
existed if Galileo's attention had been equally directed to that object;
the singular elegance of some of his geometrical constructions indicates
great talent for this as well as for his own more favourite
speculations. But he was far more profitably employed: geometry and pure
mathematics already far outstripped any useful application of their
results to physical science, and it was the business of Galileo's life
to bring up the latter to the same level. He found abstract theorems
already demonstrated in sufficient number for his purpose, nor was there
occasion to task his genius in search of new methods of inquiry, till
all was exhausted which could be learned from those already in use. The
result of his labours was that in the age immediately succeeding
Galileo, the study of nature was no longer in arrear of the abstract
theories of number and measure; and when the genius of Newton pressed it
forward to a still higher degree of perfection, it became necessary to
discover at the same time more powerful instruments of investigation.
This alternating process has been successfully continued to the present
time; the analyst acts as the pioneer of the naturalist, so that the
abstract researches, which at first have no value but in the eyes of
those to whom an elegant formula, in its own beauty, is a source of
pleasure as real and as refined as a painting or a statue, are often
found to furnish the only means for penetrating into the most intricate
and concealed phenomena of natural philosophy.

Descartes and Delambre agree in suspecting that Galileo preferred the
dialogistic form for his treatises, because it afforded a ready
opportunity for him to praise his own inventions: the reason which he
himself gave is, the greater facility for introducing new matter and
collateral inquiries, such as he seldom failed to add each time that he
reperused his work. We shall select in the first place enough to show
the extent of his knowledge on the principal subject, motion, and shall
then allude as well as our limits will allow to the various other points
incidentally brought forward.

The dialogues are between the same speakers as in the "System of the
World;" and in the first Simplicio gives Aristotle's proof,[144] that
motion in a vacuum is impossible, because according to him bodies move
with velocities in the compound proportion of their weights and the
rarities of the mediums through which they move. And since the density
of a vacuum bears no assignable ratio to that of any medium in which
motion has been observed, any body which should employ time in moving
through the latter, would pass through the same distance in a vacuum
instantaneously, which is impossible. Salviati replies by denying the
axioms, and asserts that if a cannon ball weighing 200 lbs., and a
musket ball weighing half a pound, be dropped together from a tower 200
yards high, the former will not anticipate the latter by so much as a
foot; "and I would not have you do as some are wont, who fasten upon
some saying of mine that may want a hair's breadth of the truth, and
under this hair they seek to hide another man's blunder as big as a
cable. Aristotle says that an iron ball weighing 100 lbs. will fall from
the height of 100 yards while a weight of one pound falls but one yard:
I say they will reach the ground together. They find the bigger to
anticipate the less by two inches, and under these two inches they seek
to hide Aristotle's 99 yards." In the course of his reply to this
argument Salviati formally announces the principle which is the
foundation of the whole of Galileo's theory of motion, and which must
therefore be quoted in his own words:--"A heavy body has by nature an
intrinsic principle of moving towards the common centre of heavy things;
that is to say, to the centre of our terrestrial globe, with a motion
continually accelerated in such manner that in equal times there are
always equal additions of velocity. This is to be understood as holding
true only when all accidental and external impediments are removed,
amongst which is one that we cannot obviate, namely, the resistance of
the medium. This opposes itself, less or more, accordingly as it is to
open more slowly or hastily to make way for the moveable, which being by
its own nature, as I have said, continually accelerated, consequently
encounters a continually increasing resistance in the medium, until at
last the velocity reaches that degree, and the resistance that power,
that they balance each other; all further acceleration is prevented, and
the moveable continues ever after with an uniform and equable motion."
That such a limiting velocity is not greater than some which may be
exhibited may be proved as Galileo suggested by firing a bullet upwards,
which will in its descent strike the ground with less force than it
would have done if immediately from the mouth of the gun; for he argued
that the degree of velocity which the air's resistance is capable of
diminishing must be greater than that which could ever be reached by a
body falling naturally from rest. "I do not think the present occasion a
fit one for examining the cause of this acceleration of natural motion,
on which the opinions of philosophers are much divided; some referring
it to the approach towards the centre, some to the continual diminution
of that part of the medium remaining to be divided, some to a certain
extrusion of the ambient medium, which uniting again behind the moveable
presses and hurries it forwards. All these fancies, with others of the
like sort, we might spend our time in examining, and with little to gain
by resolving them. It is enough for our author at present that we
understand his object to be the investigation and examination of some
phenomena of a motion so accelerated, (no matter what may be the cause,)
that the momenta of velocity, from the beginning to move from rest,
increase in the simple proportion in which the time increases, which is
as much as to say, that in equal times are equal additions of velocity.
And if it shall turn out that the phenomena demonstrated on this
supposition are verified in the motion of falling and naturally
accelerated weights, we may thence conclude that the assumed definition
does describe the motion of heavy bodies, and that it is true that their
acceleration varies in the ratio of the time of motion."

When Galileo first published these Dialogues on Motion, he was obliged
to rest his demonstrations upon another principle besides, namely, that
the velocity acquired in falling down all inclined planes of the same
perpendicular height is the same. As this result was derived directly
from experiment, and from that only, his theory was so far imperfect
till he could show its consistency with the above supposed law of
acceleration. When Viviani was studying with Galileo, he expressed his
dissatisfaction at this chasm in the reasoning; the consequence of which
was, that Galileo, as he lay the same night, sleepless through
indisposition, discovered the proof which he had long sought in vain,
and introduced it into the subsequent editions. The third dialogue is
principally taken up with theorems on the direct fall of bodies, their
times of descent down differently inclined planes, which in planes of
the same height he determined to be as the lengths, and with other
inquiries connected with the same subject, such as the straight lines of
shortest descent under different data, &c.

[Illustration]

The fourth dialogue is appropriated to projectile motion, determined
upon the principle that the horizontal motion will continue the same as
if there were no vertical motion, and the vertical motion as if there
were no horizontal motion. "Let AB represent a horizontal line or plane
placed on high, on which let a body be carried with an equable motion
from A towards B, and the support of the plane being taken away at B,
let the natural motion downwards due to the body's weight come upon it
in the direction of the perpendicular BN. Moreover let the straight line
BE drawn in the direction AB be taken to represent the flow, or measure,
of the time, on which let any number of equal parts BC, CD, DE, &c. be
marked at pleasure, and from the points C, D, E, let lines be drawn
parallel to BN; in the first of these let any part CI be taken, and let
DF be taken four times as great as CI, EH nine times as great, and so
on, proportionally to the squares of the lines BC, BD, BE, &c., or, as
we say, in the double proportion of these lines. Now if we suppose that
whilst by its equable horizontal motion the body moves from B to C, it
also descends by its weight through CI, at the end of the time denoted
by BC it will be at I. Moreover in the time BD, double of BC, it will
have fallen four times as far, for in the first part of the Treatise it
has been shewn that the spaces fallen through by a heavy body vary as
the squares of the times. Similarly at the end of the time BE, or three
times BC, it will have fallen through EH, and will be at H. And it is
plain that the points I, F, H, are in the same parabolical line BIFH.
The same demonstration will apply if we take any number of equal
particles of time of whatever duration."

The curve called here a Parabola by Galileo, is one of those which
results from cutting straight through a Cone, and therefore is called
also one of the Conic Sections, the curious properties of which curves
had drawn the attention of geometricians long before Galileo thus began
to point out their intimate connexion with the phenomena of motion.
After the proposition we have just extracted, he proceeds to anticipate
some objections to the theory, and explains that the course of a
projectile will not be accurately a parabola for two reasons; partly on
account of the resistance of the air, and partly because a horizontal
line, or one equidistant from the earth's centre, is not straight, but
circular. The latter cause of difference will, however, as he says, be
insensible in all such experiments as we are able to make. The rest of
the Dialogue is taken up with different constructions for determining
the circumstances of the motion of projectiles, as their range, greatest
height, &c.; and it is proved that, with a given force of projection,
the range will be greatest when a ball is projected at an elevation of
45°, ranges of all angles equally inclined above and below 45°
corresponding exactly to each other.

[Illustration]

One of the most interesting subjects discussed in these dialogues is the
famous notion of Nature's horror of a vacuum or empty space, which the
old school of philosophy considered as impossible to be obtained.
Galileo's notions of it were very different; for although he still
unadvisedly adhered to the old phrase to denote the resistance
experienced in endeavouring to separate two smooth surfaces, he was so
far from looking upon a vacuum as an impossibility, that he has
described an apparatus by which he endeavoured to measure the force
necessary to produce one. This consisted of a cylinder, into which is
tightly fitted a piston; through the centre of the piston passes a rod
with a conical valve, which, when drawn down, shuts the aperture
closely, supporting a basket. The space between the piston and cylinder
being filled full of water poured in through the aperture, the valve is
closed, the vessel reversed, and weights are added till the piston is
drawn forcibly downwards. Galileo concluded that the weight of the
piston, rod, and added weights, would be the measure of the force of
resistance to the vacuum which he supposed would take place between the
piston and lower surface of the water. The defects in this apparatus for
the purpose intended are of no consequence, so far as regards the
present argument, and it is perhaps needless to observe that he was
mistaken in supposing the water would not descend with the piston. This
experiment occasions a remark from Sagredo, that he had observed that a
lifting-pump would not work when the water in the cistern had sunk to
the depth of thirty-five feet below the valve; that he thought the pump
was injured, and sent for the maker of it, who assured him that no pump
upon that construction would lift water from so great a depth. This
story is sometimes told of Galileo, as if he had said sneeringly on this
occasion that Nature's horror of a vacuum does not extend beyond
thirty-five feet; but it is very plain that if he had made such an
observation, it would have been seriously; and in fact by such a
limitation he deprived the notion of the principal part of its
absurdity. He evidently had adopted the common notion of suction, for he
compares the column of water to a rod of metal suspended from its upper
end, which may be lengthened till it breaks with its own weight. It is
certainly very extraordinary that he failed to observe how simply these
phenomena may be explained by a reference to the weight of the elastic
atmosphere, which he was perfectly well acquainted with, and endeavoured
by the following ingenious experiment to determine:--"Take a large glass
flask with a bent neck, and round its mouth tie a leathern pipe with a
valve in it, through which water may be forced into the flask with a
syringe without suffering any air to escape, so that it will be
compressed within the bottle. It will be found difficult to force in
more than about three-fourths of what the flask will hold, which must be
carefully weighed. The valve must then be opened, and just so much air
will rush out as would in its natural density occupy the space now
filled by the water. Weigh the vessel again; the difference will show
the weight of that quantity of air."[145] By these means, which the
modern experimentalist will see were scarcely capable of much accuracy,
Galileo found that air was four hundred times lighter than water,
instead of ten times, which was the proportion fixed on by Aristotle.
The real proportion is about 830 times.

The true theory of the rise of water in a lifting-pump is commonly dated
from Torricelli's famous experiment with a column of mercury, in 1644,
when he found that the greatest height at which it would stand is
fourteen times less than the height at which water will stand, which is
exactly the proportion of weight between water and mercury. The
following curious letter from Baliani, in 1630, shows that the original
merit of suggesting the real cause belongs to him, and renders it still
more unaccountable that Galileo, to whom it was addressed, should not at
once have adopted the same view of the subject:--"I have believed that a
vacuum may exist naturally ever since I knew that the air has sensible
weight, and that you taught me in one of your letters how to find its
weight exactly, though I have not yet succeeded with that experiment.
From that moment I took up the notion that it is not repugnant to the
nature of things that there should be a vacuum, but merely that it is
difficult to produce. To explain myself more clearly: if we allow that
the air has weight, there is no difference between air and water except
in degree. At the bottom of the sea the weight of the water above me
compresses everything round my body, and it strikes me that the same
thing must happen in the air, we being placed at the bottom of its
immensity; we do not feel its weight, nor the compression round us,
because our bodies are made capable of supporting it. But if we were in
a vacuum, then the weight of the air above our heads would be felt. It
would be felt very great, but not infinite, and therefore determinable,
and it might be overcome by a force proportioned to it. In fact I
estimate it to be such that, to make a vacuum, I believe we require a
force greater than that of a column of water thirty feet high."[146]

[Illustration]

This subject is introduced by some observations on the force of
cohesion, Galileo seeming to be of opinion that, although it cannot be
adequately accounted for by "the great and principal resistance to a
vacuum, yet that perhaps a sufficient cause may be found by considering
every body as composed of very minute particles, between every two of
which is exerted a similar resistance." This remark serves to lead to a
discussion on indivisibles and infinite quantities, of which we shall
merely extract what Galileo gives as a curious paradox suggested in the
course of it. He supposes a basin to be formed by scooping a hemisphere
out of a cylinder, and a cone to be taken of the same depth and base as
the hemisphere. It is easy to show, if the cone and scooped cylinder be
both supposed to be cut by the same plane, parallel to the one on which
both stand, that the area of the ring CDEF thus discovered in the
cylinder is equal to the area of the corresponding circular section AB
of the cone, wherever the cutting plane is supposed to be.[147] He then
proceeds with these remarkable words:--"If we raise the plane higher and
higher, one of these areas terminates in the circumference of a circle,
and the other in a point, for such are the upper rim of the basin and
the top of the cone. Now since in the diminution of the two areas they
to the very last maintain their equality to one another, it is in my
thoughts proper to say that the highest and ultimate terms[148] of such
diminutions are equal, and not one infinitely bigger than the other. It
seems therefore that the circumference of a large circle may be said to
be equal to one single point. And why may not these be called equal if
they be the last remainders and vestiges left by equal magnitudes[149]?"

We think no one can refuse to admit the probability, that Newton may
have found in such passages as these the first germ of the idea of his
prime and ultimate ratios, which afterwards became in his hands an
instrument of such power. As to the paradoxical result, Descartes
undoubtedly has given the true answer to it in saying that it only
proves that the line is not a greater area than the point is. Whilst on
this subject, it may not be uninteresting to remark that something
similar to the doctrine of fluxions seems to have been lying dormant in
the minds of the mathematicians of Galileo's era, for Inchoffer
illustrates his argument in the treatise we have already mentioned, that
the Copernicans may deduce some true results from what he terms their
absurd hypothesis, by observing, that mathematicians may deduce the
truth that a line is length without breadth, from the false and
physically impossible supposition that a point flows, and that a line is
the fluxion of a point.[150]

A suggestion that perhaps fire dissolves bodies by insinuating itself
between their minute particles, brings on the subject of the violent
effects of heat and light; on which Sagredo inquires, whether we are to
take for granted that the effect of light does or does not require time.
Simplicio is ready with an answer, that the discharge of artillery
proves the transmission of light to be instantaneous, to which Sagredo
cautiously replies, that nothing can be gathered from that experiment
except that light travels more swiftly than sound; nor can we draw any
decisive conclusion from the rising of the sun. "Who can assure us that
he is not in the horizon before his rays reach our sight?" Salviati then
mentions an experiment by which he endeavoured to examine this question.
Two observers are each to be furnished with a lantern: as soon as the
first shades his light, the second is to discover his, and this is to be
repeated at a short distance till the observers are perfect in the
practice. The same thing is to be tried at the distance of several
miles, and if the first observer perceive any delay between shading his
own light and the appearance of his companion's, it is to be attributed
to the time taken by the light in traversing twice the distance between
them. He allows that he could discover no perceptible interval at the
distance of a mile, at which he had tried the experiment, but recommends
that with the help of a telescope it should be tried at much greater
distances. Sir Kenelm Digby remarks on this passage: "It may be objected
(if there be some observable tardity in the motion of light) that the
sunne would never be truly in that place in which unto our eyes he
appeareth to be; because that it being seene by means of the light which
issueth from it, if that light required time to move in, the sunne
(whose motion is so swifte) would be removed from the place where the
light left it, before it could be with us to give tidings of him. To
this I answer, allowing peradventure that it may be so, who knoweth the
contrary? Or what inconvenience would follow if it be admitted[151]?"

The principal thing remaining to be noticed is the application of the
theory of the pendulum to musical concords and dissonances, which are
explained, in the same manner as by Kepler in his "Harmonices Mundi," to
result from the concurrence or opposition of vibrations in the air
striking upon the drum of the ear. It is suggested that these vibrations
may be made manifest by rubbing the finger round a glass set in a large
vessel of water; "and if by pressure the note is suddenly made to rise
to the octave above, every one of the undulations which will be seen
regularly spreading round the glass, will suddenly split into two,
proving that the vibrations that occasion the octave are double those
belonging to the simple note." Galileo then describes a method he
discovered by accident of measuring the length of these waves more
accurately than can be done in the agitated water. He was scraping a
brass plate with an iron chisel, to take out some spots, and moving the
tool rapidly upon the plate, he occasionally heard a hissing and
whistling sound, very shrill and audible, and whenever this occurred,
and then only, he observed the light dust on the plate to arrange itself
in a long row of small parallel streaks equidistant from each other. In
repeated experiments he produced different tones by scraping with
greater or less velocity, and remarked that the streaks produced by the
acute sounds stood closer together than those from the low notes. Among
the sounds produced were two, which by comparison with a viol he
ascertained to differ by an exact fifth; and measuring the spaces
occupied by the streaks in both experiments, he found thirty of the one
equal to forty-five of the other, which is exactly the known proportion
of the lengths of strings of the same material which sound a fifth to
each other.[152]

Salviati also remarks, that if the material be not the same, as for
instance if it be required to sound an octave to a note on catgut, on a
wire of the same length, the weight of the wire must be made four times
as great, and so for other intervals. "The immediate cause of the forms
of musical intervals is neither the length, the tension, nor the
thickness, but the proportion of the numbers of the undulations of the
air which strike upon the drum of the ear, and make it vibrate in the
same intervals. Hence we may gather a plausible reason of the different
sensations occasioned to us by different couples of sounds, of which we
hear some with great pleasure, some with less, and call them accordingly
concords, more or less perfect, whilst some excite in us great
dissatisfaction, and are called discords. The disagreeable sensation
belonging to the latter probably arises from the disorderly manner in
which the vibrations strike the drum of the ear; so that for instance a
most cruel discord would be produced by sounding together two strings,
of which the lengths are to each other as the side and diagonal of a
square, which is the discord of the false fifth. On the contrary,
agreeable consonances will result from those strings of which the
numbers of vibrations made in the same time are commensurable, "to the
end that the cartilage of the drum may not undergo the incessant torture
of a double inflexion from the disagreeing percussions." Something
similar may be exhibited to the eye by hanging up pendulums of different
lengths: "if these be proportioned so that the times of their vibrations
correspond with those of the musical concords, the eye will observe with
pleasure their crossings and interweavings still recurring at
appreciable intervals; but if the times of vibration be incommensurate,
the eye will be wearied and worn out with following them."

The second dialogue is occupied entirely with an investigation of the
strength of beams, a subject which does not appear to have been examined
by any one before Galileo beyond Aristotle's remark, that long beams are
weaker, because they are at once the weight, the lever, and the fulcrum;
and it is in the development of this observation that the whole theory
consists. The principle assumed by Galileo as the basis of his inquiries
is, that the force of cohesion with which a beam resists a cross
fracture in any section may all be considered as acting at the centre of
gravity of the section, and that it breaks always at the lowest point:
from this he deduced that the effect of the weight of a prismatic beam
in overcoming the resistance of one end by which it is fastened to a
wall, varies directly as the square of the length, and inversely as the
side of the base. From this it immediately follows, that if for instance
the bone of a large animal be three times as long as the corresponding
one in a smaller beast, it must be nine times as thick to have the same
strength, provided we suppose in both cases that the materials are of
the same consistence. An elegant result which Galileo also deduced from
this theory, is that the form of such a beam, to be equally strong in
every part, should be that of a parabolical prism, the vertex of the
parabola being the farthest removed from the wall. As an easy mode of
describing the parabolic curve for this purpose, he recommends tracing
the line in which a heavy flexible string hangs. This curve is not an
accurate parabola: it is now called a catenary; but it is plain from the
description of it in the fourth dialogue, that Galileo was perfectly
aware that this construction is only approximately true. In the same
place he makes the remark, which to many is so paradoxical, that no
force, however great, exerted in a horizontal direction, can stretch a
heavy thread, however slender, into an accurately straight line.

The fifth and sixth dialogues were left unfinished, and annexed to the
former ones by Viviani after Galileo's death: the fragment of the fifth,
which is on the subject of Euclid's Definition of Ratio, was at first
intended to have formed a part of the third, and followed the first
proposition on equable motion: the sixth was intended to have embodied
Galileo's researches on the nature and laws of Percussion, on which he
was employed at the time of his death. Considering these solely as
fragments, we shall not here make any extracts from them.


FOOTNOTES:

[140] Joh. Bernouilli, Opera Omnia, Lausannæ, 1744. tom. i. p. 192.

[141] Pantometria, 1591.

[142] Lettres de Descartes. Paris, 1657.

[143] Math. Coll. vol. ii.

[144] Phys. Lib. iv. c. 8.

[145] It has been recently proposed to determine the density of
high-pressure steam by a process analogous to this.

[146] Venturi, vol. ii.

[147] Galileo also reasons in the same way on the equality of the solids
standing on the cutting plane, but one is sufficient for our present
purpose.

[148] Gli altissimi e ultimi termini.

[149] Le ultime reliquie e vestigie lasciate da grandezze eguali.

[150] Punctum fluere, et lineam esse fluxum puncti. Tract. Syllept.
Romæ, 1633.

[151] "Treatise of the Nature of Bodies. London, 1665."

[152] This beautiful experiment is more easily tried by drawing the bow
of a violin across the edge of glass strewed with fine dry sand. Those
who wish to see more on the subject may consult Chladni's 'Acoustique.'




CHAPTER XVIII.

    _Correspondence on Longitudes.--Pendulum Clock._


IN the spring of 1636, having finished his Dialogues on Motion, Galileo
resumed the plan of determining the longitude by means of Jupiter's
satellites. Perhaps he suspected something of the private intrigue which
thwarted his former expectations from the Spanish government, and this
may have induced him on the present occasion to negotiate the matter
without applying for Ferdinand's assistance and recommendation.
Accordingly he addressed himself to Lorenz Real, who had been Governor
General of the Dutch possessions in India, freely and unconditionally
offering the use of his theory to the States General of Holland. Not
long before, his opinion had been requested by the commissioners
appointed at Paris to examine and report on the practicability of
another method proposed by Morin,[153] which consisted in observing the
distance of the moon from a known star. Morin was a French philosopher,
principally known as an astrologer and zealous Anti-Copernican; but his
name deserves to be recorded as undoubtedly one of the first to
recommend a method, which, under the name of a Lunar distance, is now in
universal practice.

The monthly motion of the moon is so rapid, that her distance from a
given star sensibly varies in a few minutes even to the unassisted eye;
and with the aid of the telescope, we can of course appreciate the
change more accurately. Morin proposed that the distances of the moon
from a number of fixed stars lying near her path in the heavens should
be beforehand calculated and registered for every day in the year, at a
certain hour, in the place from which the longitudes were to be
reckoned, as for instance at Paris. Just as in the case of the eclipses
of Jupiter's satellites, the observer, when he saw that the moon had
arrived at the registered distance, would know the hour at Paris: he
might also make allowance for intermediate distances. Observing at the
same instant the hour on board his ship, the difference between the two
would show his position in regard of longitude. In using this method as
it is now practised, several modifications are to be attended to,
without which it would be wholly useless, in consequence of the
refraction of the atmosphere, and the proximity of the moon to the
earth. Owing to the latter cause, if two spectators should at the same
instant of time, but in different places, measure the distance of the
moon in the East, from a star still more to the eastward, it would
appear greater to the more easterly spectator than to the other
observer, who as seen from the star would be standing more directly
behind the moon. The mode of allowing for these alterations is taught by
trigonometry and astronomy.

The success of this method depends altogether upon the exact knowledge
which we now have of the moon's course, and till that knowledge was
perfected it would have been found altogether illusory. Such in fact was
the judgment which Galileo pronounced upon it. "As to Morin's book on
the method of finding the longitude by means of the moon's motion, I say
freely that I conceive this idea to be as accurate in theory, as
fallacious and impossible in practice. I am sure that neither you nor
any one of the other four gentlemen can doubt the possibility of finding
the difference of longitude between two meridians by means of the moon's
motion, provided we are sure of the following requisites: First, an
Ephemeris of the moon's motion exactly calculated for the first meridian
from which the others are to be reckoned; secondly, exact instruments,
and convenient to handle, in taking the distance between the moon and a
fixed star; thirdly, great practical skill in the observer; fourthly,
not less accuracy in the scientific calculations, and astronomical
computations; fifthly, very perfect clocks to number the hours, or other
means of knowing them exactly, &c. Supposing, I say, all these elements
free from error, the longitude will be accurately found; but I reckon it
more easy and likely to err in all of these together, than to be
practically right in one alone. Morin ought to require his judges to
assign, at their pleasure, eight or ten moments of different nights
during four or six months to come, and pledge himself to predict and
assign by his calculations the distances of the moon at those determined
instants from some star which would then be near her. If it is found
that the distances assigned by him agree with those which the quadrant
or sextant[154] will actually show, the judges would be satisfied of his
success, or rather of the truth of the matter, and nothing would remain
but to show that his operations were such as could be performed by men
of moderate skill, and also practicable at sea as well as on land. I
incline much to think that an experiment of this kind would do much
towards abating the opinion and conceit which Morin has of himself,
which appears to me so lofty, that I should consider myself the eighth
sage, if I knew the half of what Morin presumes to know."

It is probable that Galileo was biassed by a predilection for his own
method, on which he had expended so much time and labour; but the
objections which he raises against Morin's proposal in the foregoing
letter are no other than those to which at that period it was
undoubtedly open. With regard to his own, he had already, in 1612, given
a rough prediction of the course of Jupiter's satellites, which had been
found to agree tolerably well with subsequent observations; and since
that time, amid all his other employments, he had almost
unintermittingly during twenty-four years continued his observations,
for the sake of bringing the tables of their motions to as high a state
of perfection as possible. This was the point to which the inquiries of
the States in their answer to Galileo's frank proposal were principally
directed. They immediately appointed commissioners to communicate with
him, and report the various points on which they required information.
They also sent him a golden chain, and assured him that in the case of
the design proving successful, he should have no cause to complain of
their want of gratitude and generosity. The commissioners immediately
commenced an active correspondence with him, in the course of which he
entered into more minute details with regard to the methods by which he
proposed to obviate the practical difficulties of the necessary
observations.

It is worth noticing that the secretary to the Prince of Orange, who was
mainly instrumental in forming this commission, was Constantine
Huyghens, father of the celebrated mathematician of that name, of whom
it has been said that he seemed destined to complete the discoveries of
Galileo; and it is not a little remarkable, that Huyghens nowhere in his
published works makes any allusion to this connexion between his father
and Galileo, not even during the discussion that arose some years later
on the subject of the pendulum clock, which must necessarily have forced
it upon his recollection.

The Dutch commissioners had chosen one of their number to go into Italy
for the purpose of communicating personally with Galileo, but he
discouraged this scheme, from a fear of its giving umbrage at Rome. The
correspondence being carried on at so great a distance necessarily
experienced many tedious delays, till in the very midst of Galileo's
labours to complete his tables, he was seized with the blindness which
we have already mentioned. He then resolved to place all the papers
containing his observations and calculations for this purpose in the
hands of Renieri, a former pupil of his, and then professor of
mathematics at Pisa, who undertook to finish and to forward them into
Holland. Before this was done, a new delay was occasioned by the deaths
which speedily followed each other of every one of the four
commissioners; and for two or three years the correspondence with
Holland was entirely interrupted. Constantine Huyghens, who was capable
of appreciating the value of the scheme, succeeded after some trouble in
renewing it, but only just before the death of Galileo himself, by which
of course it was a second time broken off; and to complete the singular
series of obstacles by which the trial of this method was impeded, just
as Renieri, by order of the Duke of Tuscany, was about to publish the
ephemeris and tables which Galileo had entrusted to him, and which the
Duke told Viviani he had seen in his possession, he also was attacked
with a mortal malady; and upon his death the manuscripts were nowhere to
be found, nor has it since been discovered what became of them. Montucla
has intimated his suspicions that Renieri himself destroyed them, from a
consciousness that they were insufficient for the purpose to which it
was intended to apply them; a bold conjecture, and one which ought to
rest upon something more than mere surmise: for although it may be
considered certain, that the practical value of these tables would be
very inconsiderable in the present advanced state of knowledge, yet it
is nearly as sure that they were unique at that time, and Renieri was
aware of the value which Galileo himself had set upon them, and should
not be lightly accused of betraying his trust in so gross a manner. In
1665, Borelli calculated the places of the satellites for every day in
the ensuing year, which he professed to have deduced (by desire of the
Grand Duke) from Galileo's tables;[155] but he does not say whether or
not these tables were the same that had been in Renieri's possession.

We have delayed till this opportunity to examine how far the invention
of the pendulum clock belongs to Galileo. It has been asserted that the
isochronism of the pendulum had been noticed by Leonardo da Vinci, but
the passage on which this assertion is founded (as translated from his
manuscripts by Venturi) scarcely warrants this conclusion. "A rod which
engages itself in the opposite teeth of a spur-wheel can act like the
arm of the balance in clocks, that is to say, it will act alternately,
first on one side of the wheel, then on the opposite one, without
interruption." If Da Vinci had constructed a clock on this principle,
and recognized the superiority of the pendulum over the old balance, he
would surely have done more than merely mention it as affording an
unintermitted motion "like the arm of the balance." The use of the
balance is supposed to have been introduced at least as early as the
fourteenth century. Venturi mentions the drawing and description of a
clock in one of the manuscripts of the King's Library at Paris, dated
about the middle of the fifteenth century, which as he says nearly
resembles a modern watch. The balance is there called "The circle
fastened to the stem of the pallets, and moved by the force with
it."[156] In that singularly wild and extravagant book, entitled "A
History of both Worlds," by Robert Flud, are given two drawings of the
wheel-work of the clocks and watches in use before the application of
the pendulum. An inspection of them will show how little remained to be
done when the isochronism of the pendulum was discovered. _Fig. 1._
represents "the large clocks moved by a weight, such as are put up in
churches and turrets; _fig. 2._ the small ones moved by a spring, such
as are worn round the neck, or placed on a shelf or table. The use of
the chain is to equalize the spring, which is strongest at the beginning
of its motion."[157] This contrivance of the chain is mentioned by
Cardan, in 1570, and is probably still older. In both figures the name
given to the cross bar, with the weight attached to it, is "the time or
balance (_tempus seu libratio_) by which the motion is equalized." The
manner in which Huyghens first applied the pendulum is shown in _fig.
3._[158] The action in the old clocks of the balance, or _rake_, as it
was also called, was by checking the motion of the descending weight
till its inertia was overcome; it was then forced round till the
opposite pallet engaged in the toothed wheel. The balance was thus
suddenly and forcibly reduced to a state of rest, and again set in
motion in the opposite direction. It will be observed that these
balances wanted the spiral spring introduced in all modern watches,
which has a property of isochronism similar to that of the pendulum.
Hooke is generally named as the discoverer of this property of springs,
and as the author of its application to the improvement of watches, but
the invention is disputed with him by Huyghens. Lahire asserts[159] that
the isochronism of springs was communicated to Huyghens at Paris by
Hautefeuille, and that this was the reason why Huyghens failed to obtain
the patent he solicited for the construction of spring watches. A great
number of curious contrivances at this early period in the history of
Horology, may be seen in Schott's Magia Naturæ, published at Nuremberg
in 1664.

[Illustration: _Fig. 2. Fig. 1. Fig. 3._]

Galileo was early convinced of the importance of his pendulum to the
accuracy of astronomical observations; but the progress of invention is
such that the steps which on looking back seem the easiest to make, are
often those which are the longest delayed. Galileo recognized the
principle of the isochronism of the pendulum, and recommended it as a
measurer of time in 1583; yet fifty years later, although constantly
using it, he had not devised a more convenient method of doing so, than
is contained in the following description taken from his "Astronomical
Operations."

"A very exact time-measurer for minute intervals of time, is a heavy
pendulum of any size hanged by a fine thread, which, if removed from the
perpendicular and allowed to swing freely, always completes its
vibrations, be they great or small, in exactly the same time."[160]

The mode of finding exactly by means of this the quantity of any time
reduced to hours, minutes, seconds, &c., which are the divisions
commonly used among astronomers, is this:--"Fit up a pendulum of any
length, as for instance about a foot long, and count patiently (only for
once) the number of vibrations during a natural day. Our object will be
attained if we know the exact revolution of the natural day. The
observer must then fix a telescope in the direction of any star, and
continue to watch it till it disappears from the field of view. At that
instant he must begin to count the vibrations of the pendulum,
continuing all night and the following day till the return of the same
star within the field of view of the telescope, and its second
disappearance, as on the first night. Bearing in recollection the total
number of vibrations thus made in twenty-four hours, the time
corresponding to any other number of vibrations will be immediately
given by the Golden Rule."

A second extract out of Galileo's Dutch correspondence, in 1637, will
show the extent of his improvements at that time:--"I come now to the
second contrivance for increasing immensely the exactness of
astronomical observations. I allude to my time-measurer, the precision
of which is so great, and such, that it will give the exact quantity of
hours, minutes, seconds, and even thirds, if their recurrence could be
counted; and its constancy is such that two, four, or six such
instruments will go on together so equably that one will not differ from
another so much as the beat of a pulse, not only in an hour, but even in
a day or a month."--"I do not make use of a weight hanging by a thread,
but a heavy and solid pendulum, made for instance of brass or copper, in
the shape of a circular sector of twelve or fifteen degrees, the radius
of which may be two or three palms, and the greater it is the less
trouble will there be in attending it. This sector, such as I have
described, I make thickest in the middle radius, tapering gradually
towards the edges, where I terminate it in a tolerably sharp line, to
obviate as much as possible the resistance of the air, which is the sole
cause of its retardation."--[These last words deserve notice, because,
in a previous discussion, Galileo had observed that the parts of the
pendulum nearest the point of suspension have a tendency to vibrate
quicker than those at the other end, and seems to have thought
erroneously that the stoppage of the pendulum is partly to be attributed
to this cause.]--"This is pierced in the centre, through which is passed
an iron bar shaped like those on which steelyards hang, terminated below
in an angle, and placed on two bronze supports, that they may wear away
less during a long motion of the sector. If the sector (when accurately
balanced) be removed several degrees from its perpendicular position, it
will continue a reciprocal motion through a very great number of
vibrations before it will stop; and in order that it may continue its
motion as long as is wanted, the attendant must occasionally give it a
smart push, to carry it back to large vibrations." Galileo then
describes as before the method of counting the vibrations in the course
of a day, and gives the rule that the lengths of two similar pendulums
will have the same proportion as the squares of their times of
vibration. He then continues: "Now to save the fatigue of the assistant
in continually counting the vibrations, this is a convenient
contrivance: A very small and delicate needle extends out from the
middle of the circumference of the sector, which in passing strikes a
rod fixed at one end; this rod rests upon the teeth of a wheel as light
as paper, placed in a horizontal plane near the pendulum, having round
it teeth cut like those of a saw, that is to say, with one side of each
tooth perpendicular to the rim of the wheel and the other inclined
obliquely. The rod striking against the perpendicular side of the tooth
moves it, but as the same rod returns against the oblique side, it does
not move it the contrary way, but slips over it and falls at the foot of
the following tooth, so that the motion of the wheel will be always in
the same direction. And by counting the teeth you may see at will the
number of teeth passed, and consequently the number of vibrations and of
particles of time elapsed. You may also fit to the axis of this first
wheel a second, with a small number of teeth, touching another greater
toothed wheel, &c. But it is superfluous to point out this to you, who
have by you men very ingenious and well skilled in making clocks and
other admirable machines; and on this new principle, that the pendulum
makes its great and small vibrations in the same time exactly, they will
invent contrivances more subtle than any I can suggest; and as the error
of clocks consists principally in the disability of workmen hitherto to
adjust what we call the balance of the clock, so that it may vibrate
regularly, my very simple pendulum, which is not liable to any
alteration, affords a mean of maintaining the measures of time always
equal." The contrivance thus described would be somewhat similar to the
annexed representation, but it is almost certain that no such instrument
was actually constructed.

[Illustration]

It must be owned that Galileo greatly overrated the accuracy of his
timekeeper; and in asserting so positively that which he had certainly
not experienced, he seems to depart from his own principles of
philosophizing. It will be remarked that in this passage he still is of
the erroneous opinion, that all the vibrations great or small of the
same pendulum take exactly the same time; and we have not been able to
find any trace of his having ever held a different opinion, unless
perhaps in the Dialogues, where he says, "If the vibrations are not
exactly equal, they are at least insensibly different." This is very
much at variance with the statement in the Memoirs of the Academia del
Cimento, edited by their secretary Magalotti, on the credit of which
Galileo's claim to the pendulum-clock chiefly rests. It is there said
that experience shows that the smallest vibrations are rather the
quickest, "as Galileo announced after the observation, which in 1583 he
was the first to make of their approximate equality." It is not possible
immediately in connexion with so glaring a misstatement, to give
implicit credence to the assertion in the next sentence, that "_to
obviate this inconvenience_" Galileo was the first to contrive a clock,
constructed in 1649, by his son Vincenzo, in which, by the action of a
weight or spring, the pendulum was constrained to move always from the
same height. Indeed it appears as if Magalotti did not always tell this
story in the same manner, for he is referred to as the author of the
account given by Becher, "that Galileo himself made a pendulum-clock one
of which was sent to Holland," plainly insinuating that Huyghens was a
mere copyist.[161] These two accounts therefore serve to invalidate each
other's credibility. Tiraboschi[162] asserts that, at the time he wrote,
the mathematical professor at Pisa was in possession of the identical
clock constructed by Treffler under Vincenzo's directions; and quotes a
letter from Campani, to whom it was shown by Ferdinand, "old, rusty, and
unfinished as Galileo's son made it before 1649." Viviani on the other
hand says that Treffler constructed this same clock some time after
Vincenzo's death (which happened in 1649), on a different principle from
Vincenzo's ideas, although he says distinctly that he heard Galileo
describe an application of the pendulum to a clock similar to Huyghens'
contrivance. Campani did not actually see this clock till 1659, which
was three years after Huyghens' invention, so that perhaps Huyghens was
too easily satisfied when, on occasion of the answer which Ferdinand
sent to his complaints of the Memorie del Cimento he wrote to Bouillaud,
"I must however believe, since such a prince assures me, that Galileo
had this idea before me."

There is another circumstance almost amounting to a proof that it was an
afterthought to attribute the merit of constructing the pendulum-clock
to Galileo, for on the reverse of a medal struck by Viviani, and
inscribed "to the memory of his excellent instructor,"[163] is a rude
exhibition of the principal objects to which Galileo's attention was
directed. The pendulum is represented simply by a weight attached to a
string hanging on the face of a rock. It is probable that, in a design
expressly intended to commemorate Galileo's inventions, Viviani would
have introduced the timekeeper in the most perfect form to which it had
been brought by him. Riccioli,[164] whose industry was unwearied in
collecting every fact and argument which related in any way to the
astronomical and mechanical knowledge and opinions of his time,
expressly recommends swinging a pendulum, or perpendicular as it was
often called (only a few years before Huyghens' publication), as much
more accurate _than any clock_.[165] Join to all these arguments
Huyghens' positive assertion, that if Galileo had conceived any such
idea, he at least was entirely ignorant of it,[166] and no doubt can
remain that the merit of the original invention (such as it was) rests
entirely with Huyghens. The step indeed seems simple enough for a less
genius than his: for the property of the pendulum was known, and the
conversion of a rotatory into a reciprocating motion was known; but the
connexion of the one with the other having been so long delayed, we must
suppose that difficulties existed where we are not now able to perceive
them, for Huyghens' improvement was received with universal admiration.

There may be many who will consider the pendulum as undeserving so long
a discussion; who do not know or remember that the telescope itself has
hardly done more for the precision of astronomical observations than
this simple instrument, not to mention the invaluable convenience of an
uniform and accurate timekeeper in the daily intercourse of life. The
patience and industry of modern observers are often the theme of
well-merited praise, but we must look with a still higher degree of
wonder on such men as Tycho Brahe and his contemporaries, who were
driven by the want of any timekeeper on which they could depend to the
most laborious expedients, and who nevertheless persevered to the best
of their ability, undisgusted either by the tedium of such processes, or
by the discouraging consciousness of the necessary imperfection of their
most approved methods and instruments.

The invariable regularity of the pendulum's motion was soon made
subservient to ulterior purposes beyond that of merely registering time.
We have seen the important assistance it afforded in establishing the
laws of motion; and when the theory founded on those laws was extended
and improved, the pendulum was again instrumental, by a species of
approximate reasoning familiar to all who are acquainted with physical
inquiries, in pointing out by its minute irregularities in different
parts of the earth, a corresponding change in the weight of all bodies
in those different situations, supposed to be the consequence of a
greater distance from the axis of the earth's rotation; since that would
occasion the force of attraction to be counterbalanced by an increased
centrifugal force. The theory which kept pace with the constantly
increasing accuracy of such observations, proving consistent in all
trials of it, has left little room for future doubts; and in this manner
the pendulum in intelligent hands became the simplest instrument for
ascertaining the form of the globe which we inhabit. An English
astronomer, who corresponded with Kepler under the signature of Brutius
(whose real name perhaps might be Bruce), had already declared his
belief in 1603, that "the earth on which we tread is neither round nor
globular, but more nearly of an oval figure."[167] There is nothing to
guide us to the grounds on which he formed this opinion, which was
perhaps only a lucky guess. Kepler's note upon it is: "This is not
altogether to be contemned."

A farther use of the pendulum is in furnishing a general and unperishing
standard of measure. This application is suggested in the third volume
of the 'Reflections' of Mersenne, published in 1647, where he observes
that it may be best for the future not to divide time into hours,
minutes, and seconds, but to express its parts by the number of
vibrations of a pendulum of given length, swinging through a given arc.
It was soon seen that it would be more convenient to invert this
process, and to choose as an unit of length the pendulum which should
make a certain number of vibrations in the unit of time, naturally
determined by the revolution of the earth on its axis. Our Royal
Society took an active part in these experiments, which seem,
notwithstanding their utility, to have met from the first with much of
the same ridicule which was lavished upon them by the ignorant, when
recently repeated for the same purpose. "I contend," says Graunt[168] in
a dedication to the Royal Society, dated 1662, "against the envious
schismatics of your society (who think you do nothing unless you
presently transmute metals, make butter and cheese without milk, and, as
their own ballad hath it, make leather without hides), by asserting the
usefulness of even all your preparatory and luciferous experiments,
being not the ceremonies, but the substance and principles of useful
arts. For I find in trade the want of an universal measure, and have
heard musicians wrangle about the just and uniform keeping of time in
their consorts, and therefore cannot with patience hear that your
labours about vibrations, eminently conducing to both, should be
slighted, nor your pendula called swing-swangs with scorn."[169]


FOOTNOTES:

[153] One of the Commissioners was the father of Blaise Pascal.

[154] These instruments were very inferior to those now in use under the
same name. See "Treatise on Opt. Instrum."

[155] Theoricæ Mediceorum Planetarum, Florentiæ, 1666.

[156] Circulus affixus virgæ paletorum qui cum eâ de vi movetur.

[157] Utriusque Cosmi Historia. Oppenhemii, 1617.

[158] Huygenii Opera. Lugduni, 1724.

[159] Mémoires de l'Academie, 1717.

[160] See page 84.

[161] De nova Temporis dimetiendi ratione. Londini, 1680.

[162] Storia della Lett. Ital.

[163] Museum Mazuchellianum, vol. ii. Tab. cvii. p. 29.

[164] Almagestum Novum, vol. i.

[165] Quovis horologio accuratius.

[166] Clarorum Belgarum ad Ant. Magliabech. Epistolæ. Florence, 1745,
tom. i. p. 235.

[167] Kepleri Epistolæ.

[168] Natural and Political Observations. London, 1665.

[169] See also Hudibras, Part II. Cant. III.

    They're guilty by their own confessions
    Of felony, and at the Sessions
    Upon the bench I will so handle 'em,
    That the vibration of this pendulum
    Shall make all taylors' yards of one
    Unanimous opinion;
    A thing he long has vaunted of,
    But now shall make it out of proof.

Hudibras was certainly written before 1663: ten years later Huyghens
speaks of the idea of so employing the pendulum as a common one.




CHAPTER XIX.

    _Character of Galileo--Miscellaneous details--his
    Death--Conclusion._


THE remaining years of Galileo's life were spent at Arcetri, where
indeed, even if the Inquisition had granted his liberty, his increasing
age and infirmities would probably have detained him. The rigid caution
with which he had been watched in Florence was in great measure relaxed,
and he was permitted to see the friends who crowded round him to express
their respect and sympathy. The Grand Duke visited him frequently, and
many distinguished strangers, such as Gassendi and Deodati, came into
Italy solely for the purpose of testifying their admiration of his
character. Among other visitors the name of Milton will be read with
interest: we may probably refer to the effects of this interview the
allusions to Galileo's discoveries, so frequently introduced into his
poem. Milton mentions in his 'Areopagitica,' that he saw Galileo whilst
in Italy, but enters into no details of his visit.

Galileo was fond of society, and his cheerful and popular manners
rendered him an universal favourite among those who were admitted to his
intimacy. Among these, Viviani, who formed one of his family during the
three last years of his life, deserves particular notice, on account of
the strong attachment and almost filial veneration with which he ever
regarded his master and benefactor. His long life, which was prolonged
to the completion of his 81st year in 1703, enabled him to see the
triumphant establishment of the truths on account of which Galileo had
endured so many insults; and even in his old age, when in his turn he
had acquired a claim to the reverence of a younger generation, our Royal
Society, who invited him among them in 1696, felt that the complimentary
language in which they addressed him as the first mathematician of the
age would have been incomplete and unsatisfactory without an allusion to
the friendship that gained him the cherished title of "The last pupil of
Galileo."[170]

Torricelli, another of Galileo's most celebrated followers, became a
member of his family in October, 1641: he first learned mathematics from
Castelli, and occasionally lectured for him at Rome, in which manner he
was employed when Galileo, who had seen his book 'On Motion,' and
augured the greatest success from such a beginning, invited him to his
house--an offer which Torricelli eagerly embraced, although he enjoyed
the advantages of it but for a short time. He afterwards succeeded
Galileo in his situation at the court of Florence,[171] but survived him
only a few years.

It is from the accounts of Viviani and Gherardini that we principally
draw the following particulars of Galileo's person and character:--Signor
Galileo was of a cheerful and pleasant countenance, especially in his
old age, square built, and well proportioned in stature, and rather
above the middle size. His complexion was fair and sanguine, his eyes
brilliant, and his hair of a reddish cast. His constitution was
naturally strong, but worn out by fatigue of mind and body, so as
frequently to be reduced to a state of the utmost weakness. He was
subject to attacks of hypochondria, and often molested by severe and
dangerous illnesses, occasioned in great measure by his sleepless
nights, the whole of which he frequently spent in astronomical
observations. During upwards of forty-eight years of his life, he was
tormented with acute rheumatic pains, suffering particularly on any
change of weather. He found himself most free from these pains whilst
residing in the country, of which consequently he became very fond:
besides, he used to say that in the country he had greater freedom to
read the book of Nature, which lay there open before him. His library
was very small, but well chosen, and open to the use of the friends whom
he loved to see assembled round him, and whom he was accustomed to
receive in the most hospitable manner. He ate sparingly himself; but was
particularly choice in the selection of his wines, which in the latter
part of his life were regularly supplied out of the Grand Duke's
cellars. This taste gave an additional stimulus to his agricultural
pursuits, and many of his leisure hours were spent in the cultivation
and superintendence of his vineyards. It should seem that he was
considered a good judge of wine; for Viviani has preserved one of his
receipts in a collection of miscellaneous experiments. In it he strongly
recommends that for wine of the first quality, that juice only should be
employed, which is pressed out by the mere weight of the heaped grapes,
which would probably be that of the ripest fruit. The following letter,
written in his 74th year, is dated, "From my prison at Arcetri.--I am
forced to avail myself of your assistance and favour, agreeably to your
obliging offers, in consequence of the excessive chill of the weather,
and of old age, and from having drained out my grand stock of a hundred
bottles, which I laid in two years ago; not to mention some minor
particulars during the last two months, which I received from my Serene
Master, the Most Eminent Lord Cardinal, their Highnesses the Princes,
and the Most Excellent Duke of Guise, besides cleaning out two barrels
of the wine of this country. Now, I beg that with all due diligence and
industry, and with consideration, and taking counsel with the most
refined palates, you will provide me with two cases, that is to say,
with forty flasks of different wines, the most exquisite that you can
find: take no thought of the expense, because I stint myself so much in
all other pleasures that I can afford to lay out something at the
request of Bacchus, without giving offence to his two companions Ceres
and Venus. You must be careful to leave out neither Scillo nor Carino (I
believe they meant to call them Scylla and Charybdis), nor the country
of my master, Archimedes of Syracuse, nor Greek wines, nor clarets, &c.
&c. The expense I shall easily be able to satisfy, but not the infinite
obligation."

In his expenditure Galileo observed a just mean between avarice and
profusion: he spared no cost necessary for the success of his many and
various experiments, and spent large sums in charity and hospitality,
and in assisting those in whom he discovered excellence in any art or
profession, many of whom he maintained in his own house. His temper was
easily ruffled, but still more easily pacified. He seldom conversed on
mathematical or philosophical topics except among his intimate friends;
and when such subjects were abruptly brought before him, as was often
the case by the numberless visitors he was in the habit of receiving, he
showed great readiness in turning the conversation into more popular
channels, in such manner however that he often contrived to introduce
something to satisfy the curiosity of the inquirers. His memory was
uncommonly tenacious, and stored with a vast variety of old songs and
stories, which he was in the constant habit of quoting and alluding to.
His favourite Italian authors were Ariosto, Petrarca, and Berni, great
part of whose poems he was able to repeat. His excessive admiration of
Ariosto determined the side which he took against Tasso in the virulent
and unnecessary controversy which has divided Italy so long on the
respective merits of these two great poets; and he was accustomed to say
that reading Tasso after Ariosto was like tasting cucumbers after
melons. When quite a youth, he wrote a great number of critical remarks
on Tasso's Gerusalemme Liberata, which one of his friends borrowed, and
forgot to return. For a long time it was thought that the manuscript had
perished, till the Abbé Serassi discovered it, whilst collecting
materials for his Life of Tasso, published at Rome in 1785. Serassi
being a violent partizan of Tasso, but also unwilling to lose the credit
of the discovery, copied the manuscript, but without any intention of
publishing it, "till he could find leisure for replying properly to the
sophistical and unfounded attacks of a critic so celebrated on other
accounts." He announced his discovery as having been made "in one of the
famous libraries at Rome," which vague indication he with some reason
considered insufficient to lead to a second discovery. On Serassi's
death his copy was found, containing a reference to the situation of the
original; the criticisms were published, and form the greatest part of
the last volume of the Milan edition of Galileo's works. The manuscript
was imperfect at the time of this second discovery, several leaves
having been torn out, it is not known by whom.

The opinion of the most judicious Italian critics appears to be, that it
would have been more for Galileo's credit if these remarks had never
been made public: they are written in a spirit of flippant violence,
such as might not be extraordinary in a common juvenile critic, but
which it is painful to notice from the pen of Galileo. Two or three
sonnets are extant written by Galileo himself, and in two instances he
has not scrupled to appropriate the conceits of the poet he affected to
undervalue.[172] It should be mentioned that Galileo's matured taste
rather receded from the violence of his early prejudices, for at a later
period of his life he used to shun comparing the two; and when forced to
give an opinion he said, "that Tasso's appeared the finer poem, but that
Ariosto gave him the greater pleasure." Besides these sonnets, there is
extant a short burlesque poem written by him, "In abuse of Gowns," when,
on his first becoming Professor at Pisa, he found himself obliged by
custom to wear his professional habit in every company. It is written
not without humour, but does not bear comparison with Berni, whom he
imitated.

There are several detached subjects treated of by Galileo, which may be
noticed in this place. A letter by him containing the solution of a
problem in Chances is probably the earliest notice extant of the
application of mathematics to that interesting subject: the
correspondence between Pascal and Fermat, with which its history is
generally made to begin, not having taken place till at least twelve
years later. There can be little doubt after the clear account of Carlo
Dati, that Galileo was the first to examine the curve called the
Cycloid, described by a point in the rim of a wheel rolling on a
straight line, which he recommended as a graceful form for the arch of a
bridge at Pisa. He even divined that the area contained between it and
its base is exactly three times that of the generating circle. He seems
to have been unable to verify this guess by strict geometrical
reasoning, for Viviani tells an odd story, that in order to satisfy his
doubts he cut out several large cycloids of pasteboard, but finding the
weight in every trial to be rather less than three times that of the
circle, he suspected the proportion to be irrational, and that there was
some error in his estimation; the inquiry he abandoned was afterwards
resumed with success by his pupil Torricelli.[173]

The account which Lagalla gives of an experiment shown in his presence
by Galileo, carries the observation of the phosphorescence of the
Bologna stone at least as far back as 1612.[174] Other writers mention
the name of an alchymist, who according to them discovered it
accidentally in 1603. Cesi, Lagalla, and one or two others, had passed
the night at Galileo's house, with the intention of observing Venus and
Saturn; but, the night being cloudy, the conversation turned on other
matters, and especially on the nature of light, "on which Galileo took a
small wooden box at daybreak before sunrise, and showed us some small
stones in it, desiring us to observe that they were not in the least
degree luminous. Having then exposed them for some time to the twilight,
he shut the window again; and in the midst of the dark room showed us
the stones, shining and glistening with a faint light, which we saw
presently decay and become extinguished." In 1640, Liceti attempted to
refer the effect of the earthshine upon the moon to a similar
phosphorescent quality of that luminary, to which Galileo, then aged 76,
replied by a long and able letter, enforcing the true explanation he had
formerly given.

Although quite blind, and nearly deaf, the intellectual powers of
Galileo remained to the end of his life; but he occasionally felt that
he was overworking himself, and used to complain to his friend Micanzio
that he found his head too busy for his body. "I cannot keep my restless
brain from grinding on, although with great loss of time; for whatever
idea comes into my head with respect to any novelty, drives out of it
whatever I had been thinking of just before." He was busily engaged in
considering the nature of the force of percussion, and Torricelli was
employed in arranging his investigations for a continuation of the
'Dialogues on Motion,' when he was seized with an attack of fever and
palpitation of the heart, which, after an illness of two months, put an
end to his long, laborious, and useful life, on the 8th of January,
1642, just one year before his great successor Newton was born.

The malice of his enemies was scarcely allayed by his death. His right
of making a will was disputed, as having died a prisoner to the
Inquisition, as well as his right to burial in consecrated ground. These
were at last conceded, but Urban anxiously interfered to prevent the
design of erecting a monument to him in the church of Santa Croce, in
Florence, for which a large sum had been subscribed. His body was
accordingly buried in an obscure corner of the church, which for upwards
of thirty years after his death was unmarked even by an inscription to
his memory. It was not till a century later that the splendid monument
was erected which now covers his and Viviani's remains. When their
bodies were disinterred in 1737 for the purpose of being removed to
their new resting-place, Capponi, the president of the Florentine
Academy, in a spirit of spurious admiration, mutilated Galileo's body,
by removing the thumb and forefinger of the right-hand, and one of the
vertebræ of the back, which are still preserved in some of the Italian
museums. The monument was put up at the expense of his biographer,
Nelli, to whom Viviani's property descended, charged with the condition
of erecting it. Nor was this the only public testimony which Viviani
gave of his attachment. The medal which he struck in honour of Galileo
has already been mentioned; he also, as soon as it was safe to do so,
covered every side of the house in which he lived with laudatory
inscriptions to the same effect. A bust of Galileo was placed over the
door, and two bas-reliefs on each side representing some of his
principal discoveries. Not less than five other medals were struck in
honour of him during his residence at Padua and Florence, which are all
engraved in Venturi's Memoirs.

There are several good portraits of Galileo extant, two of which, by
Titi and Subtermanns, are engraved in Nelli's Life of Galileo. Another
by Subtermanns is in the Florentine Gallery, and an engraving from a
copy of this is given by Venturi. There is also a very fine engraving
from the original picture. An engraving from another original picture is
in the frontispiece of the Padua edition of his works. Salusbury seems
in the following passage to describe a portrait of Galileo painted by
himself: "He did not contemn the other inferior arts, for he had a good
hand in sculpture and carving; but his particular care was to paint
well. By the pencil he described what his telescope discovered; in one
he exceeded art, in the other, nature. Osorius, the eloquent bishop of
Sylva, esteems one piece of Mendoza the wise Spanish minister's
felicity, to have been this, that he was contemporary to Titian, and
that by his hand he was drawn in a fair tablet. And Galilæus, lest he
should want the same good fortune, made so great a progress in this
curious art, that he became his own _Buonarota_; and because there was
no other copy worthy of his pencil, drew himself." No other author makes
the slightest allusion to such a painting; and it appears more likely
that Salusbury should be mistaken than that so interesting a portrait
should have been entirely lost sight of.

Galileo's house at Arcetri was standing in 1821, when Venturi visited
it, and found it in the same state in which Galileo might be supposed to
have left it. It is situated nearly a mile from Florence, on the
south-eastern side, and about a gun-shot to the north-west of the
convent of St. Matthew. Nelli placed a suitable inscription over the
door of the house, which belonged in 1821 to a Signor Alimari.[175]

Although Nelli's Life of Galileo disappointed the expectations that had
been formed of it, it is impossible for any admirer of Galileo not to
feel the greatest degree of gratitude towards him, for the successful
activity with which he rescued so many records of the illustrious
philosopher from destruction. After Galileo's death, the principal part
of his books, manuscripts, and instruments, were put into the charge of
Viviani, who was himself at that time an object of great suspicion; most
of them he thought it prudent to conceal, till the superstitious
outcries against Galileo should be silenced. At Viviani's death, he left
his library, containing a very complete collection of the works of all
the mathematicians who had preceded him (and amongst them those of
Galileo, Torricelli, and Castelli, all which were enriched with notes
and additions by himself), to the hospital of St. Mary at Florence,
where an extensive library already existed. The directors of the
hospital sold this unique collection in 1781, when it became entirely
dispersed. The manuscripts in Viviani's possession passed to his nephew,
the Abbé Panzanini, together with the portraits of the chief personages
of the Galilean school, Galileo's instruments, and, among other
curiosities, the emerald ring which he wore as a member of the Lyncean
Academy. A great number of these books and manuscripts were purchased at
different times by Nelli, after the death of Panzanini, from his
relations, who were ignorant or regardless of their value. One of his
chief acquisitions was made by an extraordinary accident, related by
Tozzetti with the following details, which we repeat, as they seem to
authenticate the story:--"In the spring of 1739, the famous Doctor Lami
went out according to his custom to breakfast with some of his friends
at the inn of the Bridge, by the starting-place; and as he and Sig.
Nelli were passing through the market, it occurred to them to buy some
Bologna sausages from the pork-butcher, Cioci, who was supposed to excel
in making them. They went into the shop, had their sausages cut off and
rolled in paper, which Nelli put into his hat. On reaching the inn, and
calling for a plate to put them in, Nelli observed that the paper in
which they had been rolled was one of Galileo's letters. He cleaned it
as well as he could with his napkin, and put it into his pocket without
saying a word to Lami; and as soon as he returned into the city, and
could get clear of him, he flew to the shop of Cioci, who told him that
a servant whom he did not know brought him from time to time similar
letters, which he bought by weight as waste paper. Nelli bought all that
remained, and on the servant's next reappearance in a few days, he
learned the quarter whence they came, and after some time succeeded at a
small expense in getting into his own possession an old corn-chest,
containing all that still remained of the precious treasures which
Viviani had concealed in it ninety years before."[176]

The earliest biographical notice of Galileo is that in the Obituary of
the Mercurio Italico, published at Venice in 1647, by Vittorio Siri. It
is very short, but contains an exact enumeration of his principal works
and discoveries. Rossi, who wrote under the name of Janus Nicius
Erythræus, introduced an account of Galileo in his Pinacotheca Imaginum
Illustrium, in which the story of his illegitimacy first made its
appearance. In 1664, Salusbury published a life of Galileo in the second
volume of his Mathematical Collections, the greater part of which is a
translation of Galileo's principal works. Almost the whole edition of
the second volume of Salusbury's book was burnt in the great fire of
London. Chauffepié says that only one copy is known to be extant in
England: this is now in the well-known library of the Earl of
Macclesfield, to whose kindness the author is much indebted for the use
he has been allowed to make of this unique volume. A fragment of this
second volume is in the Bodleian Library at Oxford. The translations in
the preceding pages are mostly founded upon Salusbury's version.
Salusbury's account, although that of an enthusiastic admirer of
Galileo, is too prolix to be interesting: the general style of the
performance may be guessed from the title of the first chapter--'Of Man
in general, and how he excelleth all the other Animals.' After informing
his readers that Galileo was born at Pisa, he proceeds:--"Italy is
affirmed to have been the first that peopled the world after the
universal deluge, being governed by Janus, Cameses, and Saturn, &c." His
description of Galileo's childhood is somewhat quaint. "Before others
had left making of dirt pyes, he was framing of diagrams; and whilst
others were whipping of toppes, he was considering the cause of their
motion." It is on the whole tolerably correct, especially if we take
into account that Salusbury had not yet seen Viviani's Life, though
composed some years earlier.

The Life of Galileo by Viviani was first written as an outline of an
intended larger work, but this latter was never completed. This sketch
was published in the Memoirs of the Florentine Academy, of which Galileo
had been one of the annual presidents, and afterwards prefixed to the
complete editions of Galileo's works; it is written in a very agreeable
and flowing style, and has been the groundwork of most subsequent
accounts. Another original memoir by Niccolò Gherardini, was published
by Tozzetti. A great number of references to authors who have treated of
Galileo is given by Sach in his Onomasticon. An approved Latin memoir by
Brenna is in the first volume of Fabroni's Vitæ Italorum Illustrium; he
has however fallen into several errors: this same work contains the
lives of several of his principal followers.

The article in Chauffepié's Continuation of Bayle's Dictionary does not
contain anything which is not in the earlier accounts.

Andrès wrote an essay entitled 'Saggio sulla Filosofia del Galileo,'
published at Mantua 1776; and Jagemann published his 'Geschichte des
Leben des Galileo' at Leipzig, in 1787;[177] neither of these the author
has been able to meet with. An analysis of the latter may be seen in
Kästner's 'Geschichte der Mathematik, Göttingen, 1800,' from which it
does not appear to contain any additional details. The 'Elogio del
Galileo' by Paolo Frisi, first published at Leghorn in 1775, is, as its
title expresses, rather in the nature of a panegyric than of a
continuous biographical account. It is written with very great elegance
and intimate knowledge of the subjects of which it treats. Nelli gave
several curious particulars with respect to Galileo in his 'Saggio di
Storia Letteraria Fiorentina, Lucca, 1759;' and in 1793 published his
large work entitled 'Vita e Commercio Letterario di Galileo Galilei.' So
uninteresting a book was probably never written from such excellent
materials. Two thick quarto volumes are filled with repetitions of the
accounts that were already in print, the bulky preparation of which
compelled the author to forego the publication of the vast collection of
original documents which his unwearied zeal and industry had collected.
This defect has been in great measure supplied by Venturi in 1818 and
1821, who has not only incorporated in his work many of Nelli's
manuscripts, but has brought together a number of scattered notices of
Galileo and his writings from a variety of outlying sources--a service
which the writer is able to appreciate from having gone through the
greatest part of the same labour before he was fortunate enough to meet
with Venturi's book. Still there are many letters cited by Nelli, which
do not appear either in his book or Venturi's. Carlo Dati, in 1663,
quotes "the registers of Galileo's correspondence arranged in
alphabetical order, in ten large volumes."[178] The writer has no means
of ascertaining what collection this may have been; it is difficult to
suppose that one so arranged should have been lost sight of. It is
understood that a life of Galileo is preparing at this moment in
Florence, by desire of the present Grand Duke, which will probably throw
much additional light on the character and merits of this great and
useful philosopher.

The first editions of his various treatises, as mentioned by Nelli, are
given below. Clement, in his 'Bibliothèque Curieuse,' has pointed out
such among them, and the many others which have been printed, as have
become rare.

The Florentine edition is the one used by the Academia della Crusca for
their references; for which reason its paging is marked in the margin of
the edition of Padua, which is much more complete, and is the one which
has been on the present occasion principally consulted.

The latter contains the Dialogue on the System, which was not suffered
to be printed in the former editions. The twelve first volumes of the
last edition of Milan are a mere transcript of that of Padua: the
thirteenth contains in addition the Letter to the Grand Duchess, the
Commentary on Tasso, with some minor pieces. A complete edition is still
wanted, embodying all the recently discovered documents, and omitting
the verbose commentaries, which, however useful when they were written,
now convey little information that cannot be more agreeably and more
profitably learned in treatises of a later date.

Such was the life, and such were the pursuits, of this extraordinary
man. The numberless inventions of his acute industry; the use of the
telescope, and the brilliant discoveries to which it led; the patient
investigation of the laws of weight and motion; must all be looked upon
as forming but a part of his real merits, as merely particular
demonstrations of the spirit in which he everywhere withstood the
despotism of ignorance, and appealed boldly from traditional opinions to
the judgments of reason and common sense. He claimed and bequeathed to
us the right of exercising our faculties in examining the beautiful
creation which surrounds us. Idolized by his friends, he deserved their
affection by numberless acts of kindness; by his good humour, his
affability, and by the benevolent generosity with which he devoted
himself and a great part of his limited income to advance their talents
and fortunes. If an intense desire of being useful is everywhere worthy
of honour; if its value is immeasurably increased, when united to genius
of the highest order; if we feel for one who, notwithstanding such
titles to regard, is harassed by cruel persecution,--then none deserve
our sympathy, our admiration, and our gratitude, more than Galileo.


_List of Galileo's Works._

  Le Operazioni del Compasso Geom. e Milit.
                                            Padova, 1606.
  Fol. Difesa di Gal. Galilei contr. all. cal. et impost. di Bald. Capra
                                            Venezza, 1607. 4to.
  Sydereus Nuncius                          Venetiis, 1610. 4to.
  Discorso int. alle cose che stanno in su l'Acqua
                                            Firenze, 1612. 4to.
  Novantiqua SS. PP. Doctrina de S. Scripturæ Testimoniis
                                            Argent, 1612. 4to.
  Istoria e Demostr. int. alle Macchie Solari
                                            Roma, 1613. 4to.
  Risp. alle oppos. del S. Lod. delle Colombe e del S. Vinc. di Grazia
                                            Firenze, 1615. 4to.
  Discorso delle Comete di Mario Guiducci
                                            Firenze, 1619. 4to.
  Dialogo sopra i due Massimi Sistemi del Mondo
                                            Firenze, 1632. 4to.
  Discorso e Demostr. intorno alle due nuove Scienze
                                            Leida, 1638. 4to.
  Della Scienza Meccanica                   Ravenna, 1649. 4to.
  Trattato della Sfera                      Roma, 1655. 4to.
  Discorso sopra il Flusso e Reflusso. (Scienze Fisiche di Tozzetti.)
                                            Firenze, 1780. 4to.
  Considerazioni sul Tasso                  Roma, 1793.
  Trattato della Fortificazione. (Memorie di Venturi.)
                                            Modena, 1818. 4to.

The editions of his collected works (in which is contained much that was
never published separately) are--

  Opere di Gal. Galilei, Linc. Nob. Fior. &c.
                                             Bologna, 1656. 2 vols. 4to.
  Opere di Gal. Galilei, Nob. Fior. Accad. Linc. &c.
                                             Firenze, 1718. 3 vols. 4to.
  Opere di Gal. Galilei                      Padova, 1744. 4 vols. 4to.
  Opere di Gal. Galilei                      Milano, 1811. 13 vols. 8vo.


CORRECTIONS.

  _Page Co. Line._

    5   1     2,
      _Add_: His instructor was the celebrated botanist, Andreas
      Cæsalpinus, who was professor of medicine at Pisa from 1567 to 1592.
      Hist. Acad. Pisan.; Pisis, 1791.

    8   2    18,
      _Add_: According to Kästner, his German name was Wursteisen.

    8   2    21, _for_ 1588 _read_ 1586.
   15   1    57, _for_ 1632 _read_ 1630.
   17   1    29,
      Salusbury alludes to the instrument described and figured in "The
      Use of the Sector, Crosse Staffe, and other Instruments. London,
      1624." It is exactly Galileo's Compass.

   17   1    52, _for_ Burg, a German, _read_ Burgi, a Swiss.
   27   2    17,
      The author here called Brutti was an Englishman: his real name,
      perhaps, was Bruce. See p. 99.

   50   1    14,
      Kepler's Epitome was not published till 1619: it was then inserted
      in the Index.

   73   1    60, _for_ under _read_ turned from.
   80   2    44, _for_ any _read_ an indefinitely small.


FOOTNOTES:

[170] The words of his diploma are: Galilæi in mathematicis disciplinis
discipulus, in ærumnis socius, Italicum ingenium ita perpolivit optimis
artibus ut inter mathematicos sæculi nostri facile princeps per orbem
litterarium numeretur.--Tiraboschi.

[171] On this occasion the taste of the time showed itself in the
following anagram:--

    Evangelista Torricellieus,
    En virescit Galilæus alter.

[172] Compare Son. ii. v. 8 & 9; and Son. iii. v. 2 & 3, with Ger. Lib.
c. iv. st. 76, and c. vii. st. 19.--The author gladly owns his
obligation for these remarks to the kindness of Sig. Panizzi, Professor
of Italian in the University of London.

[173] Lettera di Timauro Antiate. Firenze, 1663.

[174] De phænomenis in orbe Lunæ. Venetiis, 1612.

[175] Venturi.

[176] Notizie sul Ingrandimento delle Scienze Fisiche. Firenze, 1780.

[177] Venturi.

[178] Lettera di Timauro Antiate.




LIFE OF KEPLER.




CHAPTER I.

    _Introduction--Birth and Education of Kepler--He is appointed
      Astronomical Professor at Gratz--Publishes the 'Mysterium
      Cosmographicum.'_


IN the account of the life and discoveries of Galileo, we have
endeavoured to inculcate the safety and fruitfulness of the method
followed by that great reformer in his search after physical truth. As
his success furnishes the best instance of the value of the inductive
process, so the failures and blunders of his adversaries supply equally
good examples of the dangers and the barrenness of the opposite course.
The history of JOHN KEPLER might, at the first view, suggest conclusions
somewhat inconsistent with this remark. Every one who is but moderately
acquainted with astronomy is familiar with the discoveries which that
science owes to him; the manner in which he made them is, perhaps, not
so generally known. This extraordinary man pursued, almost invariably,
the hypothetical method. His life was passed in speculating on the
results of a few principles assumed by him, from very precarious
analogies, as the causes of the phenomena actually observed in Nature.
We nevertheless find that he did, in spite of this unphilosophical
method, arrive at discoveries which have served as guides to some of the
most valuable truths of modern science.

The difficulty will disappear if we attend more closely to the details
of Kepler's investigations. We shall perceive that to an unusual degree
of rashness in the formation of his systems, he added a quality very
rarely possessed by philosophers of the hypothetical school. One of the
greatest intellectual vices of the latter was a wilful blindness to the
discrepancy of facts from their creed, a perverse and obstinate
resistance to physical evidence, leading not unfrequently to an attempt
at disguising the truth. From this besetting sin of the school, which
from an intellectual fault often degenerated into a moral one, Kepler
was absolutely free. Scheme after scheme, resting originally upon little
beyond his own glowing imagination, but examined and endeared by the
ceaseless labour of years, was unhesitatingly sacrificed, as soon as its
insufficiency became indisputable, to make room for others as little
deserving support. The history of philosophy affords no more remarkable
instance of sincere uncompromising love of truth. To this virtue he owed
his great discoveries: it must be attributed to his unhappy method that
he made no more.

In considering this opinion upon the real nature of Kepler's title to
fame, it ought not to be forgotten that he has exposed himself at a
disadvantage on which certainly very few philosophers would venture. His
singular candour allowed him to comment upon his own errors with the
same freedom as if scrutinizing the work of a stranger; careless whether
the impression on his readers were favourable or otherwise to himself,
provided it was instructive. Few writers have spoken so much, and so
freely of themselves, as Kepler. He records, on almost every occasion,
the train of thought by which he was led to each of the discoveries that
eventually repaid his perseverance; and he has thus given us a most
curious and interesting view of the workings of a mind of great, though
eccentric power. "In what follows," says he (when introducing a long
string of suppositions, of which he had already discovered the fallacy),
"let the reader pardon my credulity, whilst working out all these
matters by my own ingenuity. For it is my opinion that the occasions by
which men have acquired a knowledge of celestial phenomena are not less
admirable than the discoveries themselves." Agreeing altogether with
this opinion in its widest application, we have not scrupled, in the
following sketch, to introduce at some length an account even of
Kepler's erroneous speculations; they are in themselves very amusing,
and will have the additional utility of proving the dangerous tendency
of his method; they will show by how many absurd theories, and how many
years of wasted labour, his real discoveries and services to science lie
surrounded.

JOHN KEPLER was born (as we are assured by his earliest biographer
Hantsch) in long. 29° 7´, lat. 48° 54´, on the 21st day of December,
1571. On this spot stands the imperial city of Weil, in the duchy of
Wirtemberg. His parents were Henry Kepler and Catherine Guldenmann, both
of noble, though decayed families. Henry Kepler, at the time of his
marriage, was a petty officer in the Duke of Wirtemberg's service; and a
few years after the birth of his eldest son John, he joined the army
then serving in the Netherlands. His wife followed him, leaving their
son, then in his fifth year, at Leonberg, under the care of his
grandfather. He was a seven months child, very weak and sickly; and
after recovering with difficulty from a severe attack of small-pox, he
was sent to school in 1577. Henry Kepler's limited income was still
farther reduced on his return into Germany, the following year, in
consequence of the absconding of one of his acquaintance, for whom he
had incautiously become surety. His circumstances were so much narrowed
by this misfortune, that he was obliged to sell his house, and nearly
all that he possessed, and for several years he supported his family by
keeping a tavern at Elmendingen. This occasioned great interruption to
young Kepler's education; he was taken from school, and employed in
menial services till his twelfth year, when he was again placed in the
school at Elmendingen. In the following year he was again seized with a
violent illness, so that his life was almost despaired of. In 1586, he
was admitted into the monastic school of Maulbronn, where the cost of
his education was defrayed by the Duke of Wirtemberg. This school was
one of those established on the suppression of the monasteries at the
Reformation, and the usual course of education followed there required
that the students, after remaining a year in the superior classes,
should offer themselves for examination at the college of Tubingen for
the degree of bachelor: they then returned to their school with the
title of veterans; and after completing the studies taught there, they
were admitted as resident students at Tubingen, proceeded in about a
year to the degree of master, and were then allowed to commence their
course of theology. The three years of Kepler's life following his
admission to Maulbronn, were marked by periodical returns of several of
the disorders which had well nigh proved fatal to him in his childhood.
During the same time disagreements arose between his parents, in
consequence of which his father quitted his home, and soon after died
abroad. After his father's departure, his mother also quarrelled with
her relations, having been treated, says Hantsch, "with a degree of
barbarity by her husband and brother-in-law that was hardly exceeded
even by her own perverseness:" one of his brothers died, and the
family-affairs were in the greatest confusion. Notwithstanding these
disadvantages, Kepler took his degree of master in August 1591,
attaining the second place in the annual examination. The first name on
the list was John Hippolytus Brentius.

Whilst he was thus engaged at Tubingen, the astronomical lectureship at
Gratz, the chief town of Styria, became vacant by the death of George
Stadt, and the situation was offered to Kepler. Of this first occasion
of turning his thoughts towards astronomy, he has himself given the
following account: "As soon as I was of an age to feel the charms of
philosophy, I embraced every part of it with intense desire, but paid no
especial regard to astronomy. I had indeed capacity enough for it, and
learned without difficulty the geometrical and astronomical theorems
occurring in the usual course of the school, being well grounded in
figures, numbers, and proportions. But those were compulsory
studies--there was nothing to show a particular turn for astronomy. I
was educated at the expense of the Duke of Wirtemberg, and when I saw
such of my companions as the duke selected to send abroad shrink in
various ways from their employments, out of fondness for home, I, who
was more callous, had early made up my mind to go with the utmost
readiness whithersoever I might be sent. The first offering itself was
an astronomical post, which I was in fact forced to accept by the
authority of my tutors; not that I was alarmed, in the manner I had
condemned in others, by the remoteness of the situation, but by the
unexpected and contemptible nature of the office, and by the slightness
of my information in this branch of philosophy. I entered on it,
therefore, better furnished with talent than knowledge: with many
protestations that I was not abandoning my claim to be provided for in
some other more brilliant profession. What progress I made in the first
two years of my studies, may be seen in my 'Mysterium Cosmographicum;'
and the encouragement given me by my tutor, Mästlin, to take up the
science of astronomy, may be read in the same book, and in his letter
which is prefixed to the 'Narrative of Rheticus.' I looked on that
discovery as of the highest importance, and still more so, because I saw
how greatly it was approved by Mästlin."

The nature of the singular work to which Kepler thus refers with so much
complacency, will be best shown by quoting some of the most remarkable
parts of it, and especially the preface, in which he briefly details
some of the theories he successively examined and rejected, before
detecting (as he imagined he had here done) the true cause of the number
and order of the heavenly bodies. The other branches of philosophy with
which he occupied himself in his younger years, were those treated by
Scaliger in his 'Exoteric Exercises,' to the study of which book Kepler
attributed the formation of many of his opinions; and he tells us that
he devoted much time "to the examination of the nature of heaven, of
souls, of genii, of the elements, of the essence of fire, of the cause
of fountains, the ebb and flow of the tide, the shape of the continents,
and inland seas, and things of this sort." He also says, that by his
first success with the heavens, his hopes were greatly inflamed of
discovering similar analogies in the rest of the visible world, and for
this reason, named his book merely a Prodromus, or Forerunner, meaning,
at some future period, to subjoin the Aftercomer, or Sequel. But this
intention was never fulfilled; either his imagination failed him, or,
what is more likely, the laborious calculations in which his
astronomical theories engaged him, left him little time for turning his
attention to objects unconnected with his first pursuit.

It is seldom that we are admitted to trace the progress of thought in
those who have distinguished themselves by talent and originality; and
although the whole of the following speculations begin and end in error,
yet they are so characteristic, and exhibit such an extraordinary
picture of the extravagances into which Kepler's lively imagination was
continually hurrying him, that we cannot refrain from citing nearly the
whole preface. From it, better than from any enumeration of
peculiarities, the reader will at once apprehend the nature of his
disposition.

"When I was attending the celebrated Mästlin, six years ago, at
Tubingen, I was disturbed by the manifold inconveniences of the common
theory of the universe, and so delighted with Copernicus, whom Mästlin
was frequently in the habit of quoting with great respect, that I not
only often defended his propositions in the physical disputations of the
candidates, but also wrote a correct essay on the primary motion,
maintaining, that it is caused by the rotation of the earth. And I was
then at that point that I attributed to the earth the motion of the sun
on physical (or, if you will, on metaphysical) grounds, as Copernicus
had done for mathematical reasons. And, by this practice, I came by
degrees, partly from Mästlin's instructions, and partly from my own
efforts, to understand the superior mathematical convenience of the
system of Copernicus beyond Ptolemy's. This labour might have been
spared me, by Joachim Rheticus, who has shortly and clearly explained
everything in his first Narrative. While incidentally engaged in these
labours, in the intermission of my theology, it happened conveniently
that I succeeded George Stadt in his situation at Gratz, where the
nature of my office connected me more closely with these studies.
Everything I had learned from Mästlin, or had acquired of myself, was
there of great service to me in explaining the first elements of
astronomy. And, as in Virgil, '_Fama mobilitate viget, viresque acquirit
eundo_,' so it was with me, that the diligent thought on these things
was the occasion of still further thinking: until, at last, in the year
1595, when I had some intermission of my lectures allowed me, I brooded
with the whole energy of my mind on this subject. There were three
things in particular, of which I pertinaciously sought the causes why
they are not other than they are: the number, the size, and the motion
of the orbits. I attempted the thing at first with numbers, and
considered whether one of the orbits might be double, triple, quadruple,
or any other multiple of the others, and how much, according to
Copernicus, each differed from the rest. I spent a great deal of time in
that labour, as if it were mere sport, but could find no equality either
in the proportions or the differences, and I gained nothing from this
beyond imprinting deeply in my memory the distances as assigned by
Copernicus; unless, perhaps, reader, this record of my various attempts
may force your assent, backwards and forwards, as the waves of the sea;
until tired at length, you will willingly repose yourself, as in a safe
haven, on the reasons explained in this book. However, I was comforted
in some degree, and my hopes of success were supported as well by other
reasons which will follow presently, as by observing that the motions in
every case seemed to be connected with the distances, and that where
there was a great gap between the orbits, there was the same between the
motions. And I reasoned, that if God had adapted motions to the orbits
in some relation to the distances, it was probable that he had also
arrayed the distances themselves in relation to something else.

"Finding no success by this method, I tried another, of singular
audacity. I inserted a new planet between Mars and Jupiter, and another
between Venus and Mercury, both of which I supposed invisible, perhaps
on account of their smallness, and I attributed to each a certain period
of revolution.[179] I thought that I could thus contrive some equality
of proportions, increasing between every two, from the sun to the fixed
stars. For instance, the Earth is nearer Venus in parts of the
terrestrial orbit, than Mars is to the Earth in parts of the orbit of
Mars. But not even the interposition of a new planet sufficed for the
enormous gap between Mars and Jupiter; for the proportion of Jupiter to
the new planet was still greater than that of Saturn to Jupiter. And
although, by this supposition, I got some sort of a proportion, yet
there was no reasonable conclusion, no certain determination of the
number of the planets either towards the fixed stars, till we should get
as far as them, nor ever towards the Sun, because the division in this
proportion of the residuary space within Mercury might be continued
without end. Nor could I form any conjecture, from the mobility of
particular numbers, why, among an infinite number, so few should be
moveable. The opinion advanced by Rheticus in his Narrative is
improbable, where he reasons from the sanctity of the number six to the
number of the six moveable heavens; for he who is inquiring of the frame
of the world itself, must not derive reasons from these numbers, which
have gained importance from things of later date.

"I sought again, in another way, whether the distance of every planet is
not as the residuum of a sine; and its motion as the residuum of the
sine of the complement in the same quadrant.

[Illustration]

"Conceive the square AB to be constructed, whose side AC is equal to the
semidiameter of the universe. From the angle B opposite to A the place
of the sun, or centre of the world, describe the quadrant DC with the
radius BC. Then in AC, the true radius of the world, let the sun, fixed
stars, and planets be marked at their respective distances, and from
these points draw lines parallel to BC, meeting the quadrant. I imagined
the moving force acting on each of the planets to be in the proportion
of these parallels. In the line of the sun is infinity, because AD is
touched, and not cut, by the quadrant: therefore the moving force is
infinite in the sun, as deriving no motion except from its own act. In
Mercury the infinite line is cut off at K, and therefore at this point
the motion is comparable with the others. In the fixed stars the line is
altogether lost, and compressed into a mere point C; therefore at that
point there is no moving force. This was the theorem, which was to be
tried by calculation; but if any one will reflect that two things were
wanting to me, first, that I did not know the size of the _Sinus Totus_,
that is, the radius of the proposed quadrant; secondly, that the
energies of the motions were not thus expressed otherwise than in
relation one to another; whoever, I say, well considers this, will
doubt, not without reason, as to the progress I was likely to make in
this difficult course. And yet, with unremitting labour, and an infinite
reciprocation of sines and arcs, I did get so far as to be convinced
that this theory could not hold.

"Almost the whole summer was lost in these annoying labours; at last, by
a trifling accident, I lighted more nearly on the truth. I looked on it
as an interposition of Providence, that I should obtain by chance, what
I had failed to discover with my utmost exertions; and I believed this
the more, because I prayed constantly that I might succeed, if
Copernicus had really spoken the truth. It happened on the 9th or
19th[180] day of July, in the year 1595, that, having occasion to show,
in my lecture-room, the passages of the great conjunctions through eight
signs, and how they pass gradually from one trine aspect to another, I
inscribed in a circle a great number of triangles, or quasi-triangles,
so that the end of one was made the beginning of another. In this manner
a smaller circle was shadowed out by the points in which the lines
crossed each other.

[Illustration: A Scheme of the great Conjunctions of SATURN & JUPITER,
their leaps through eight Signs, and their passages through all the four
Triplicities of the Zodiac.]

"The radius of a circle inscribed in a triangle is half the radius of
that described about it; therefore the proportion between these two
circles struck the eye as almost identical with that between Saturn and
Jupiter, and the triangle is the first figure, just as Saturn and
Jupiter are the first planets. On the spot I tried the second distance
between Jupiter and Mars with a square, the third with a pentagon, the
fourth with a hexagon. And as the eye again cried out against the second
distance between Jupiter and Mars, I combined the square with a triangle
and a pentagon. There would be no end of mentioning every trial. The
failure of this fruitless attempt was the beginning of the last
fortunate one; for I reflected, that in this way I should never reach
the sun, if I wished to observe the same rule throughout; nor should I
have any reason why there were six, rather than twenty or a hundred
moveable orbits. And yet figures pleased me, as being quantities, and as
having existed before the heavens; for quantity was created with matter,
and the heavens afterwards. But if (this was the current of my
thoughts), in relation to the quantity and proportion of the six orbits,
as Copernicus has determined them among the infinite other figures, five
only could be found having peculiar properties above the rest, my
business would be done. And then again it struck me, what have plane
figures to do among solid orbits? Solid bodies ought rather to be
introduced. This, reader, is the invention and the whole substance of
this little work; for if any one, though but moderately skilled in
geometry, should hear these words hinted, the five regular solids will
directly occur to him with the proportions of their circumscribed and
inscribed spheres: he has immediately before his eyes that scholium of
Euclid to the 18th proposition of his 13th Book, in which it is proved
to be impossible that there should be, or be imagined, more than five
regular bodies.

"What is worthy of admiration (since I had then no proof of any
prerogatives of the bodies with regard to their order) is, that
employing a conjecture which was far from being subtle, derived from the
distances of the planets, I should at once attain my end so happily in
arranging them, that I was not able to change anything afterwards with
the utmost exercise of my reasoning powers. In memory of the event, I
write down here for you the sentence, just as it fell from me, and in
the words in which it was that moment conceived:--The Earth is the
circle, the measurer of all; round it describe a dodecahedron, the
circle including this will be Mars. Round Mars describe a tetrahedron,
the circle including this will be Jupiter. Describe a cube round
Jupiter, the circle including this will be Saturn. Now, inscribe in the
Earth an icosahedron, the circle inscribed in it will be Venus. Inscribe
an octahedron in Venus, the circle inscribed in it will be Mercury. This
is the reason of the number of the planets.

[Illustration]

"This was the cause, and such the success, of my labour: now read my
propositions in this book. The intense pleasure I have received from
this discovery never can be told in words. I regretted no more the time
wasted; I tired of no labour; I shunned no toll of reckoning; days and
nights I spent in calculations; until I could see whether this opinion
would agree with the orbits of Copernicus, or whether my joy was to
vanish into air. I willingly subjoin that sentiment of Archytas, as
given by Cicero: 'If I could mount up into heaven, and thoroughly
perceive the nature of the world, and beauty of the stars, that
admiration would be without a charm for me, unless I had some one like
you, reader, candid, attentive, and eager for knowledge, to whom to
describe it.' If you acknowledge this feeling, and are candid, you will
refrain from blame, such as not without cause I anticipate; but if,
leaving that to itself, you fear lest these things be not ascertained,
and that I have shouted triumph before victory, at least approach these
pages, and learn the matter in consideration: you will not find, as just
now, new and unknown planets interposed; that boldness of mine is not
approved, but those old ones very little loosened, and so furnished by
the interposition (however absurd you may think it) of rectilinear
figures, that in future you may give a reason to the rustics when they
ask for the hooks which keep the skies from falling.--Farewell."

In the third chapter Kepler mentions, that a thickness must be allowed
to each orb sufficient to include the greatest and least distance of
the planet from the sun. The form and result of his comparison with the
real distances are as follows:--

                                                               Book V.
  If the   {Saturn } be taken {Jupiter = 577}              {635 Ch. 9
  inner    {Jupiter} at 1000  {Mars    = 333} According to {333--14
  Surface  {Mars   } then the {Earth   = 795} Copernicus   {757--19
  of the   {Earth  } outer    {Venus   = 795}  they are    {794--21, 22
  orbit of {Venus  } one of   {Mercury = 577}              {723--27

It will be observed, that Kepler's results were far from being entirely
satisfactory; but he seems to have flattered himself, that the
differences might be attributed to erroneous measurements. Indeed, the
science of observation was then so much in its infancy, that such an
assertion might be made without incurring much risk of decisive
refutation.

Kepler next endeavoured to determine why the regular solids followed in
this rather than any other order; and his imagination soon created a
variety of essential distinctions between the cube, pyramid, and
dodecahedron, belonging to the superior planets, and the other two.

The next question examined in the book, is the reason why the zodiac is
divided into 360 degrees; and on this subject, he soon becomes enveloped
in a variety of subtle considerations, (not very intelligible in the
original, and still more difficult to explain shortly to others
unacquainted with it,) in relation to the divisions of the musical
scale; the origin of which he identifies with his five favourite solids.
The twentieth chapter is appropriated to a more interesting inquiry,
containing the first traces of his finally successful researches into
the proportion between the distances of the planets, and the times of
their motions round the sun. He begins with the generally admitted fact,
that the more distant planets move more slowly; but in order to show
that the proportion, whatever it may be, is not the simple one of the
distances, he exhibits the following little Table:--

             [Saturn]
  +---------+--------+
  |         |D. Scr. |[Jupiter]
  +---------+--------+---------+
  |[Saturn] |10759.12| D. Scr. |[Mars]
  +---------+--------+---------+--------+
  |[Jupiter]| 6159   | 4332.37 |D. Scr. |[Earth]
  +---------+--------+---------+--------+-------+
  |[Mars]   | 1785   | 1282    | 686.59 |D. Scr.|[Venus]
  +---------+--------+---------+--------+-------+-------+
  |[Earth]  | 1174   |  843    | 452    |365.15 |D. Scr.| [Mercury]
  +---------+--------+---------+--------+-------+-------+----------+
  |[Venus]  |  844   |  606    | 325    |262.30 |224.42 | D. Scr.  |
  +---------+--------+---------+--------+-------+-------+----------+
  |[Mercury]|  434   |  312    | 167    |135    |115    |  87.58   |

At the head of each vertical column is placed the real time (in days and
sexagesimal parts) of the revolution of the planet placed above it, and
underneath the days due to the other inferior planets, if they observed
the proportion of distance. Hence it appears that this proportion in
every case gives a time greater than the truth; as for instance, if the
earth's rate of revolution were to Jupiter's in the proportion of their
distances, the second column shows that the time of her period would be
843 instead of 365¼ days; so of the rest. His next attempt was to
compare them by two by two, in which he found that he arrived at a
proportion something like the proportion of the distances, although as
yet far from obtaining it exactly. This process amounts to taking the
quotients obtained by dividing the period of each planet by the period
of the one next beyond.

          { [Saturn] 10759.27} be successively     { [Jupiter] 403
  For if  { [Jupiter] 4332.37} taken to consist of { [Mars]    159
  each    {                  } 1000 equal parts,   {
  of the  { [Mars]     686.59} the periods of      { [Earth]   532
  periods { [Earth]    365.15} the planet next     { [Venus]   615
  of      {                  } below will contain  {
          { [Venus]    244.42} of those parts in   { [Mercury] 392

  But if the distance of each planet in    {[Jupiter] 572
    succession be taken to consist of      {[Mars]    290
    1000 equal parts, the distance of      {[Earth]   658
    the next below will contain, according {[Venus]   719
    to Copernicus, in                      {[Mercury] 500

From this table he argued that to make the proportions agree, we must
assume one of two things, "either that the moving intelligences of the
planets are weakest in those which are farthest from the Sun, or that
there is one moving intelligence in the Sun, the common centre forcing
them all round, but those most violently which are nearest, and that it
languishes in some sort, and grows weaker at the most distant, because
of the remoteness and the attenuation of the virtue."

We stop here to insert a note added by Kepler to the later editions, and
shall take advantage of the same interruption to warn the reader not to
confound this notion of Kepler with the theory of a gravitating force
towards the Sun, in the sense in which we now use those words. According
to our theory, the effect of the presence of the Sun upon the planet is
to pull it towards the centre in a straight line, and the effect of the
motion thus produced combined with the motion of the planet, which if
undisturbed would be in a straight line inclined to the direction of the
radius, is, that it describes a curve round the Sun. Kepler considered
his planets as perfectly quiet and unwilling to move when left alone;
and that this virtue supposed by him to proceed in every direction out
of the Sun, swept them round, just as the sails of a windmill would
carry round anything which became entangled in them. In other parts of
his works Kepler mentions having speculated on a real attractive force
in the centre; but as he knew that the planets are not always at the
same distance from the Sun, and conceived erroneously, that to remove
them from their least to their greatest distance a repulsive force must
be supposed alternating with an attractive one, he laid aside this
notion as improbable. In a note he acknowledges that when he wrote the
passage just quoted, imbued as he then was with Scaliger's notions on
moving intelligences, he literally believed "that each planet was moved
by a living spirit, but afterwards came to look on the moving cause as a
corporeal though immaterial substance, something in the nature of light
which is observed to diminish similarly at increased distances." He then
proceeds as follows in the original text.

"Let us then assume, as is very probable, that motion is dispensed by
the sun in the same manner as light. The proportion in which light
emanating from a centre is diminished, is taught by optical writers: for
there is the same quantity of light, or of the solar rays, in the small
circles as in the large; and therefore, as it is more condensed in the
former, more attenuated in the latter, a measure of the attenuation may
be derived from the proportion of the circles themselves, both in the
case of light and of the moving virtue. Therefore, by how much the orbit
of Venus is greater than that of Mercury, in the same proportion will
the motion of the latter be stronger, or more hurried, or more swift, or
more powerful, or by whatever other word you like to express the fact,
than that of the former. But a larger orbit would require a
proportionably longer time of revolution, even though the moving force
were the same. Hence it follows that the one cause of a greater distance
of the planet from the Sun, produces a double effect in increasing the
period, and conversely the increase of the periods will be double the
difference of the distances. Therefore, half the increment added to the
shorter period ought to give the true proportion of the distances, so
that the sum should represent the distance of the superior planet, on
the same scale on which the shorter period represents the distance of
the interior one. For instance, the period of Mercury is nearly 88 days;
that of Venus is 224-2/3, the difference is 136-2/3: half of this is
68-1/3, which, added to 88, gives 156-1/3. The mean distance of Venus
ought, therefore, to be, in proportion to that of Mercury, as 156-1/3 to
88. If this be done with all the planets, we get the following results,
taking successively, as before, the distance of each planet at 1000.

  The distance in   } [Jupiter] 574  But according { 572
  parts of which    } [Mars]    274  to Copernicus { 290
  the distance of   } [Earth]   694  they are      { 658
  the next superior } [Venus]   762  respectively  { 719
  planet contains   }                              {
  1000, is at       } [Mercury] 563                { 500

As you see, we have now got nearer the truth."

Finding that this theory of the rate of diminution would not bring him
quite close to the result he desired to find, Kepler immediately
imagined another. This latter occasioned him a great deal of perplexity,
and affords another of the frequently recurring instances of the waste
of time and ingenuity occasioned by his impetuous and precipitate
temperament. Assuming the distance of any planet, as for instance of
Mars, to be the unit of space, and the virtue at that distance to be the
unit of force, he supposed that as many particles as the virtue at the
Earth gained upon that of Mars, so many particles of distance did the
Earth lose. He endeavoured to determine the respective positions of the
planets upon this theory, by the rules of false position, but was much
astonished at finding the same exactly as on his former hypothesis. The
fact was, as he himself discovered, although not until after several
years, that he had become confused in his calculation; and when half
through the process, had retraced his steps so as of course to arrive
again at the numbers from which he started, and which he had taken from
his former results. This was the real secret of the identity of the two
methods; and if, when he had taken the distance of Mars at 1000, instead
of assuming the distance of the earth at 694, as he did, he had taken
any other number, and operated upon it in the same manner, he would
have had the same reason for relying on the accuracy of his supposition.
As it was, the result utterly confounded him; and he was obliged to
leave it with the remark, that "the two theories are thus proved to be
the same in fact, and only different in form; although how that can
possibly be, I have never to this day been able to understand."--His
perplexity was very reasonable; they are by no means the same; it was
only his method of juggling with the figures which seemed to connect
them.

Notwithstanding all its faults, the genius and unwearied perseverance
displayed by Kepler in this book, immediately ranked him among
astronomers of the first class; and he received the most flattering
encomiums from many of the most celebrated; among others, from Galileo
and Tycho Brahe, whose opinion he invited upon his performance. Galileo
contented himself with praising in general terms the ingenuity and good
faith which appeared so conspicuously in it. Tycho Brahe entered into a
more detailed criticism of the work, and, as Kepler shrewdly remarked,
showed how highly he thought of it by advising him to try to adapt
something of the same kind to the Tychonic system. Kepler also sent a
copy of his book to the imperial astronomer, Raimar, with a
complimentary letter, in which he exalted him above all other
astronomers of the age. Raimar had surreptitiously acquired a notion of
Tycho Brahe's theory, and published it as his own; and Tycho, in his
letter, complained of Kepler's extravagant flattery. This drew a long
apologetical reply from Kepler, in which he attributed the admiration he
had expressed of Raimar to his own want of information at that time,
having since met with many things in Euclid and Regiomontanus, which he
then believed original in Raimar. With this explanation, Tycho professed
himself perfectly satisfied.


FOOTNOTES:

[179] The following scrupulous note added by Kepler in 1621 to a
subsequent edition of this work, deserves to be quoted. It shows how
entirely superior he was to the paltriness of attempting to appropriate
the discoveries of others, of which many of his contemporaries had
exhibited instances even on slighter pretences than this passage might
have afforded him. The note is as follows: "Not circulating round
Jupiter like the Medicæan stars. Be not deceived. I never had them in my
thoughts, but, like the other primary planets, including the sun in the
centre of the system within their orbits."

[180] This inconvenient mode of dating was necessary before the new or
Gregorian style was universally adopted.




CHAPTER II.

    _Kepler's Marriage--He joins Tycho Brahe at Prague--Is appointed
      Imperial Mathematician--Treatise on the New Star._


THE publication of this extraordinary book, early as it occurs in the
history of Kepler's life, was yet preceded by his marriage. He had
contemplated this step so early as 1592; but that suit having been
broken off, he paid his addresses, in 1596, to Barbara Muller von
Muhleckh. This lady was already a widow for the second time, although
two years younger than Kepler himself. On occasion of this alliance he
was required to prove the nobility of his family, and the delay
consequent upon the inquiry postponed the marriage till the following
year. He soon became involved in difficulties in consequence of this
inconsiderate engagement: his wife's fortune was less than he had been
led to expect, and he became embroiled on that account with her
relations. Still more serious inconvenience resulted to him from the
troubled state in which the province of Styria was at that time, arising
out of the disputes in Bohemia and the two great religious parties into
which the empire was now divided, the one headed by Rodolph, the feeble
minded emperor,--the other by Matthias, his ambitious and enterprising
brother.

In the year following his marriage, he thought it prudent, on account of
some opinions he had unadvisedly promulgated, (of what nature does not
very distinctly appear,) to withdraw himself from Gratz into Hungary.
Thence he transmitted several short treatises to his friend Zehentmaier,
at Tubingen--"On the Magnet," "On the Cause of the Obliquity of the
Ecliptic," and "On the Divine Wisdom, as shown in the Creation." Little
is known of these works beyond the notice taken of them in Zehentmaier's
answers. Kepler has himself told us, that his magnetic philosophy was
built upon the investigations of Gilbert, of whom he always justly spoke
with the greatest respect.

About the same time a more violent persecution had driven Tycho Brahe
from his observatory of Uraniburg, in the little island of Hueen, at the
entrance of the Baltic. This had been bestowed on him by the munificence
of Frederick I. of Denmark, who liberally furnished him with every means
of prosecuting his astronomical observations. After Frederick's death,
Tycho found himself unable to withstand the party which had constantly
opposed him, and was forced, at a great loss and much inconvenience, to
quit his favourite island. On the invitation of the emperor, Rudolph
II., he then betook himself, after a short stay at Hamburg, to the
castle of Benach, near Prague, which was assigned to him with an annual
pension of three thousand florins, a truly munificent provision in those
times and that country.

Kepler had been eager to see Tycho Brahe since the latter had intimated
that his observations had led him to a more accurate determination of
the excentricities of the orbits of the planets. By help of this, Kepler
hoped that his theory might be made to accord more nearly with the
truth; and on learning that Tycho was in Bohemia, he immediately set out
to visit him, and arrived at Prague in January, 1600. From thence he
wrote a second letter to Tycho, not having received the answer to his
former apology, again excusing himself for the part he had appeared to
take with Raimar against him. Tycho replied immediately in the kindest
manner, and begged he would repair to him directly:--"Come not as a
stranger, but as a very welcome friend; come and share in my
observations with such instruments as I have with me, and as a dearly
beloved associate." During his stay of three or four months at Benach,
it was settled that Tycho should apply to the emperor, to procure him
the situation of assistant in the observatory. Kepler then returned to
Gratz, having previously received an intimation, that he might do so in
safety. The plan, as it had been arranged between them was, that a
letter should be procured from the emperor to the states of Styria,
requesting that Kepler might join Tycho Brahe for two years, and retain
his salary during that time: a hundred florins were to be added annually
by the emperor, on account of the greater dearness of living at Prague.
But before everything was concluded, Kepler finally threw up his
situation at Gratz, in consequence of new dissensions. Fearing that this
would utterly put an end to his hopes of connecting himself with Tycho,
he determined to revive his claims on the patronage of the Duke of
Wirtemberg. With this view he entered into correspondence with Mästlin
and some of his other friends at Tubingen, intending to prosecute his
medical studies, and offer himself for the professorship of medicine in
that university. He was dissuaded from this scheme by the pressing
instances of Tycho, who undertook to exert himself in procuring a
permanent settlement for him from the emperor, and assured him, even if
that attempt should fail, that the language he had used when formerly
inviting him to visit him at Hamburg, should not be forgotten. In
consequence of this encouragement, Kepler abandoned his former scheme,
and travelled again with his wife to Prague. He was detained a long time
on the road by violent illness, and his money became entirely exhausted.
On this he wrote complainingly to Tycho, that he was unable without
assistance to travel even the short distance which still separated them,
far less to await much longer the fulfilment of the promises held out to
him.

By his subsequent admissions, it appears that for a considerable time he
lived entirely on Tycho's bounty, and by way of return, he wrote an
essay against Raimar, and against a Scotchman named Liddell, professor
at Rostoch and Helmstadt, who, like Raimar, had appropriated to himself
the credit of the Tychonic system. Kepler never adopted this theory, and
indeed, as the question merely regarded priority of invention, there
could be no occasion, in the discussion, for an examination of its
principles.

This was followed by a transaction, not much to Kepler's credit, who in
the course of the following year, and during a second absence from
Prague, fancied that he had some reason to complain of Tycho's
behaviour, and wrote him a violent letter, filled with reproaches and
insults. Tycho appears to have behaved in this affair with great
moderation: professing to be himself occupied with the marriage of his
daughter, he gave the care of replying to Kepler's charges, to Ericksen,
one of his assistants, who, in a very kind and temperate letter, pointed
out to him the ingratitude of his behaviour, and the groundlessness of
his dissatisfaction. His principal complaint seems to have been, that
Tycho had not sufficiently supplied his wife with money during his
absence. Ericksen's letter produced an immediate and entire change in
Kepler's temper, and it is only from the humble recantation which he
instantaneously offered that we learn the extent of his previous
violence. "Most noble Tycho," these are the words of his letter, "how
shall I enumerate or rightly estimate your benefits conferred on me! For
two months you have liberally and gratuitously maintained me, and my
whole family; you have provided for all my wishes; you have done me
every possible kindness; you have communicated to me everything you hold
most dear; no one, by word or deed, has intentionally injured me in
anything: in short, not to your children, your wife, or yourself have
you shown more indulgence than to me. This being so, as I am anxious to
put upon record, I cannot reflect without consternation that I should
have been so given up by God to my own intemperance, as to shut my eyes
on all these benefits; that, instead of modest and respectful gratitude,
I should indulge for three weeks in continual moroseness towards all
your family, in headlong passion, and the utmost insolence towards
yourself, who possess so many claims on my veneration from your noble
family, your extraordinary learning, and distinguished reputation.
Whatever I have said or written against the person, the fame, the
honour, and the learning of your excellency; or whatever, in any other
way, I have injuriously spoken or written, (if they admit no other more
favourable interpretation,) as to my grief I have spoken and written
many things, and more than I can remember; all and everything I recant,
and freely and honestly declare and profess to be groundless, false, and
incapable of proof." Hoffmann, the president of the states of Styria,
who had taken Kepler to Prague on his first visit, exerted himself to
perfect the reconciliation, and this hasty quarrel was entirely passed
over.

On Kepler's return to Prague, in September, 1601, he was presented to
the Emperor by Tycho, and honoured with the title of Imperial
Mathematician, on condition of assisting Tycho in his calculations.
Kepler desired nothing more than this condition, since Tycho was at that
time probably the only person in the world who possessed observations
sufficient for the reform which he now began to meditate in the theory
of astronomy. Rudolph appears to have valued both Tycho Brahe and Kepler
as astrologers rather than astronomers; but although unable to
appreciate rightly the importance of the task they undertook, of
compiling a new set of astronomical tables founded upon Tycho's
observations, yet his vanity was flattered with the prospect of his name
being connected with such a work, and he made liberal promises to defray
the expense of the new Rudolphine Tables. Tycho's principal assistant at
this time was Longomontanus, who altered his name to this form,
according to the prevalent fashion of giving to every name a Latin
termination. Lomborg or Longbierg was the name, not of his family, but
of the village in Denmark, where he was born, just as Müller was seldom
called by any other name than Regiomontanus, from his native town
Königsberg, as George Joachim Rheticus was so surnamed from Rhetia, the
country of the Grisons, and as Kepler himself was sometimes called
Leonmontanus, from Leonberg, where he passed his infancy. It was agreed
between Longomontanus and Kepler, that in discussing Tycho's
observations, the former should apply himself especially to the Moon,
and the latter to Mars, on which planet, owing to its favourable
position, Tycho was then particularly engaged. The nature of these
labours will be explained when we come to speak of the celebrated book
"On the Motions of Mars."

This arrangement was disturbed by the return of Longomontanus into
Denmark, where he had been offered an astronomical professorship, and
still more by the sudden death of Tycho Brahe himself in the following
October. Kepler attended him during his illness, and after his death
undertook to arrange some of his writings. But, in consequence of a
misunderstanding between him and Tycho's family, the manuscripts were
taken out of his hands; and when, soon afterwards, the book appeared,
Kepler complained heavily that they had published, without his consent
or knowledge, the notes and interlineations added by him for his own
private guidance whilst preparing it for publication.

On Tycho's death, Kepler succeeded him as principal mathematician to the
emperor; but although he was thus nominally provided with a liberal
salary, it was almost always in arrear. The pecuniary embarrassments in
which he constantly found himself involved, drove him to the resource of
gaining a livelihood by casting nativities. His peculiar temperament
rendered him not averse from such speculations, and he enjoyed
considerable reputation in this line, and received ample remuneration
for his predictions. But although he did not scruple, when consulted, to
avail himself in this manner of the credulity of his contemporaries, he
passed over few occasions in his works of protesting against the
futility of this particular genethliac astrology. His own astrological
creed was in a different strain, more singular, but not less
extravagant. We shall defer entering into any details concerning it,
till we come to treat of his book on Harmonics, in which he has
collected and recapitulated the substance of his scattered opinions on
this strange subject.

His next works deserving notice are those published on occasion of the
new star which shone out with great splendour in 1604, in the
constellation Cassiopeia.[181] Immediately on its appearance, Kepler
wrote a short account of it in German, marked with all the oddity which
characterises most of his productions. We shall see enough of his
astronomical calculations when we come to his book on Mars; the
following passage will probably be found more amusing.

After comparing this star with that of 1572, and mentioning that many
persons who had seen it maintained this to be the brighter of the two,
since it was nearly twice the size of its nearest neighbour, Jupiter, he
proceeds as follows:--"Yonder one chose for its appearance a time no way
remarkable, and came into the world quite unexpectedly, like an enemy
storming a town, and breaking into the market-place before the citizens
are aware of his approach; but ours has come exactly in the year of
which astrologers have written so much about the fiery trigon that
happens in it;[182] just in the month in which (according to Cyprian)
Mars comes up to a very perfect conjunction with the other two superior
planets; just in the day when Mars has joined Jupiter, and just in the
place where this conjunction has taken place. Therefore the apparition
of this star is not like a secret hostile irruption, as was that one of
1572, but the spectacle of a public triumph, or the entry of a mighty
potentate; when the couriers ride in some time before, to prepare his
lodgings, and the crowd of young urchins begin to think the time
over-long to wait: then roll in, one after another, the ammunition, and
money, and baggage waggons, and presently the trampling of horse, and
the rush of people from every side to the streets and windows; and when
the crowd have gazed with their jaws all agape at the troops of knights;
then at last, the trumpeters, and archers, and lackeys, so distinguish
the person of the monarch, that there is no occasion to point him out,
but every one cries out of his own accord--'Here we have him!'--What it
may portend is hard to determine, and thus much only is certain, that it
comes to tell mankind either nothing at all, or high and weighty news,
quite beyond human sense and understanding. It will have an important
influence on political and social relations; not indeed by its own
nature, but, as it were, accidentally through the disposition of
mankind. First, it portends to the booksellers great disturbances, and
tolerable gains; for almost every _Theologus_, _Philosophicus_,
_Medicus_, and _Mathematicus_, or whoever else, having no laborious
occupation intrusted to him, seeks his pleasure _in studiis_, will make
particular remarks upon it, and will wish to bring these remarks to the
light. Just so will others, learned and unlearned, wish to know its
meaning, and they will buy the authors who profess to tell them. I
mention these things merely by way of example, because, although thus
much can be easily predicted without great skill, yet may it happen just
as easily, and in the same manner, that the vulgar, or whoever else is
of easy faith, or it may be, crazy, may wish to exalt himself into a
great prophet; or it may even happen that some powerful lord, who has
good foundation and beginning of great dignities, will be cheered on by
this phenomenon to venture on some new scheme, just as if God had set up
this star in the darkness merely to enlighten them."

It would hardly be supposed, from the tenor of this last passage, that
the writer of it was not a determined enemy to astrological predictions
of every description. In 1602 he had published a disputation, not now
easily met with, "On the Principles of Astrology," in which it seems
that he treated the professed astrologers with great severity. The
essence of this book is probably contained in the second treatise on the
new star, which he published in 1606.[183] In this volume he inveighs
repeatedly against the vanity and worthlessness of ordinary astrology,
declaring at the same time, that the professors of that art know that
this judgment is pronounced by one well acquainted with its principles.
"For if the vulgar are to pronounce who is the best astrologer, my
reputation is known to be of the highest order; if they prefer the
judgment of the learned, they are already condemned. Whether they stand
with me in the eyes of the populace, or I fall with them before the
learned, in both cases I am in their ranks; I am on a level with them; I
cannot be renounced."

The theory which Kepler proposed to substitute is intimated shortly in
the following passage: "I maintain that the colours and aspects, and
conjunctions of the planets, are impressed on the natures or faculties
of sublunary things, and when they occur, that these are excited as well
in forming as in moving the body over whose motion they preside. Now let
no one conceive a prejudice that I am anxiously seeking to mend the
deplorable and hopeless cause of astrology by far-fetched subtilties and
miserable quibbling. I do not value it sufficiently, nor have I ever
shunned having astrologers for my enemies. But a most unfailing
experience (as far as can be hoped in natural phenomena) of the
excitement of sublunary natures by the conjunctions and aspects of the
planets, has instructed and compelled my unwilling belief."

After exhausting other topics suggested by this new star, he examines
the different opinions on the cause of its appearance. Among others he
mentions the Epicurean notion, that it was a fortuitous concourse of
atoms, whose appearance in this form was merely one of the infinite
number of ways in which, since the beginning of time, they have been
combined. Having descanted for some time on this opinion, and declared
himself altogether hostile to it, Kepler proceeds as follows:--"When I
was a youth, with plenty of idle time on my hands, I was much taken with
the vanity, of which some grown men are not ashamed, of making anagrams,
by transposing the letters of my name, written in Greek, so as to make
another sentence: out of [Iôannês Keplêros] I made [Seirênôn
kapêlos];[184] in Latin, out of _Joannes Keplerus_ came _Serpens in
akuleo_.[185] But not being satisfied with the meaning of these words,
and being unable to make another, I trusted the thing to chance, and
taking out of a pack of playing cards as many as there were letters in
the name, I wrote one upon each, and then began to shuffle them, and at
each shuffle to read them in the order they came, to see if any meaning
came of it. Now, may all the Epicurean gods and goddesses confound this
same chance, which, although I spent a good deal of time over it, never
showed me anything like sense even from a distance.[186] So I gave up my
cards to the Epicurean eternity, to be carried away into infinity, and,
it is said, they are still flying about there, in the utmost confusion
among the atoms, and have never yet come to any meaning. I will tell
these disputants, my opponents, not my own opinion, but my wife's.
Yesterday, when weary with writing, and my mind quite dusty with
considering these atoms, I was called to supper, and a salad I had asked
for was set before me. It seems then, said I aloud, that if pewter
dishes, leaves of lettuce, grains of salt, drops of water, vinegar, and
oil, and slices of egg, had been flying about in the air from all
eternity, it might at last happen by chance that there would come a
salad. Yes, says my wife, but not so nice and well dressed as this of
mine is."


FOOTNOTES:

[181] See Life of Galileo, p. 16.

[182] The fiery trigon occurs about once in every 800 years, when
Saturn, Jupiter, and Mars are in the three fiery signs, Aries, Leo, and
Sagittarius.

[183] The copy of this work in the British Museum is Kepler's
presentation copy to our James I. On the blank leaf, opposite the
title-page, is the following inscription, apparently in the author's
hand-writing:--"Regi philosophanti, philosophus serviens, Platoni
Diogenes, Britannias tenenti, Pragæ stipem mendicans ab Alexandro, e
dolio conductitio, hoc suum philosophema misit et commendavit."

[184] The tapster of the Sirens.

[185] A serpent in his sting.

[186] In one of his anonymous writings Kepler has anagrammatized his
name, _Joannes Keplerus_, in a variety of other forms, probably selected
from the luckiest of his shuffles:--"_Kleopas Herennius, Helenor
Kapuensis, Raspinus Enkeleo, Kanones Pueriles._"




CHAPTER III.

    _Kepler publishes his Supplement to Vitellion--Theory of
      Refraction._


DURING several years Kepler remained, as he himself forcibly expressed
it, begging his bread from the emperor at Prague, and the splendour of
his nominal income served only to increase his irritation, at the real
neglect under which he nevertheless persevered in his labours. His
family was increasing, and he had little wherewith to support them
beyond the uncertain proceeds of his writings and nativities. His salary
was charged partly on the states of Silesia, partly on the imperial
treasury; but it was in vain that repeated orders were procured for the
payment of the arrears due to him. The resources of the empire were
drained by the constant demands of an engrossing war, and Kepler had not
sufficient influence to enforce his claims against those who thought
even the smallest sum bestowed upon him ill spent, in fostering
profitless speculations. In consequence of this niggardliness, Kepler
was forced to postpone the publication of the Rudolphine Tables, which
he was engaged in constructing from his own and Tycho Brahe's
observations, and applied himself to other works of a less costly
description. Among these may be mentioned a "Treatise on Comets,"
written on occasion of one which appeared in 1607: in this he suggests
that they are planets moving in straight lines. The book published in
1604, which he entitles "A Supplement to Vitellion," may be considered
as containing the first reasonable and consistent theory of optics,
especially in that branch of it usually termed dioptrics, which relates
to the theory of vision through transparent substances. In it was first
explained the true use of the different parts of the eye, to the
knowledge of which Baptista Porta had already approached very nearly,
though he stopped short of the accurate truth. Kepler remarked the
identity of the mechanism in the eye with that beautiful invention of
Porta's, the camera obscura; showing, that the light which falls from
external objects on the eye is refracted through a transparent
substance, called, from its form and composition, the crystalline lens,
and makes a picture on the fine net-work of nerves, called the retina,
which lies at the back of the eye. The manner in which the existence of
this coloured picture on the retina causes to the individual the
sensation of sight, belongs to a theory not purely physical; and beyond
this point Kepler did not attempt to go.

The direction into which rays of light (as they are usually called) are
bent or refracted in passing through the air and other transparent
substances or mediums, is discussed in this treatise at great length.
Tycho Brahe had been the first astronomer who recognized the necessity
of making some allowance on this account in the observed heights of the
stars. A long controversy arose on this subject between Tycho Brahe and
Rothman, the astronomer at Hesse Cassel, a man of unquestionable talent,
but of odd and eccentric habits. Neither was altogether in the right,
although Tycho had the advantage in the argument. He failed however to
establish the true law of refraction, and Kepler has devoted a chapter
to an examination of the same question. It is marked by precisely the
same qualities as those appearing so conspicuously in his astronomical
writings:--great ingenuity; wonderful perseverance; bad philosophy. That
this may not be taken solely upon assertion, some samples of it are
subjoined. The writings of the authors of this period are little read or
known at the present day; and it is only by copious extracts that any
accurate notion can be formed of the nature and value of their labours.
The following tedious specimen of Kepler's mode of examining physical
phenomena is advisedly selected to contrast with his astronomical
researches: though the luck and consequently the fame that attended his
divination were widely different on the two occasions, the method
pursued was the same. After commenting on the points of difference
between Rothman and Tycho Brahe, Kepler proceeds to enumerate his own
endeavours to discover the law of refraction.

"I did not leave untried whether, by assuming a horizontal refraction
according to the density of the medium, the rest would correspond with
the sines of the distances from the vertical direction, but calculation
proved that it was not so: and indeed there was no occasion to have
tried it, for thus the refractions would increase according to the same
law in all mediums, which is contradicted by experiment.

"The same kind of objection may be brought against the cause of
refraction alleged by Alhazen and Vitellion. They say that the light
seeks to be compensated for the loss sustained at the oblique impact; so
that in proportion as it is enfeebled by striking against the denser
medium, in the same degree does it restore its energy by approaching the
perpendicular, that it may strike the bottom of the denser medium with
greater force; for those impacts are most forcible which are direct. And
they add some subtle notions, I know not what, how the motion of
obliquely incident light is compounded of a motion perpendicular and a
motion parallel to the dense surface, and that this compound motion is
not destroyed, but only retarded by meeting the denser medium.

[Illustration]

"I tried another way of measuring the refraction, which should include
the density of the medium and the incidence: for, since a denser medium
is the cause of refraction, it seems to be the same thing as if we were
to prolong the depth of the medium in which the rays are refracted into
as much space as would be filled by the denser medium under the force of
the rarer one.

"Let A be the place of the light, BC the surface of the denser medium,
DE its bottom. Let AB, AG, AF be rays falling obliquely, which would
arrive at D, I, H, if the medium were uniform. But because it is denser,
suppose the bottom to be depressed to KL, determined by this that there
is as much of the denser matter contained in the space DC as of the
rarer in LC: and thus, on the sinking of the whole bottom DE, the points
D, I, H, E will descend vertically to L, M, N, K. Join the points BL,
GM, FN, cutting DE in O, P, Q; the refracted rays will be ABO, AGP,
AFQ."--"This method is refuted by experiment; it gives the refractions
near the perpendicular AC too great in respect of those near the
horizon. Whoever has leisure may verify this, either by calculation or
compasses. It may be added that the reasoning itself is not very
sure-footed, and, whilst seeking to measure other things, scarcely takes
in and comprehends itself." This reflection must not be mistaken for the
dawn of suspicion that his examination of philosophical questions began
not altogether at the right end: it is merely an acknowledgment that he
had not yet contrived a theory with which he was quite satisfied before
it was disproved by experiment.

After some experience of Kepler's miraculous good fortune in seizing
truths across the wildest and most absurd theories, it is not easy to
keep clear of the opposite feeling of surprise whenever any of his
extravagancies fail to discover to him some beautiful law of nature. But
we must follow him as he plunges deeper in this unsuccessful inquiry;
and the reader must remember, in order fully to appreciate this method
of philosophizing, that it is almost certain that Kepler laboured upon
every one of the gratuitous suppositions that he makes, until positive
experiment satisfied him of their incorrectness.

"I go on to other methods. Since density is clearly connected with the
cause of the refractions, and refraction itself seems a kind of
compression of light, as it were, towards the perpendicular, it occurred
to me to examine whether there was the same proportion between the
mediums in respect of density and the parts of the bottom illuminated by
the light, when let into a vessel, first empty, and afterwards filled
with water. This mode branches out into many: for the proportion may be
imagined, either in the straight lines, as if one should say that the
line EQ, illuminated by refraction, is to EH illuminated directly, as
the density of the one medium is to that of the other--Or another may
suppose the proportion to be between FC and FH--Or it may be conceived
to exist among surfaces, or so that some power of EQ should be to some
power of EH in this proportion, or the circles or similar figures
described on them. In this manner the proportion of EQ to EP would be
double that of EH to EI--Or the proportion may be conceived existing
among the solidities of the pyramidal frustums FHEC, FQEC--Or, since the
proportion of the mediums involves a threefold consideration, since they
have density in length, breadth, and thickness, I proceeded also to
examine the cubic proportions among the lines EQ, EH.

"I also considered other lines. From any of the points of refraction as
G, let a perpendicular GY be dropped upon the bottom. It may become a
question whether possibly the triangle IGY, that is, the base IY, is
divided by the refracted ray GP, in the proportion of the densities of
the mediums.

"I have put all these methods here together, because the same remark
disproves them all. For, in whatever manner, whether as line, plane, or
pyramid, EI observes a given proportion to EP, or the abbreviated line
YI to YP, namely, the proportion of the mediums, it is sure that EI, the
tangent of the distance of the point A from the vertex, will become
infinite, and will, therefore make EP or YP, also infinite. Therefore,
IGP, the angle of refraction, will be entirely lost; and, as it
approaches the horizon, will gradually become less and less, which is
contrary to experiment.

"I tried again whether the images are equally removed from their points
of refraction, and whether the ratio of the densities measures the least
distance. For instance, supposing E to be the image, C the surface of
the water, K the bottom, and CE to CK in the proportion of the densities
of the mediums. Now, let F, G, B, be three other points of refraction
and images at S, T, V, and let CE be equal to FS, GT, and BV. But
according to this rule an image E would still be somewhat raised in the
perpendicular AK, which is contrary to experiment, not to mention other
contradictions. Thirdly, whether the proportion of the mediums holds
between FH and FX, supposing H to be the place of the image? Not at all.
For so, CE would be in the same proportion to CK, so that the height of
the image would always be the same, which we have just refuted.
Fourthly, whether the raising of the image at E is to the raising at H,
as CE to FH? Not in the least; for so the images either would never
begin to be raised, or, having once begun, would at last be infinitely
raised, because FH at last becomes infinite. Fifthly, whether the images
rise in proportion to the sines of the inclinations? Not at all; for so
the proportion of ascent would be the same in all mediums. Sixthly, are
then the images raised at first, and in perpendicular radiation,
according to the proportion of the mediums, and do they subsequently
rise more and more according to the sines of the inclinations? For so
the proportion would be compound, and would become different in
different mediums. There is nothing in it: for the calculation disagreed
with experiment. And generally it is in vain to have regard to the image
or the place of the image, for that very reason, that it is imaginary.
For there is no connexion between the density of the medium or any real
quality or refraction of the light, and an accident of vision, by an
error of which the image happens.

"Up to this point, therefore, I had followed a nearly blind mode of
inquiry, and had trusted to good fortune; but now I opened the other
eye, and hit upon a sure method, for I pondered the fact, that the image
of a thing seen under water approaches closely to the true ratio of the
refraction, and almost measures it; that it is low if the thing is
viewed directly from above; that by degrees it rises as the eye passes
towards the horizon of the water. Yet, on the other hand, the reason
alleged above, proves that the measure is not to be sought in the image,
because the image is not a thing actually existing, but arises from a
deception of vision which is purely accidental. By a comparison of these
conflicting arguments, it occurred to me at length, to seek the causes
themselves of the existence of the image under water, and in these
causes the measure of the refractions. This opinion was strengthened in
me by seeing that opticians had not rightly pointed out the cause of the
image which appears both in mirrors and in water. And this was the
origin of that labour which I undertook in the third chapter. Nor,
indeed, was that labour trifling, whilst hunting down false opinions of
all sorts among the principles, in a matter rendered so intricate by the
false traditions of optical writers; whilst striking out half a dozen
different paths, and beginning anew the whole business. How often did it
happen that a rash confidence made me look upon that which I sought with
such ardour, as at length discovered!

"At length I cut this worse than Gordian knot of catoptrics by analogy
alone, by considering what happens in mirrors, and what must happen
analogically in water. In mirrors, the image appears at a distance from
the real place of the object, not being itself material, but produced
solely by reflection at the polished surface. Whence it followed in
water also, that the images rise and approach the surface, not according
to the law of the greater or less density in the water, as the view is
less or more oblique, but solely because of the refraction of the ray of
light passing from the object to the eye. On which assumption, it is
plain that every attempt I had hitherto made to measure refractions by
the image, and its elevation, must fall to the ground. And this became
more evident when I discovered the true reason why the image is in the
same perpendicular line with the object both in mirrors and in dense
mediums. When I had succeeded thus far by analogy in this most difficult
investigation, as to the place of the image, I began to follow out the
analogy further, led on by the strong desire of measuring refraction.
For I wished to get hold of some measure of some sort, no matter how
blindly, having no fear but that so soon as the measure should be
accurately known, the cause would plainly appear. I went to work as
follows. In convex mirrors the image is diminished, and just so in rarer
mediums; in denser mediums it is magnified, as in concave mirrors. In
convex mirrors the central parts of the image approach, and recede in
concave farther than towards the circumference; the same thing happens
in different mediums, so that in water the bottom appears depressed, and
the surrounding parts elevated. Hence it appears that a denser medium
corresponds with a concave reflecting surface, and a rarer one with a
convex one: it was clear, at the same time, that the plane surface of
the water affects a property of curvature. I was, therefore, to
excogitate causes consistent with its having this effect of curvature,
and to see if a reason could be given, why the parts of the water
surrounding the incident perpendicular should represent a greater
density than the parts just under the perpendicular. And so the thing
came round again to my former attempts, which being refuted by reason
and experiment, I was forced to abandon the search after a cause. I then
proceeded to measurements."

Kepler then endeavoured to connect his measurements of different
quantities of refraction with the conic sections, and was tolerably well
pleased with some of his results. They were however not entirely
satisfactory, on which he breaks off with the following sentence: "Now,
reader, you and I have been detained sufficiently long whilst I have
been attempting to collect into one faggot the measure of different
refractions: I acknowledge that the cause cannot be connected with this
mode of measurement: for what is there in common between refractions
made at the plane surfaces of transparent mediums, and mixtilinear conic
sections? Wherefore, _quod Deus bene vortat_, we will now have had
enough of the causes of this measure; and although, even now, we are
perhaps erring something from the truth, yet it is better, by working
on, to show our industry, than our laziness by neglect."

Notwithstanding the great length of this extract, we must add the
concluding paragraph of the Chapter, directed, as we are told in the
margin, against the "Tychonomasticks:"--

"I know how many blind men at this day dispute about colours, and how
they long for some one to give some assistance by argument to their rash
insults of Tycho, and attacks upon this whole matter of refractions;
who, if they had kept to themselves their puerile errors and naked
ignorance, might have escaped censure; for that may happen to many great
men. But since they venture forth publicly, and with thick books and
sounding titles, lay baits for the applause of the unwary, (for
now-a-days there is more danger from the abundance of bad books, than
heretofore from the lack of good ones,) therefore let them know that a
time is set for them publicly to amend their own errors. If they longer
delay doing this, it shall be open, either to me or any other, to do to
these unhappy meddlers in geometry as they have taken upon themselves to
do with respect to men of the highest reputation. And although this
labour will be despicable, from the vile nature of the follies against
which it will be directed, yet so much more necessary than that which
they have undertaken against others, as he is a greater public nuisance,
who endeavours to slander good and necessary inventions, than he who
fancies he has found what is impossible to discover. Meanwhile, let them
cease to plume themselves on the silence which is another word for their
own obscurity."

Although Kepler failed, as we have seen, to detect the true law of
refraction, (which was discovered some years later by Willibrord Snell,
a Flemish mathematician,) there are many things well deserving notice in
his investigations. He remarked, that the quantity of refraction would
alter, if the height of the atmosphere should vary; and also, that it
would be different at different temperatures. Both these sources of
variation are now constantly taken into account, the barometer and
thermometer giving exact indications of these changes. There is also a
very curious passage in one of his letters to Bregger, written in 1605,
on the subject of the colours in the rainbow. It is in these
words:--"Since every one sees a different rainbow, it is possible that
some one may see a rainbow in the very place of my sight. In this case,
the medium is coloured at the place of my vision, to which the solar ray
comes to me through water, rain, or aqueous vapours. For the rainbow is
seen when the sun is shining between rain, that is to say, when the sun
also is visible. Why then do I not see the sun green, yellow, red, and
blue, if vision takes place according to the mode of illumination? I
will say something for you to attack or examine. The sun's rays are not
coloured, except with a definite quantity of refraction. Whether you are
in the optical chamber, or standing opposite glass globes, or walking in
the morning dew, everywhere it is obvious that a certain and definite
angle is observed, under which, when seen in dew, in glass, in water,
the sun's splendour appears coloured, and under no other angle. There is
no colouring by mere reflexion, without the refraction of a denser
medium." How closely does Kepler appear, in this passage, to approach
the discovery which forms not the least part of Newton's fame!

We also find in this work a defence of the opinion that the planets are
luminous of themselves; on the ground that the inferior planets would,
on the contrary supposition, display phases like those of the moon when
passing between us and the sun. The use of the telescope was not then
known; and, when some years later the form of the disk of the planets
was more clearly defined with their assistance, Kepler had the
satisfaction of finding his assertions verified by the discoveries of
Galileo, that these changes do actually take place. In another of his
speculations, connected with the same subject, he was less fortunate. In
1607 a black spot appeared on the face of sun, such as may almost always
be seen with the assistance of the telescope, although they are seldom
large enough to be visible to the unassisted eye. Kepler saw it for a
short time, and mistook it for the planet Mercury, and with his usual
precipitancy hastened to publish an account of his observation of this
rare phenomenon. A few years later, Galileo discovered with his glasses,
a great number of similar spots; and Kepler immediately retracted the
opinion announced in his treatise, and acknowledged his belief that
previous accounts of the same occurrence which he had seen in old
authors, and which he had found great difficulty in reconciling with his
more accurate knowledge of the motions of Mercury, were to be referred
to a like mistake. On this occasion of the invention of the telescope,
Kepler's candour and real love of truth appeared in a most favourable
light. Disregarding entirely the disagreeable necessity, in consequence
of the discoveries of this new instrument, of retracting several
opinions which he had maintained with considerable warmth, he ranged
himself at once on the side of Galileo, in opposition to the bitter and
determined hostility evinced by most of those whose theories were
endangered by the new views thus offered of the heavens. Kepler's
quarrel with his pupil, Horky, on this account, has been mentioned in
the "Life of Galileo;" and this is only a selected instance from the
numerous occasions on which he espoused the same unpopular side of the
argument. He published a dissertation to accompany Galileo's
"Intelligencer of the Stars," in which he warmly expressed his
admiration of that illustrious inquirer into nature. His conduct in this
respect was the more remarkable, as some of his most intimate friends
had taken a very opposite view of Galileo's merit, and seem to have
laboured much to disturb their mutual regard; Mästlin especially,
Kepler's early instructor, seldom mentioned to him the name of Galileo,
without some contemptuous expression of dislike. These statements have
rather disturbed the chronological order of the account of Kepler's
works. We now return to the year 1609, in which he published his great
and extraordinary book, "On the Motions of Mars;" a work which holds the
intermediate place, and is in truth the connecting link, between the
discoveries of Copernicus and Newton.




CHAPTER IV.

    _Sketch of the Astronomical Theories before Kepler._


KEPLER had begun to labour upon these commentaries from the moment when
he first made Tycho's acquaintance; and it is on this work that his
reputation should be made mainly to rest. It is marked in many places
with his characteristic precipitancy, and indeed one of the most
important discoveries announced in it (famous among astronomers by the
name of the Equable Description of Areas) was blundered upon by a lucky
compensation of errors, of the nature of which Kepler remained ignorant
to the very last. Yet there is more of the inductive method in this than
in any of his other publications; and the unwearied perseverance with
which he exhausted years in hunting down his often renewed theories,
till at length he seemed to arrive at the true one, almost by having
previously disproved every other, excites a feeling of astonishment
nearly approaching to awe. It is wonderful how he contrived to retain
his vivacity and creative fancy amongst the clouds of figures which he
conjured up round him; for the slightest hint or shade of probability
was sufficient to plunge him into the midst of the most laborious
computations. He was by no means an accurate calculator, according to
the following character which he has given of himself:--"Something of
these delays must be attributed to my own temper, for _non omnia
possumus omnes_, and I am totally unable to observe any order; what I do
suddenly, I do confusedly, and if I produce any thing well arranged, it
has been done ten times over. Sometimes an error of calculation
committed by hurry, delays me a great length of time. I could indeed
publish an infinity of things, for though my reading is confined, my
imagination is abundant, but I grow dissatisfied with such confusion: I
get disgusted and out of humour, and either throw them away, or put them
aside to be looked at again; or, in other words, to be written again,
for that is generally the end of it. I entreat you, my friends, not to
condemn me for ever to grind in the mill of mathematical calculations:
allow me some time for philosophical speculations, my only delight."

He was very seldom able to afford the expense of maintaining an
assistant, and was forced to go through most of the drudgery of his
calculations by himself; and the most confirmed and merest arithmetician
could not have toiled more doggedly than Kepler did in the work of which
we are about to speak.

In order that the language of his astronomy may be understood, it is
necessary to mention briefly some of the older theories. When it had
been discovered that the planets did not move regularly round the earth,
which was supposed to be fixed in the centre of the world, a mechanism
was contrived by which it was thought that the apparent irregularity
could be represented, and yet the principle of uniform motion, which was
adhered to with superstitious reverence, might be preserved. This, in
its simplest form, consisted in supposing the planet to move uniformly
in a small circle, called an _epicycle_, the centre of which moved with
an equal angular motion in the opposite direction round the earth.[187]
The circle D_d_, described by D, the centre of the epicycle, was called
the _deferent_. For instance, if the planet was supposed to be at A when
the centre of the epicycle was at D, its position, when the centre of
the epicycle had removed to _d_, would be at _p_, found by drawing _dp_
parallel to DA. Thus, the angle _adp_, measuring the motion of the
planet in its epicycle, would be equal to DE_d_, the angle described by
the centre of the epicycle in the deferent. The angle _p_E_d_ between
E_p_, the direction in which a planet so moving would be seen from the
earth, supposed to be at E, and E_d_ the direction in which it would
have been seen had it been moving in the centre of the deferent, was
called the equation of the orbit, the word equation, in the language of
astronomy, signifying what must be added or taken from an irregularly
varying quantity to make it vary uniformly.

[Illustration]

As the accuracy of observations increased, minor irregularities were
discovered, which were attempted to be accounted for by making a second
deferent of the epicycle, and making the centre of a second epicycle
revolve in the circumference of the first, and so on, or else by
supposing the revolution in the epicycle not to be completed in exactly
the time in which its centre is carried round the deferent. Hipparchus
was the first to make a remark by which the geometrical representation
of these inequalities was considerably simplified. In fact, if EC be
taken equal to _pd_, C_d_ will be a parallelogram, and consequently
C_p_ equal to E_d_, so that the machinery of the first deferent and
epicycle amounts to supposing that the planet revolves uniformly in a
circle round the point C, not coincident with the place of the earth.
This was consequently called the excentric theory, in opposition to the
former or concentric one, and was received as a great improvement. As
the point _d_ is not represented by this construction, the equation to
the orbit was measured by the angle C_p_E, which is equal to _p_E_d_. It
is not necessary to give any account of the manner in which the old
astronomers determined the magnitudes and positions of these orbits,
either in the concentric or excentric theory, the present object being
little more than to explain the meaning of the terms it will be
necessary to use in describing Kepler's investigations.

To explain the irregularities observed in the other planets, it became
necessary to introduce another hypothesis, in adopting which the
severity of the principle of uniform motion was somewhat relaxed. The
machinery consisted partly of an excentric deferent round E, the earth,
and on it an epicycle, in which the planet revolved uniformly; but the
centre of the epicycle, instead of revolving uniformly round C, the
centre of the deferent, as it had hitherto been made to do, was
supposed to move in its circumference with an uniform angular motion
round a third point, Q; the necessary effect of which supposition was,
that the linear motion of the centre of the epicycle ceased to be
uniform. There were thus three points to be considered within the
deferent; E, the place of the earth; C, the centre of the deferent, and
sometimes called the centre of the orbit; and Q, called the centre of
the equant, because, if any circle were described round Q, the planet
would appear to a spectator at Q, to be moving equably in it. It was
long uncertain what situation should be assigned to the centre of the
equant, so as best to represent the irregularities to a spectator on the
earth, until Ptolemy decided on placing it (in every case but that of
Mercury, the observations on which were very doubtful) so that C, the
centre of the orbit, lay just half way in the straight line, joining Q,
the centre of equable motion, and E, the place of the earth. This is the
famous principle, known by the name of the bisection of the
excentricity.

[Illustration]

The first equation required for the planet's motion was thus supposed to
be due to the displacement of E, the earth, from Q, the centre of
uniform motion, which was called the excentricity of the equant: it
might be represented by the angle _d_EM, drawing EM parallel to Q_d_;
for clearly M would have been the place of the centre of the epicycle at
the end of a time proportional to D_d_, had it moved with an equable
angular motion round E instead of Q. This angle _d_EM, or its equal
E_d_Q, was called the equation of the centre (_i.e._ of the centre of
the epicycle); and is clearly greater than if EQ, the excentricity of
the equant, had been no greater than EC, called the excentricity of the
orbit. The second equation was measured by the angle subtended at E by
_d_, the centre of the epicycle, and _p_ the planet's place in its
circumference: it was called indifferently the equation of the orbit, or
of the argument. In order to account for the apparent stations and
retrogradations of the planets, it became necessary to suppose that many
revolutions in the latter were completed during one of the former. The
variations of latitude of the planets were exhibited by supposing not
only that the planes of their deferents were oblique to the plane of the
ecliptic, and that the plane of the epicycle was also oblique to that of
the deferent, but that the inclination of the two latter was continually
changing, although Kepler doubts whether this latter complication was
admitted by Ptolemy. In the inferior planets, it was even thought
necessary to give to the plane of the epicycle two oscillatory motions
on axes at right angles to each other.

The astronomers at this period were much struck with a remarkable
connexion between the revolutions of the superior planets in their
epicycles, and the apparent motion of the sun; for when in conjunction
with the sun, as seen from the earth, they were always found to be in
the apogee, or point of greatest distance from the earth, of their
epicycle; and when in opposition to the Sun, they were as regularly in
the perigee, or point of nearest approach of the epicycle. This
correspondence between two phenomena, which, according to the old
astronomy, were entirely unconnected, was very perplexing, and it seems
to have been one of the facts which led Copernicus to substitute the
theory of the earth's motion round the sun.

As time wore on, the superstructure of excentrics and epicycles, which
had been strained into representing the appearances of the heavens at a
particular moment, grew out of shape, and the natural consequence of
such an artificial system was, that it became next to impossible to
foresee what ruin might be produced in a remote part of it by any
attempt to repair the derangements and refit the parts to the changes,
as they began to be remarked in any particular point. In the ninth
century of our era, Ptolemy's tables were already useless, and all those
that were contrived with unceasing toil to supply their place, rapidly
became as unserviceable as they. Still the triumph of genius was seen in
the veneration that continued to be paid to the assumptions of Ptolemy
and Hipparchus; and even when the great reformer, Copernicus, appeared,
he did not for a long time intend to do more than slightly modify their
principles. That which he found difficult in the Ptolemaic system, was
none of the inconveniences by which, since the establishment of the new
system, it has become common to demonstrate the inferiority of the old
one; it was the displacement of the centre of the equant from the centre
of the orbit that principally indisposed him against it, and led him to
endeavour to represent the appearances by some other combinations of
really uniform circular motions.

There was an old system, called the Egyptian, according to which Saturn,
Jupiter, Mars, and the Sun circulated round the earth, the sun carrying
with it, as two moons or satellites, the other two planets, Venus and
Mercury. This system had never entirely lost credit: it had been
maintained in the fifth century by Martianus Capella[188], and indeed it
was almost sanctioned, though not formally taught, by Ptolemy himself,
when he made the mean motion of the sun the same as that of the centres
of the epicycles of both these planets. The remark which had also been
made by the old astronomers, of the connexion between the motion of the
sun and the revolutions of the superior planets in their epicycles, led
him straight to the expectation that he might, perhaps, produce the
uniformity he sought by extending the Egyptian system to these also, and
this appears to have been the shape in which his reform was originally
projected. It was already allowed that the centre of the orbits of all
the planets was not coincident with the earth, but removed from it by
the space EC. This first change merely made EC the same for all the
planets, and equal to the mean distance of the earth from the sun. This
system afterwards acquired great celebrity through its adoption by Tycho
Brahe, who believed it originated with himself. It might perhaps have
been at this period of his researches, that Copernicus was struck with
the passages in the Latin and Greek authors, to which he refers as
testifying the existence of an old belief in the motion of the earth
round the sun. He immediately recognised how much this alteration would
further his principles of uniformity, by referring all the planetary
motions to one centre, and did not hesitate to embrace it. The idea of
explaining the daily and principal apparent motions of the heavenly
bodies by the revolution of the earth on its axis, would be the
concluding change, and became almost a necessary consequence of his
previous improvements, as it was manifestly at variance with his
principles to give to all the planets and starry worlds a rapid daily
motion round the centre of the earth, now that the latter was removed
from its former supposed post in the centre of the universe, and was
itself carried with an annual motion round another fixed point.

[Illustration]

The reader would, however, form an inaccurate notion of the system of
Copernicus, if he supposed that it comprised no more than the theory
that each planet, including the earth among them, revolved in a simple
circular orbit round the sun. Copernicus was too well acquainted with
the motions of the heavenly bodies, not to be aware that such orbits
would not accurately represent them; the motion he attributed to the
earth round the sun, was at first merely intended to account for those
which were called the second inequalities of the planets, according to
which they appear one while to move forwards, then backwards, and at
intermediate periods, stationary, and which thenceforward were also
called the optical equations, as being merely an optical illusion. With
regard to what were called the first inequalities, or physical
equations, arising from a real inequality of motion, he still retained
the machinery of the deferent and epicycle; and all the alteration he
attempted in the orbits of the superior planets was an extension of the
concentric theory to supply the place of the equant, which he considered
the blot of the system. His theory for this purpose is shown in the
accompanying diagram, where S represents the sun, D_d_, the deferent or
mean orbit of the planet, on which revolves the centre of the great
epicycle, whose radius, DF, was taken at ¾ of Ptolemy's excentricity of
the equant; and round the circumference of this revolved, in the
opposite direction, the centre of the little epicycle, whose radius, FP,
was made equal to the remaining ¼ of the excentricity of the equant.

The planet P revolved in the circumference of the little epicycle, in
the same direction with the centre of the great epicycle in the
circumference of the deferent, but with a double angular velocity. The
planet was supposed to be in the perigee of the little epicycle, when
its centre was in the apogee of the greater; and whilst, for instance, D
moved equably though the angle DS_d_, F moved through _hdf_ = DS_d_,
and P through _rfp_ = 2 DS_d_.

It is easy to show that this construction gives nearly the same result
as Ptolemy's; for the deferent and great epicycle have been already
shown exactly equivalent to an excentric circle round S, and indeed
Copernicus latterly so represented it: the effect of his construction,
as given above, may therefore be reproduced in the following simpler
form, in which only the smaller epicycle is retained:

[Illustration]

In this construction, the place of the planet is found at the end of any
time proportional to F _f_ by drawing _fr_ parallel to SF, and taking
_rfp_ = 2F _of_. Hence it is plain, if we take OQ, equal to FP, (already
assumed equal to ¼ of Ptolemy's excentricity of the equant,) since SO is
equal to ¾ of the same, that SQ is the whole of Ptolemy's excentricity
of the equant; and therefore, that Q is the position of the centre of
his equant. It is also plain if we join Q_p_, since _rfp_ = 2F _of_, and
_o_Q = _fp_, that _p_Q is parallel to _fo_, and, therefore, _p_QP is
proportional to the time; so that the planet moves uniformly about the
same point Q, as in Ptolemy's theory; and if we bisect SQ in C, which is
the position of the centre of Ptolemy's deferent, the planet will,
according to Copernicus, move very nearly, though not exactly, in the
same circle, whose radius is CP, as that given by the simple excentric
theory.

The explanation offered by Copernicus, of the motions of the inferior
planets, differed again in form from that of the others. He here
introduced what was called a _hypocycle_, which, in fact, was nothing
but a deferent not including the sun, round which the centre of the
orbit revolved. An epicycle in addition to the hypocycle was introduced
into Mercury's orbit. In this epicycle he was not supposed to revolve,
but to librate, or move up and down in its diameter. Copernicus had
recourse to this complication to satisfy an erroneous assertion of
Ptolemy with regard to some of Mercury's inequalities. He also retained
the oscillatory motions ascribed by Ptolemy to the planes of the
epicycles, in order to explain the unequal latitudes observed at the
same distance from the nodes, or intersections of the orbit of the
planet with the ecliptic. Into this intricacy, also, he was led by
placing too much confidence in Ptolemy's observations, which he was
unable to satisfy by an unvarying obliquity. Other very important
errors, such as his belief that the line of nodes always coincided with
the line of apsides, or places of greatest and least distance from the
central body, (whereas, at that time, in the case of Mars, for instance,
they were nearly 90° asunder,) prevented him from accurately
representing many of the celestial phenomena.

These brief details may serve to show that the adoption or rejection of
the theory of Copernicus was not altogether so simple a question as
sometimes it may have been considered. It is, however, not a little
remarkable, while it is strongly illustrative of the spirit of the
times, that these very intricacies, with which Kepler's theories have
enabled us to dispense, were the only parts of the system of Copernicus
that were at first received with approbation. His theory of Mercury,
especially, was considered a masterpiece of subtle invention. Owing to
his dread of the unfavourable judgment he anticipated on the main
principles of his system, his work remained unpublished during forty
years, and was at last given to the world only just in time to allow
Copernicus to receive the first copy of it a few hours before his
death.


FOOTNOTES:

[187] By "the opposite direction" is meant, that while the motion in the
circumference of one circle appeared, as viewed from its centre, to be
from left to right, the other, viewed from its centre, appeared from
right to left. This must be understood whenever these or similar
expressions are repeated.

[188] Venus Mercuriusque, licet ortus occasusque quotidianos ostendunt,
tamen eorum circuli terras omnino non ambiunt, sed circa solem laxiore
ambitu circulantur. Denique circulorum suorum centron in sole
constituunt.--De Nuptiis Philologiæ et Mercurii. Vicentiæ. 1499.




CHAPTER V.

    _Account of the Commentaries on the motions of Mars--Discovery of
      the Law of the equable description of Areas, and of Elliptic
      Orbits._


WE may now proceed to examine Kepler's innovations, but it would be
doing injustice to one of the brightest points of his character, not to
preface them by his own animated exhortation to his readers. "If any one
be too dull to comprehend the science of astronomy, or too feeble-minded
to believe in Copernicus without prejudice to his piety, my advice to
such a one is, that he should quit the astronomical schools, and
condemning, if he has a mind, any or all of the theories of
philosophers, let him look to his own affairs, and leaving this worldly
travail, let him go home and plough his fields: and as often as he lifts
up to this goodly heaven those eyes with which alone he is able to see,
let him pour out his heart in praises and thanksgiving to God the
Creator; and let him not fear but he is offering a worship not less
acceptable than his to whom God has granted to see yet more clearly with
the eyes of his mind, and who both can and will praise his God for what
he has so discovered."

Kepler did not by any means underrate the importance of his labours, as
is sufficiently shewn by the sort of colloquial motto which he prefixed
to his work. It consists in the first instance of an extract from the
writings of the celebrated and unfortunate Peter Ramus. This
distinguished philosopher was professor of mathematics in Paris, and in
the passage in question, after calling on his contemporaries to turn
their thoughts towards the establishment of a system of Astronomy
unassisted by any hypothesis, he promised as an additional inducement to
vacate his own chair in favour of any one who should succeed in this
object. Ramus perished in the massacre of St. Bartholomew, and Kepler
apostrophizes him as follows:--"It is well, Ramus, that you have
forfeited your pledge, by quitting your life and professorship together:
for if you still held it, I would certainly claim it as of right
belonging to me on account of this work, as I could convince you even
with your own logic." It was rather bold in Kepler to assert his claim
to a reward held out for a theory resting on no hypothesis, by right of
a work filled with hypotheses of the most startling description; but of
the vast importance of this book there can be no doubt; and throughout
the many wild and eccentric ideas to which we are introduced in the
course of it, it is fit always to bear in mind that they form part of a
work which is almost the basis of modern Astronomy.

The introduction contains a curious criticism of the commonly-received
theory of gravity, accompanied with a declaration of Kepler's own
opinions on the same subject. Some of the most remarkable passages in it
have been already quoted in the life of Galileo; but, nevertheless, they
are too important to Kepler's reputation to be omitted here, containing
as they do a distinct and positive enunciation of the law of universal
gravitation. It does not appear, however, that Kepler estimated rightly
the importance of the theory here traced out by him, since on every
other occasion he advocated principles with which it is scarcely
reconcileable. The discussion is introduced in the following terms:--

"The motion of heavy bodies hinders many from believing that the earth
is moved by an animal motion, or rather a magnetic one. Let such
consider the following propositions. A mathematical point, whether the
centre of the universe or not, has no power, either effectively or
objectively, to move heavy bodies to approach it. Let physicians prove
if they can, that such power can be possessed by a point, which, neither
is a body, nor is conceived unless by relation alone. It is impossible
that the form[189] of a stone should, by moving its own body, seek a
mathematical point, or in other words, the centre of the universe,
without regard of the body in which that point exists. Let physicians
prove if they can, that natural things have any sympathy with that which
is nothing. Neither do heavy bodies tend to the centre of the universe
by reason that they are avoiding the extremities of the round universe;
for their distance from the centre is insensible, in proportion to their
distance from the extremities of the universe. And what reason could
there be for this hatred? How strong, how wise must those heavy bodies
be, to be able to escape so carefully from an enemy lying on all sides
of them: what activity in the extremities of the world to press their
enemy so closely! Neither are heavy bodies driven into the centre by the
whirling of the first moveable, as happens in revolving water. For if we
assume such a motion, either it would not be continued down to us, or
otherwise we should feel it, and be carried away with it, and the earth
also with us; nay, rather, we should be hurried away first, and the
earth would follow; all which conclusions are allowed by our opponents
to be absurd. It is therefore plain that the vulgar theory of gravity is
erroneous.

"The true theory of gravity is founded on the following axioms:--Every
corporeal substance, so far forth as it is corporeal, has a natural
fitness for resting in every place where it may be situated by itself
beyond the sphere of influence of a body cognate with it. Gravity is a
mutual affection between cognate bodies towards union or conjunction
(similar in kind to the magnetic virtue), so that the earth attracts a
stone much rather than the stone seeks the earth. Heavy bodies (if we
begin by assuming the earth to be in the centre of the world) are not
carried to the centre of the world in its quality of centre of the
world, but as to the centre of a cognate round body, namely, the earth;
so that wheresoever the earth may be placed, or whithersoever it may be
carried by its animal faculty, heavy bodies will always be carried
towards it. If the earth were not round, heavy bodies would not tend
from every side in a straight line towards the centre of the earth, but
to different points from different sides. If two stones were placed in
any part of the world near each other, and beyond the sphere of
influence of a third cognate body, these stones, like two magnetic
needles, would come together in the intermediate point, each approaching
the other by a space proportional to the comparative mass of the other.
If the moon and earth were not retained in their orbits by their animal
force or some other equivalent, the earth would mount to the moon by a
fifty-fourth part of their distance, and the moon fall towards the earth
through the other fifty-three parts and they would there meet; assuming
however that the substance of both is of the same density. If the earth
should cease to attract its waters to itself, all the waters of the sea
would be raised and would flow to the body of the moon. The sphere of
the attractive virtue which is in the moon extends as far as the earth,
and entices up the waters; but as the moon flies rapidly across the
zenith, and the waters cannot follow so quickly, a flow of the ocean is
occasioned in the torrid zone towards the westward. If the attractive
virtue of the moon extends as far as the earth, it follows with greater
reason that the attractive virtue of the earth extends as far as the
moon, and much farther; and in short, nothing which consists of earthly
substance any how constituted, although thrown up to any height, can
ever escape the powerful operation of this attractive virtue. Nothing
which consists of corporeal matter is absolutely light, but that is
comparatively lighter which is rarer, either by its own nature, or by
accidental heat. And it is not to be thought that light bodies are
escaping to the surface of the universe while they are carried upwards,
or that they are not attracted by the earth. They are attracted, but in
a less degree, and so are driven outwards by the heavy bodies; which
being done, they stop, and are kept by the earth in their own place. But
although the attractive virtue of the earth extends upwards, as has been
said, so very far, yet if any stone should be at a distance great enough
to become sensible, compared with the earth's diameter, it is true that
on the motion of the earth such a stone would not follow altogether; its
own force of resistance would be combined with the attractive force of
the earth, and thus it would extricate itself in some degree from the
motion of the earth."

Who, after perusing such passages in the works of an author, whose
writings were in the hands of every student of astronomy, can believe
that Newton waited for the fall of an apple to set him thinking for the
first time on the theory which has immortalized his name? An apple may
have fallen, and Newton may have seen it; but such speculations as those
which it is asserted to have been the cause of originating in him had
been long familiar to the thoughts of every one in Europe pretending to
the name of natural philosopher.

As Kepler always professed to have derived his notion of a magnetic
attraction among the planetary bodies from the writings of Gilbert, it
may be worth while to insert here an extract from the "New Philosophy"
of that author, to show in what form he presented a similar theory of
the tides, which affords the most striking illustration of that
attraction. This work was not published till the middle of the
seventeenth century, but a knowledge of its contents may, in several
instances, be traced back to the period in which it was written:--

"There are two primary causes of the motion of the seas--the moon, and
the diurnal revolution. The moon does not act on the seas by its rays or
its light. How then? Certainly by the common effort of the bodies, and
(to explain it by something similar) by their magnetic attraction. It
should be known, in the first place, that the whole quantity of water is
not contained in the sea and rivers, but that the mass of earth (I mean
this globe) contains moisture and spirit much deeper even than the sea.
The moon draws this out by sympathy, so that they burst forth on the
arrival of the moon, in consequence of the attraction of that star; and
for the same reason, the quicksands which are in the sea open themselves
more, and perspire their moisture and spirits during the flow of the
tide, and the whirlpools in the sea disgorge copious waters; and as the
star retires, they devour the same again, and attract the spirits and
moisture of the terrestrial globe. Hence the moon attracts, not so much
the sea as the subterranean spirits and humours; and the interposed
earth has no more power of resistance than a table or any other dense
body has to resist the force of a magnet. The sea rises from the
greatest depths, in consequence of the ascending humours and spirits;
and when it is raised up, it necessarily flows on to the shores, and
from the shores it enters the rivers."[190]

This passage sets in the strongest light one of the most notorious
errors of the older philosophy, to which Kepler himself was remarkably
addicted. If Gilbert had asserted, in direct terms, that the moon
attracted the water, it is certain that the notion would have been
stigmatized (as it was for a long time in Newton's hands) as arbitrary,
occult, and unphilosophical: the idea of these subterranean humours was
likely to be treated with much more indulgence. A simple statement, that
when the moon was over the water the latter had a tendency to rise
towards it, was thought to convey no instruction; but the assertion that
the moon draws out subterranean spirits by sympathy, carried with it a
more imposing appearance of theory. The farther removed these humours
were from common experience, the easier it became to discuss them in
vague and general language; and those who called themselves philosophers
could endure to hear attributes bestowed on these fictitious elements
which revolted their imaginations when applied to things of whose
reality at least some evidence existed.

It is not necessary to dwell upon the system of Tycho Brahe, which was
identical, as we have said, with one rejected by Copernicus, and
consisted in making the sun revolve about the earth, carrying with it
all the other planets revolving about him. Tycho went so far as to deny
the rotation of the earth to explain the vicissitudes of day and night,
but even his favourite assistant Longomontanus differed from him in this
part of his theory. The great merit of Tycho Brahe, and the service he
rendered to astronomy, was entirely independent of any theory;
consisting in the vast accumulation of observations made by him during a
residence of fifteen years at Uraniburg, with the assistance of
instruments, and with a degree of care, very far superior to anything
known before his time in practical astronomy. Kepler is careful
repeatedly to remind us, that without Tycho's observations he could have
done nothing. The degree of reliance that might be placed on the results
obtained by observers who acknowledged their inferiority to Tycho Brahe,
maybe gathered from an incidental remark of Kepler to Longomontanus. He
had been examining Tycho's registers, and had occasionally found a
difference amounting sometimes to 4´ in the right ascensions of the same
planet, deduced from different stars on the same night. Longomontanus
could not deny the fact, but declared that it was impossible to be
always correct within such limits. The reader should never lose sight of
this uncertainty in the observations, when endeavouring to estimate the
difficulty of finding a theory that would properly represent them.

When Kepler first joined Tycho Brahe at Prague, he found him and
Longomontanus very busily engaged in correcting the theory of Mars, and
accordingly it was this planet to which he also first directed his
attention. They had formed a catalogue of the mean oppositions of Mars
during twenty years, and had discovered a position of the equant, which
(as they said) represented them with tolerable exactness. On the other
hand, they were much embarrassed by the unexpected difficulties they met
in applying a system which seemed on the one hand so accurate, to the
determination of the latitudes, with which it could in no way be made to
agree. Kepler had already suspected the cause of this imperfection, and
was confirmed in the view he took of their theory, when, on a more
careful examination, he found that they overrated the accuracy even of
their longitudes. The errors in these, instead of amounting as they
said, nearly to 2´, rose sometimes above 21´. In fact they had reasoned
ill on their own principles, and even if the foundations of their theory
had been correctly laid, could not have arrived at true results. But
Kepler had satisfied himself of the contrary, and the following diagram
shews the nature of the first alteration he introduced, not perhaps so
celebrated as some of his later discoveries, but at least of equal
consequence to astronomy, which could never have been extricated from
the confusion into which it had fallen, till this important change had
been effected.

[Illustration]

The practice of Tycho Brahe, indeed of all astronomers till the time of
Kepler, had been to fix the position of the planet's orbit and equant
from observations on its mean oppositions, that is to say, on the times
when it was precisely six signs or half a circle distant from the mean
place of the sun. In the annexed figure, let S represent the sun, C the
centre of the earth's orbit, T_t_. Tycho Brahe's practice amounted to
this, that if Q were supposed the place of the centre of the planet's
equant, the centre of P_p_ its orbit was taken in QC, and not in QS, as
Kepler suggested that it ought to be taken. The consequence of this
erroneous practice was, that the observations were deprived of the
character for which oppositions were selected, of being entirely free
from the second inequalities. It followed therefore that as part of the
second inequalities were made conducive towards fixing the relative
position of the orbit and equant, to which they did not naturally
belong, there was an additional perplexity in accounting for the
remainder of them by the size and motion of the epicycle. As the line of
nodes of every planet was also made to pass through C instead of S,
there could not fail to be corresponding errors in the latitudes. It
would only be in the rare case of an opposition of the planet in the
line CS, that the time of its taking place would be the same, whether O,
the centre of the orbit, was placed in CQ or SQ. Every other opposition
would involve an error, so much the greater as it was observed at a
greater distance from the line CS.

It was long however before Tycho Brahe could be made to acquiesce in the
propriety of the proposed alteration; and, in order to remove his doubts
as to the possibility that a method could be erroneous which, as he
still thought, had given him such accurate longitudes, Kepler undertook
the ungrateful labour of the first part of his "Commentaries." He there
shewed, in the three systems of Copernicus, Tycho Brahe, and Ptolemy,
and in both the concentric and excentric theories, that though a false
position were given to the orbit, the longitudes of a planet might be so
represented, by a proper position of the centre of the equant, as never
to err in oppositions above 5´ from those given by observation; though
the second inequalities and the latitudes would thereby be very greatly
deranged.

The change Kepler introduced, of observing apparent instead of mean
oppositions, made it necessary to be very accurate in his reductions of
the planet's place to the ecliptic; and in order to be able to do this,
a previous knowledge of the parallax of Mars became indispensable. His
next labour was therefore directed to this point; and finding that the
assistants to whom Tycho Brahe had previously committed this labour had
performed it in a negligent and imperfect manner, he began afresh with
Tycho's original observations. Having satisfied himself as to the
probable limits of his errors in the parallax on which he finally fixed,
he proceeded to determine the inclination of the orbit and the position
of the line of nodes. In all these operations his talent for
astronomical inquiries appeared pre-eminent in a variety of new methods
by which he combined and availed himself of the observations; but it
must be sufficient merely to mention this fact, without entering into
any detail. One important result may be mentioned, at which he arrived
in the course of them, the constancy of the inclination of the planet's
orbit, which naturally strengthened him in his new theory.

Having gone through these preliminary inquiries, he came at last to fix
the proportions of the orbit; and, in doing so, he determined, in the
first instance, not to assume, as Ptolemy appeared to have done
arbitrarily, the bisection of the excentricity, but to investigate its
proportion along with the other elements of the orbit, which resolution
involved him in much more laborious calculations. After he had gone over
all the steps of his theory no less than seventy times--an appalling
labour, especially if we remember that logarithms were not then
invented--his final result was, that in 1587, on the 6th of March, at
7^{h} 23´, the longitude of the aphelion of Mars was 4^{s} 28° 48´ 55´´;
that the planet's mean longitude was 6^{s} 0° 51´ 35´´; that if the
semidiameter of the orbit was taken at 100000, the excentricity was
11332; and the excentricity of the equant 18564. He fixed the radius of
the greater epicycle at 14988, and that of the smaller at 3628.

When he came to compare the longitudes as given by this, which he
afterwards called the _vicarious_ theory, with the observations at
opposition, the result seemed to promise him the most brilliant success.
His greatest error did not exceed 2´; but, notwithstanding these
flattering anticipations, he soon found by a comparison of longitudes
out of opposition and of latitudes, that it was yet far from being so
complete as he had imagined, and to his infinite vexation he soon found
that the labour of four years, which he had expended on this theory,
must be considered almost entirely fruitless. Even his favourite
principle of dividing the excentricity in a different ratio from
Ptolemy, was found to lead him into greater error than if he had
retained the old bisection. By restoring that, he made his latitudes
more accurate, but produced a corresponding change for the worse in his
longitudes; and although the errors of 8´, to which they now amounted,
would probably have been disregarded by former theorists, Kepler could
not remain satisfied till they were accounted for. Accordingly he found
himself forced to the conclusion that one of the two principles on which
this theory rested must be erroneous; either the orbit of the planet is
not a perfect circle, or there is no fixed point within it round which
it moves with an uniform angular motion. He had once before admitted the
possibility of the former of these facts, conceiving it possible that
the motion of the planets is not at all curvilinear, but that they move
in polygons round the sun, a notion to which he probably inclined in
consequence of his favourite harmonics and geometrical figures.

In consequence of the failure of a theory conducted with such care in
all its practical details, Kepler determined that his next trial should
be of an entirely different complexion. Instead of first satisfying the
first inequalities of the planet, and then endeavouring to account for
the second inequalities, he resolved to reverse the process, or, in
other words, to ascertain as accurately as possible what part of the
planet's apparent motion should be referred solely to the optical
illusion produced by the motion of the earth, before proceeding to any
inquiry of the real inequality of the planet's proper motion. It had
been hitherto taken for granted, that the earth moved equably round the
centre of its orbit; but Kepler, on resuming the consideration of it,
recurred to an opinion he had entertained very early in his astronomical
career (rather from his conviction of the existence of general laws,
than that he had then felt the want of such a supposition), that it
required an equant distinct from its orbit no less than the other
planets. He now saw, that if this were admitted, the changes it would
everywhere introduce in the optical part of the planet's irregularities
might perhaps relieve him from the perplexity in which the vicarious
theory had involved him. Accordingly he applied himself with renewed
assiduity to the examination of this important question, and the result
of his calculations (founded principally on observations of Mars'
parallax) soon satisfied him not only that the earth's orbit does
require such an equant, but that its centre is placed according to the
general law of the bisection of the excentricity which he had previously
found indispensable in the other planets. This was an innovation of the
first magnitude, and accordingly Kepler did not venture to proceed
farther in his theory, till by evidence of the most varied and
satisfactory nature, he had established it beyond the possibility of
cavil.

It may be here remarked, that this principle of the bisection of the
eccentricity, so familiar to the Ptolemaic astronomers, is identical
with the theory afterwards known by the name of the simple elliptic
hypothesis, advocated by, Seth Ward and others. That hypothesis
consisted in supposing the sun to be placed in one focus of the elliptic
orbit of the planet, whose angular motion was uniform round the other
focus. In Ptolemaic phraseology, that other focus was the centre of the
equant, and it is well known that the centre of the ellipse lies in the
middle point between the two foci.

It was at this period also, that Kepler first ventured upon the new
method of representing inequalities which terminated in one of his most
celebrated discoveries. We have already seen, in the account of the
"Mysterium Cosmographicum," that he was speculating, even at that time,
on the effects of a whirling force exerted by the sun on the planets
with diminished energy at increased distances, and on the proportion
observed between the distances of the planets from the sun, and their
periods of revolution. He seems even then to have believed in the
possibility of discovering a relation between the times and distances in
different planets. Another analogous consequence of his theory of the
radiation of the whirling force would be, that if the same planet should
recede to a greater distance from the central body, it would be acted on
by a diminished energy of revolution, and consequently, a relation might
be found between the velocity at any point of its orbit, and its
distance at that point from the sun. Hence he expected to derive a more
direct and natural method of calculating the inequalities, than from the
imaginary equant. But these ingenious ideas had been checked in the
outset by the erroneous belief which Kepler, in common with other
astronomers, then entertained of the coincidence of the earth's equant
with its orbit; in other words, by the belief that the earth's linear
motion was uniform, though it was known not to remain constantly at the
same distance from the sun. As soon as this prejudice was removed, his
former ideas recurred to him with increased force, and he set himself
diligently to consider what relation could be found between the velocity
and distance of a planet from the sun. The method he adopted in the
beginning of this inquiry was to assume as approximately correct
Ptolemy's doctrine of the bisection of the excentricity, and to
investigate some simple relation nearly representing the same effect.

In the annexed figure, S is the place of the sun, C the centre of the
planet's orbit AB_ab_, Q the centre of the equant represented by the
equal circle DE_de_, AB, _ab_, two equal small arcs described by the
planet at the apsides of its orbit: then, according to Ptolemy's
principles, the arc DE of the equant would be proportional to the time
of passing along AB, on the same scale on which _de_ would represent the
time of passing through the equal arc _ab_.

[Illustration]

QD:QA :: DE:AB, nearly; and because QS is bisected in C, QA, CA or QD,
and SA, are in arithmetical proportion: and, therefore, since an
arithmetical mean, when the difference is small, does not differ much
from a geometrical mean, QD:QA :: SA:QD, nearly. Therefore, DE:AB :: S
A:QD, nearly, and in the same manner _de_:_ab_ :: S_a_:Q_d_ nearly; and
therefore DE:_de_ :: SA:S_a_ nearly. Therefore at the apsides, the
times of passing over equal spaces, on Ptolemy's theory, are nearly as
the distances from the sun, and Kepler, with his usual hastiness,
immediately concluded that this was the accurate and general law, and
that the errors of the old theory arose solely from having departed from
it.

It followed immediately from this assumption, that after leaving the
point A, the time in which the planet would arrive at any point P of
its orbit would be proportional to, and might be represented by, the
sums of all the lines that could be drawn from S to the arc AP, on the
same scale that the whole period of revolution would be denoted by the
sum of all the lines drawn to every point of the orbit. Kepler's first
attempt to verify this supposition approximately, was made by dividing
the whole circumference of the orbit into 360 equal parts, and
calculating the distances at every one of the points of division. Then
supposing the planet to move uniformly, and to remain at the same
distance from the sun during the time of passing each one of these
divisions, (a supposition which manifestly would not differ much from
the former one, and would coincide with it more nearly, the greater was
the number of divisions taken) he proceeded to add together these
calculated distances, and hoped to find that the time of arriving at any
one of the divisions bore the same ratio to the whole period, as the sum
of the corresponding set of distances did to the sum of the whole 360.

This theory was erroneous; but by almost miraculous good fortune, he was
led by it in the following manner to the true measure. The discovery was
a consequence of the tediousness of his first method, which required, in
order to know the time of arriving at any point, that the circle should
be subdivided, until one of the points of division fell exactly upon the
given place. Kepler therefore endeavoured to discover some shorter
method of representing these sums of the distances. The idea then
occurred to him of employing for that purpose the area inclosed between
the two distances, SA, SP, and the arc AP, in imitation of the manner in
which he remembered that Archimedes had found the area of the circle, by
dividing it into an infinite number of small triangles by lines drawn
from the centre. He hoped therefore to find, that the time of passing
from A to P bore nearly the same ratio to the whole period of revolution
that the area ASP bore to the whole circle.

This last proportion is in fact accurately observed in the revolution of
one body round another, in consequence of an attractive force in the
central body. Newton afterwards proved this, grounding his demonstration
upon laws of motion altogether irreconcileable with Kepler's opinions;
and it is impossible not to admire Kepler's singular good fortune in
arriving at this correct result in spite, or rather through the means,
of his erroneous principles. It is true that the labour which he
bestowed unsparingly upon every one of his successive guesses, joined
with his admirable candour, generally preserved him from long retaining
a theory altogether at variance with observations; and if any relation
subsisted between the times and distances which could any way be
expressed by any of the geometrical quantities under consideration, he
could scarcely have failed--it might be twenty years earlier or twenty
years later,--to light upon it at last, having once put his
indefatigable fancy upon this scent. But in order to prevent an
over-estimate of his merit in detecting this beautiful law of nature,
let us for a moment reflect what might have been his fate had he
endeavoured in the same manner, and with the same perseverance, to
discover a relation, where, in reality, none existed. Let us take for
example the inclinations or the excentricities of the planetary orbits,
among which no relation has yet been discovered; and if any exists, it
is probably of too complicated a nature to be hit at a venture. If
Kepler had exerted his ingenuity in this direction, he might have wasted
his life in fruitless labour, and whatever reputation he might have left
behind him as an industrious calculator, it would have been very far
inferior to that which has procured for him the proud title of the
"Legislator of the Heavens."

However this may be, the immediate consequence of thus lighting upon the
real law observed by the earth in its passage round the sun was, that he
found himself in possession of a much more accurate method of
representing its inequalities than had been reached by any of his
predecessors; and with renewed hopes he again attacked the planet Mars,
whose path he was now able to consider undistorted by the illusions
arising out of the motion of the earth. Had the path of Mars been
accurately circular, or even as nearly approaching a circle as that of
the earth, the method he chose of determining its position and size by
means of three distances carefully calculated from his observed
parallaxes, would have given a satisfactory result; but finding, as he
soon did, that almost every set of three distances led him to a
different result, he began to suspect another error in the long-received
opinion, that the orbits of the planets must consist of a combination
of circles; he therefore, determined, in the first instance, to fix the
distances of the planet at the apsides without any reference to the form
of the intermediate orbit. Half the difference between these would, of
course, be the excentricity of the orbit; and as this quantity came out
very nearly the same as had been determined on the vicarious theory, it
seemed clear that the error of that theory, whatever it might be, did
not lie in these elements.

Kepler also found that in the case of this planet likewise, the times of
describing equal arcs at the apsides were proportional to its distances
from the sun, and he naturally expected that the method of areas would
measure the planet's motion with as much accuracy as he had found in the
case of the earth. This hope was disappointed: when he calculated the
motion of the planet by this method, he obtained places too much
advanced when near the apsides, and too little advanced at the mean
distances. He did not, on that account, immediately reject the opinion
of circular orbits, but was rather inclined to suspect the principle of
measurement, at which he felt that he had arrived in rather a precarious
manner. He was fully sensible that his areas did not accurately
represent the sums of any distances except those measured from the
centre of the circle; and for some time he abandoned the hope of being
able to use this substitution, which he always considered merely as an
approximate representation of the true measure, the sum of the
distances. But on examination he found that the errors of this
substitution were nearly insensible, and those it did in fact produce,
were in the contrary direction of the errors he was at this time
combating. As soon as he had satisfied himself of this, he ventured once
more on the supposition, which by this time had, in his eyes, almost
acquired the force of demonstration, that the orbits of the planets are
not circular, but of an oval form, retiring within the circle at the
mean distances, and coinciding with it at the apsides.

This notion was not altogether new; it had been suggested in the case of
Mercury, by Purbach, in his "Theories of the Planets." In the edition of
this work published by Reinhold, the pupil of Copernicus, we read the
following passage. "Sixthly, it appears from what has been said, that
the centre of Mercury's epicycle, by reason of the motions
above-mentioned, does not, as is the case with the other planets,
describe the circumference of a circular deferent, but rather the
periphery of a figure resembling a plane oval." To this is added the
following note by Reinhold. "The centre of the Moon's epicycle describes
a path of a lenticular shape; Mercury's on the contrary is egg-shaped,
the big end lying towards his apogee, and the little end towards his
perigee."[191] The excentricity of Mercury's orbit is, in fact, much
greater than that of any of the other planets, and the merit of making
this first step cannot reasonably be withheld from Purbach and his
commentator, although they did not pursue the inquiry so far as Kepler
found himself in a condition to do.

Before proceeding to the consideration of the particular oval which
Kepler fixed upon in the first instance, it will be necessary, in order
to render intelligible the source of many of his doubts and
difficulties, to make known something more of his theory of the moving
force by which he supposed the planets to be carried round in their
orbits. In conformity with the plan hitherto pursued, this shall be done
as much as possible in his own words.

"It is one of the commonest axioms in natural philosophy, that if two
things always happen together and in the same manner, and admit the same
measure, either the one is the cause of the other, or both are the
effect of a common cause. In the present case, the increase or languor
of motion invariably corresponds with an approach to or departure from
the centre of the universe. Therefore, either the languor is the cause
of the departure of the star, or the departure of the languor, or both
have a common cause. But no one can be of opinion that there is a
concurrence of any third thing to be a common cause of these two
effects, and in the following chapters it will be made clear that there
is no occasion to imagine any such third thing, since the two are of
themselves sufficient. Now, it is not agreeable to the nature of things
that activity or languor in linear motion should be the cause of
distance from the centre. For, distance from the centre is conceived
anteriorly to linear motion. In fact linear motion cannot exist without
distance from the centre, since it requires space for its
accomplishment, but distance from the centre can be conceived without
motion. Therefore distance is the cause of the activity of motion, and a
greater or less distance of a greater or less delay. And since distance
is of the kind of relative quantities, whose essence consists in
boundaries, (for there is no efficacy in relation _per se_ without
regard to bounds,) it follows that the cause of the varying activity of
motion rests in one of the boundaries. But the body of the planet
neither becomes heavier by receding, nor lighter by approaching.
Besides, it would perhaps be absurd on the very mention of it, that an
animal force residing in the moveable body of the planet for the purpose
of moving it, should exert and relax itself so often without weariness
or decay. It remains, therefore, that the cause of this activity and
languor resides at the other boundary, that is, in the very centre of
the world, from which the distances are computed.--Let us continue our
investigation of this moving virtue which resides in the sun, and we
shall presently recognize its very close analogy to light. And although
this moving virtue cannot be identical with the light of the sun, let
others look to it whether the light is employed as a sort of instrument,
or vehicle, to convey the moving virtue. There are these seeming
contradictions:--first, light is obstructed by opaque bodies, for which
reason if the moving virtue travelled on the light, darkness would be
followed by a stoppage of the moveable bodies. Again, light flows out in
right lines spherically, the moving virtue in right lines also, but
cylindrically; that is, it turns in one direction only, from west to
east; not in the opposite direction, not towards the poles, &c. But
perhaps we shall be able presently to reply to these objections. In
conclusion, since there is as much virtue in a large and remote circle
as in a narrow and close one, nothing of the virtue perishes in the
passage from its source, nothing is scattered between the source and the
moveable. Therefore the efflux, like that of light, is not material, and
is unlike that of odours, which are accompanied by a loss of substance,
unlike heat from a raging furnace, unlike every other emanation by which
mediums are filled. It remains, therefore, that as light which
illuminates all earthly things, is the immaterial species of that fire
which is in the body of the sun, so this virtue, embracing and moving
all the planetary bodies, is the immaterial species of that virtue which
resides in the sun itself, of incalculable energy, and so the primary
act of all mundane motion.--I should like to know who ever said that
there was anything material in light!--Guided by our notion of the
efflux of this species (or archetype), let us contemplate the more
intimate nature of the source itself. For it seems as if something
divine were latent in the body of the sun, and comparable to our own
soul, whence that species emanates which drives round the planets; just
as from the mind of a slinger the species of motion sticks to the
stones, and carries them forward, even after he who cast them has drawn
back his hand. But to those who wish to proceed soberly, reflections
differing a little from these will be offered."

Our readers will, perhaps, be satisfied with the assurance, that these
sober considerations will not enable them to form a much more accurate
notion of Kepler's meaning than the passages already cited. We shall
therefore proceed to the various opinions he entertained on the motion
of the planets.

He considered it as established by his theory, that the centre E of the
planet's epicycle (see fig. p. 33.) moved round the circumference of the
deferent D_d_, according to the law of the planet's distances; the point
remaining to be settled was the motion of the planet in the epicycle. If
it were made to move according to the same law, so that when the centre
of the epicycle reached E, the planet should be at F, taking the angle
BEF equal to BSA, it has been shewn (p. 19) that the path of F would
still be a circle, excentric from D_d_ by DA the radius of the epicycle.

But Kepler fancied that he saw many sound reasons why this could not be
the true law of motion in the epicycle, on which reasons he relied much
more firmly than on the indisputable fact, which he mentions as a
collateral proof, that it was contradicted by the observations. Some of
these reasons are subjoined: "In the beginning of the work it has been
declared to be most absurd, that a planet (even though we suppose it
endowed with mind) should form any notion of a centre, and a distance
from it, if there be no body in that centre to serve for a
distinguishing mark. And although you should say, that the planet has
respect to the sun, and knows beforehand, and remembers the order in
which the distances from the sun are comprised, so as to make a perfect
excentric; in the first place, this is rather far-fetched, and requires,
in any mind, means for connecting the effect of an accurately circular
path with the sign of an increasing and diminishing diameter of the sun.
But there are no such means, except the position of the centre of the
excentric at a given distance from the sun; and I have already said,
that this is beyond the power of a mere mind. I do not deny that a
centre may be imagined, and a circle round it; but this I do say, if the
circle exists only in imagination, with no external sign or division,
that it is not possible that the path of a moveable body should be
really ordered round it in an exact circle. Besides, if the planet
chooses from memory its just distances from the sun, so as exactly to
form a circle, it must also take from the same source, as if out of the
Prussian or Alphonsine tables, equal excentric arcs, to be described in
unequal times, and to be described by a force extraneous from the sun;
and thus would have, from its memory, a foreknowledge of what effects a
virtue, senseless and extraneous from the sun, was about to produce: all
these consequences are absurd.

"It is therefore more agreeable to reason that the planet takes no
thought, either of the excentric or epicycle; but that the work which it
accomplishes, or joins in effecting, is a libratory path in the diameter
B_b_ of the epicycle, in the direction towards the sun. The law is now
to be discovered, according to which the planet arrives at the proper
distances in any time. And indeed in this inquiry, it is easier to say
what the law is not than what it is."--Here, according to his custom,
Kepler enumerates several laws of motion by which the planet might
choose to regulate its energies, each of which is successively
condemned. Only one of them is here mentioned, as a specimen of the
rest. "What then if we were to say this? Although the motions of the
planet are not epicyclical, perhaps the libration is so arranged that
the distances from the sun are equal to what they would have been in a
real epicyclical motion.--This leads to more incredible consequences
than the former suppositions, and yet in the dearth of better opinions,
let us for the present content ourselves with this. The greater number
of absurd conclusions it will be found to involve, the more ready will a
physician be, when we come to the fifty-second chapter, to admit what
the observations testify, that the path of the planet is not circular."

The first oval path on which Kepler was induced to fix, by these and
many other similar considerations, was in the first instance very
different from the true elliptical form. Most authors would have thought
it unnecessary to detain their readers with a theory which they had once
entertained and rejected; but Kepler's work was written on a different
plan. He thus introduces an explanation of his first oval. "As soon as I
was thus taught by Brahe's very accurate observations that the orbit of
a planet is not circular, but more compressed at the sides, on the
instant I thought that I understood the natural cause of this
deflection. But the old proverb was verified in my case;--the more haste
the less speed.--For having violently laboured in the 39th chapter, in
consequence of my inability to find a sufficiently probable cause why
the orbit of the planet should be a perfect circle, (some absurdities
always remaining with respect to that virtue which resides in the body
of the planet,) and having now discovered from the observations, that
the orbit is not a perfect circle, I felt furiously inclined to believe
that if the theory which had been recognized as absurd, when employed in
the 39th chapter for the purpose of fabricating a circle, were modulated
into a more probable form, it would produce an accurate orbit agreeing
with the observations. If I had entered on this course a little more
warily, I might have detected the truth immediately. But, being blinded
by my eagerness, and not sufficiently regardful of every part of the
39th chapter, and clinging to my first opinion, which offered itself to
me with a wonderful show of probability, on account of the equable
motion in the epicycle, I got entangled in new perplexities, with which
we shall now have to struggle in this 45th chapter and the following
ones as far as the 50th chapter."

In this theory, Kepler supposed that whilst the centre of the epicycle
was moving round a circular deferent according to the law of the
planets' distances (or areas) the planet itself moved equably in the
epicycle, with the mean angular velocity of its centre in the deferent.
In consequence of this supposition, since at D, when the planet is at A
the aphelion, the motion in the deferent is less than the mean motion,
the planet will have advanced through an angle BEP greater than BEF or
BSA, through which the centre of the epicycle has moved; and
consequently, the path will lie everywhere within the circle A_a_,
except at the apsides. Here was a new train of laborious calculations to
undergo for the purpose of drawing the curve AP_a_ according to this
law, and of measuring the area of any part of it. After a variety of
fruitless attempts, for this curve is one of singular complexity, he was
reduced, as a last resource, to suppose it insensibly different from an
ellipse on the same principal axes, as an approximate means of
estimating its area. Not content even with the results so obtained, and
not being able to see very clearly what might be the effect of his
alteration in substituting the ellipse for the oval, and in other
simplifications introduced by him, he had courage enough to obtain the
sums of the 360 distances by direct calculation, as he had done in the
old circular theory.

[Illustration]

In the preface to his book he had spoken of his labours under the
allegory of a war carried on by him against the planet; and when
exulting in the early prospects of success this calculation seemed to
offer, he did not omit once more to warn his readers, in his peculiar
strain, that this exultation was premature.

"Allow me, gentle reader, to enjoy so splendid a triumph for one little
day (I mean through the five next chapters), meantime be all rumours
suppressed of new rebellion, that our preparations may not perish,
yielding us no delight. Hereafter if anything shall come to pass, we
will go through it in its own time and season; now let us be merry, as
then we will be bold and vigorous." At the time foretold, that is to
say, at the end of the five merry chapters, the bad news could no longer
be kept a secret. It is announced in the following bulletin:--"While
thus triumphing over Mars, and preparing for him, as for one altogether
vanquished, tabular prisons, and equated eccentric fetters, it is buzzed
here and there that the victory is vain, and that the war is raging anew
as violently as before. For the enemy, left at home a despised captive,
has burst all the chains of the equations, and broken forth of the
prisons of the tables. For no method of geometrically administering the
theory of the 45th chapter was able to come near the accuracy of
approximation of the vicarious theory of the 16th chapter, which gave me
true equations derived from false principles. Skirmishers, disposed all
round the circuit of the excentric, (I mean the true distances,) routed
my forces of physical causes levied out of the 45th chapter, and shaking
off the yoke, regained their liberty. And now there was little to
prevent the fugitive enemy from effecting a junction with his rebellious
supporters, and reducing me to despair, had I not suddenly sent into the
field a reserve of new physical reasonings on the rout and dispersion of
the veterans, and diligently followed, without allowing him the
slightest respite, in the direction in which he had broken out."

In plainer terms, Kepler found, after this labour was completed, that
the errors in longitude he was still subject to were precisely of an
opposite nature to those he had found with the circle; instead of being
too quick at the apsides, the planet was now too slow there, and too
much accelerated in the mean distances; and the distances obtained from
direct observation were everywhere greater, except at the apsides, than
those furnished by this oval theory. It was in the course of these
tedious investigations that he established, still more satisfactorily
than he had before done, that the inclinations of the planets' orbits
are invariable, and that the lines of their nodes pass through the
centre of the Sun, and not, as before his time had been supposed,
through the centre of the ecliptic.

When Kepler found with certainty that this oval from which he expected
so much would not satisfy the observations, his vexation was extreme,
not merely from the mortification of finding a theory confuted on which
he had spent such excessive labour, for he was accustomed to
disappointments of that kind, but principally from many anxious and
fruitless speculations as to the real physical causes why the planet did
not move in the supposed epicycle, that being the point of view, as has
been already shewn, from which he always preferred to begin his
inquiries. One part of the reasoning by which he reconciled himself to
the failure exhibits much too curious a view of the state of his mind to
be passed over in silence. The argument is founded on the difficulty
which he met with, as above mentioned, in calculating the proportions of
the oval path he had imagined. "In order that you may see the cause of
the impracticability of this method which we have just gone through,
consider on what foundations it rests. The planet is supposed to move
equably in the epicycle, and to be carried by the Sun unequably in the
proportion of the distances. But by this method it is impossible to be
known how much of the oval path corresponds to any given time, although
the distance at that part is known, unless we first know the length of
the whole oval. But the length of the oval cannot be known, except from
the law of the entry of the planet within the sides of the circle. But
neither can the law of this entry be known before we know how much of
the oval path corresponds to any given time. Here you see that there is
a _petitio principii_; and in my operations I was assuming that of which
I was in search, namely, the length of the oval. This is at least not
the fault of my understanding, but it is also most alien to the primary
Ordainer of the planetary courses: I have never yet found so
ungeometrical a contrivance in his other works. Therefore we must either
hit upon some other method of reducing the theory of the 45th chapter to
calculation; or if that cannot be done, the theory itself, suspected on
account of this _petitio principii_, will totter." Whilst his mind was
thus occupied, one of those extraordinary accidents which it has been
said never occur but to those capable of deriving advantage from them
(but which, in fact, are never noticed when they occur to any one else),
fortunately put him once more upon the right path. Half the extreme
breadth between the oval and the circle nearly represented the errors of
his distances at the mean point, and he found that this half was 429
parts of a radius, consisting of 100000 parts; and happening to advert
to the greatest optical inequality of Mars, which amounts to about 5°
18´, it struck him that 429 was precisely the excess of the secant of 5°
18´ above the radius taken at 100000. This was a ray of light, and, to
use his own words, it roused him as out of sleep. In short, this single
observation was enough to produce conviction in his singularly
constituted mind, that instead of the distances SF, he should everywhere
substitute FV, determined by drawing SV perpendicular on the line FC,
since the excess of SF above FV is manifestly that of the secant above
the radius in the optical equation SFC at that point. It is still more
extraordinary that a substitution made for such a reason should have the
luck, as is again the case, to be the right one. This substitution in
fact amounted to supposing that the planet, instead of being at the
distance SP or SF, was at S_n_; or, in other words, that instead of
revolving in the circumference, it librated in the diameter of the
epicycle, which was to him an additional recommendation. Upon this new
supposition a fresh set of distances was rapidly calculated, and to
Kepler's inexpressible joy, they were found to agree with the
observations within the limits of the errors to which the latter were
necessarily subject. Notwithstanding this success, he had to undergo,
before arriving at the successful termination of his labours, one more
disappointment. Although the distance corresponding to a time from the
aphelion represented approximately by the area ASF, was thus found to be
accurately represented by the line S_n_, there was still an error with
regard to the direction in which that distance was to be measured.
Kepler's first idea was to set it off in the direction SF, but this he
found to lead to inaccurate longitudes; and it was not until after much
perplexity, driving him, as he tells us, "almost to insanity," that he
satisfied himself that the distance SQ equal to FV ought to be taken
terminating in F_m_, the line from F perpendicular to A_a_, the line of
apsides, and that the curve so traced out by Q would be an accurate
ellipse.

[Illustration]

He then found to his equal gratification and amazement, a small part of
which he endeavoured to express by a triumphant figure on the side of
his diagram, that the error he had committed in taking the area ASF to
represent the sums of the distances SF, was exactly counterbalanced; for
this area does accurately represent the sums of the distances FV or SQ.
This compensation, which seemed to Kepler the greatest confirmation of
his theory, is altogether accidental and immaterial, resulting from the
relation between the ellipse and circle. If the laws of planetary
attraction had chanced to have been any other than those which cause
them to describe ellipses, this last singular confirmation of an
erroneous theory could not have taken place, and Kepler would have been
forced either to abandon the theory of the areas, which even then would
have continued to measure and define their motions, or to renounce the
physical opinions from which he professed to have deduced it as an
approximative truth.

These are two of the three celebrated theorems called Kepler's laws: the
first is, that the planets move in ellipses round the sun, placed in the
focus; the second, that the time of describing any arc is proportional
in the same orbit to the area included between the arc and the two
bounding distances from the sun. The third will be mentioned on another
occasion, as it was not discovered till twelve years later. On the
establishment of these two theorems, it became important to discover a
method of measuring such elliptic areas, but this is a problem which
cannot be accurately solved. Kepler, in offering it to the attention of
geometricians, stated his belief that its solution was unattainable by
direct processes, on account of the incommensurability of the arc and
sine, on which the measurement of the two parts AQ_m_, SQ_m_ depends.
"This," says he in conclusion, "this is my belief, and whoever shall
shew my mistake, and point out the true solution,

                   _Is erit mihi magnus Apollonius._"


FOOTNOTES:

[189] It is not very easy to carry the understanding aright among these
Aristotelian ideas. Many at the present day might think they understood
better what is meant, if for "form" had been written "nature."

[190] De mundo nostro sublunari, Philosóphia Nova. Amstelodami, 1651.

[191] Theoricæ novæ planetarum. G. Purbachii, Parisiis, 1553.




CHAPTER VI.

    _Kepler appointed Professor at Linz--His second marriage--Publishes
      his new Method of Gauging--Refuses a Professorship at Bologna._


WHEN presenting this celebrated book to the emperor, Kepler gave notice
that he contemplated a farther attack upon Mars's relations, father
Jupiter, brother Mercury, and the rest; and promised that he would be
successful, provided the emperor would not forget the sinews of war, and
order him to be furnished anew with means for recruiting his army. The
death of his unhappy patron, the Emperor Rodolph, which happened in
1612, barely in time to save him from the last disgrace of deposition
from the Imperial throne, seemed to put additional difficulties in the
way of Kepler's receiving the arrears so unjustly denied to him; but on
the accession of Rodolph's brother, Matthias, he was again named to his
post of Imperial Mathematician, and had also a permanent professorship
assigned to him in the University of Linz. He quitted Prague without
much regret, where he had struggled against poverty during eleven years.
Whatever disinclination he might feel to depart, arose from his
unwillingness to loosen still more the hold he yet retained upon the
wreck of Tycho Brahe's instruments and observations. Tengnagel,
son-in-law of Tycho, had abandoned astronomy for a political career, and
the other members of his family, who were principally females, suffered
the costly instruments to lie neglected and forgotten, although they had
obstructed with the utmost jealousy Kepler's attempts to continue their
utility. The only two instruments Kepler possessed of his own property,
were "An iron sextant of 2½ feet diameter, and a brass azimuthal
quadrant, of 3½ feet diameter, both divided into minutes of a degree."
These were the gift of his friend and patron, Hoffman, the President of
Styria, and with these he made all the observations which he added to
those of Tycho Brahe. His constitution was not favourable to these
studies, his health being always delicate, and suffering much from
exposure to the night air; his eyes also were very weak, as he mentions
himself in several places. In the summary of his character which he drew
up when proposing to become Tycho Brahe's assistant, he describes
himself as follows:--"For observations my sight is dull; for mechanical
operations my hand is awkward; in politics and domestic matters my
nature is troublesome and choleric; my constitution will not allow me,
even when in good health, to remain a long time sedentary (particularly
for an extraordinary time after dinner); I must rise often and walk
about, and in different seasons am forced to make corresponding changes
in my diet."

The year preceding his departure to Linz was denounced by him as
pregnant with misfortune and misery. "In the first place I could get no
money from the court, and my wife, who had for a long time been
suffering under low spirits and despondency, was taken violently ill
towards the end of 1610, with the Hungarian fever, epilepsy, and
phrenitis. She was scarcely convalescent when all my three children were
at once attacked with small-pox. Leopold with his army occupied the town
beyond the river, just as I lost the dearest of my sons, him whose
nativity you will find in my book on the new star. The town on this side
of the river where I lived was harassed by the Bohemian troops, whose
new levies were insubordinate and insolent: to complete the whole, the
Austrian army brought the plague with them into the city. I went into
Austria, and endeavoured to procure the situation which I now hold.
Returning in June, I found my wife in a decline from her grief at the
death of her son, and on the eve of an infectious fever; and I lost her
also, within eleven days after my return. Then came fresh annoyance, of
course, and her fortune was to be divided with my step-sisters. The
Emperor Rodolph would not agree to my departure; vain hopes were given
me of being paid from Saxony; my time and money were wasted together,
till on the death of the emperor, in 1612, I was named again by his
successor, and suffered to depart to Linz. These, methinks, were reasons
enough why I should have overlooked not only your letters, but even
astronomy itself."

Kepler's first marriage had not been a happy one; but the necessity in
which he felt himself of providing some one to take charge of his two
surviving children, of whom the eldest, Susanna, was born in 1602, and
Louis in 1607, determined him on entering a second time into the married
state. The account he has left us of the various negotiations which
preceded his final choice, does not, in any point, belie the oddity of
his character. His friends seem to have received a general commission to
look out for a suitable match, and in a long and most amusing letter to
the Baron Strahlendorf, we are made acquainted with the pretensions and
qualifications of no less than eleven ladies among whom his inclinations
wavered.

The first on the list was a widow, an intimate friend of his first
wife's, and who, on many accounts, appeared a most eligible match. "At
first she seemed favourably inclined to the proposal; it is certain that
she took time to consider it, but at last she very quietly excused
herself." It must have been from a recollection of this lady's good
qualities that Kepler was induced to make his offer; for we learn rather
unexpectedly, after being informed of her decision, that when he soon
afterwards paid his respects to her, it was for the first time that he
had seen her during the last six years; and he found, to his great
relief, that "there was no single pleasing point about her." The truth
seems to be that he was nettled by her answer, and he is at greater
pains than appear necessary, considering this last discovery, to
determine why she would not accept his offered hand. Among other reasons
he suggested her children, among whom were two marriageable daughters;
and it is diverting afterwards to find them also in the catalogue which
Kepler appeared to be making of all his female acquaintance. He seems to
have been much perplexed in attempting to reconcile his astrological
theory with the fact of his having taken so much trouble about a
negotiation not destined to succeed. "Have the stars exercised any
influence here? For just about this time the direction of the Mid-Heaven
is in hot opposition to Mars, and the passage of Saturn, through the
ascending point of the zodiac, in the scheme of my nativity, will happen
again next November and December. But if these are the causes, how do
they act? Is that explanation the true one which I have elsewhere given?
For I can never think of handing over to the stars the office of deities
to produce effects. Let us therefore suppose it accounted for by the
stars, that at this season I am violent in my temper and affections, in
rashness of belief, in a shew of pitiful tender-heartedness; in catching
at reputation by new and paradoxical notions, and the singularity of my
actions; in busily inquiring into, and weighing and discussing, various
reasons; in the uneasiness of my mind with respect to my choice. I thank
God that that did not happen which might have happened; that this
marriage did not take place: now for the others." Of these others, one
was too old, another in bad health, another too proud of her birth and
quarterings; a fourth had learned nothing but shewy accomplishments,
"not at all suitable to the sort of life she would have to lead with
me." Another grew impatient, and married a more decided admirer, whilst
he was hesitating. "The mischief (says he) in all these attachments was,
that whilst I was delaying, comparing, and balancing conflicting
reasons, every day saw me inflamed with a new passion." By the time he
reached the eighth, he found his match in this respect. "Fortune at
length has avenged herself on my doubtful inclinations. At first she was
quite complying, and her friends also: presently, whether she did or did
not consent, not only I, but she herself did not know. After the lapse
of a few days, came a renewed promise, which however had to be confirmed
a third time; and four days after that, she again repented her
confirmation, and begged to be excused from it. Upon this I gave her up,
and this time all my counsellors were of one opinion." This was the
longest courtship in the list, having lasted three whole months; and
quite disheartened by its bad success, Kepler's next attempt was of a
more timid complexion. His advances to No. 9, were made by confiding to
her the whole story of his recent disappointment, prudently determining
to be guided in his behaviour, by observing whether the treatment he had
experienced met with a proper degree of sympathy. Apparently the
experiment did not succeed; and almost reduced to despair, Kepler betook
himself to the advice of a friend, who had for some time past complained
that she was not consulted in this difficult negotiation. When she
produced No. 10, and the first visit was paid, the report upon her was
as follows:--"She has, undoubtedly, a good fortune, is of good family,
and of economical habits: but her physiognomy is most horribly ugly; she
would be stared at in the streets, not to mention the striking
disproportion in our figures. I am lank, lean, and spare; she is short
and thick: in a family notorious for fatness she is considered
superfluously fat." The only objection to No. 11 seems to have been her
excessive youth; and when this treaty was broken of on that account,
Kepler turned his back upon all his advisers, and chose for himself one
who had figured as No. 5 in the list, to whom he professes to have felt
attached throughout, but from whom the representations of his friends
had hitherto detained him, probably on account of her humble station.

The following is Kepler's summary of her character. "Her name is
Susanna, the daughter of John Reuthinger and Barbara, citizens of the
town of Eferdingen; the father was by trade a cabinet-maker, but both
her parents are dead. She has received an education well worth the
largest dowry, by favour of the Lady of Stahrenberg, the strictness of
whose household is famous throughout the province. Her person and
manners are suitable to mine; no pride, no extravagance; she can bear to
work; she has a tolerable knowledge how to manage a family; middle-aged,
and of a disposition and capability to acquire what she still wants. Her
I shall marry by favour of the noble baron of Stahrenberg at twelve
o'clock on the 30th of next October, with all Eferdingen assembled to
meet us, and we shall eat the marriage-dinner at Maurice's at the Golden
Lion."

Hantsch has made an absurd mistake with regard to this marriage, in
stating that the bride was only twelve years old. Kästner and other
biographers have been content to repeat the same assertion without any
comment, notwithstanding its evident improbability. The origin of the
blunder is to be found in Kepler's correspondence with Bernegger, to
whom, speaking of his wife, he says "She has been educated for twelve
years by the Lady of Stahrenberg." This is by no means a single instance
of carelessness in Hantsch; Kästner has pointed out others of greater
consequence. It was owing to this marriage, that Kepler took occasion to
write his new method of gauging, for as he tells us in his own peculiar
style "last November I brought home a new wife, and as the whole course
of Danube was then covered with the produce of the Austrian vineyards,
to be sold at a reasonable rate, I purchased a few casks, thinking it my
duty as a good husband and a father of a family, to see that my
household was well provided with drink." When the seller came to
ascertain the quantity, Kepler objected to his method of gauging, for
he allowed no difference, whatever might be the proportion of the
bulging parts. The reflections to which this incident gave rise,
terminated in the publication of the above-mentioned treatise, which
claims a place among the earliest specimens of what is now called the
modern analysis. In it he extended several properties of plane figures
to segments of cones and cylinders, from the consideration that "these
solids are incorporated circles," and, therefore, that those properties
are true of the whole which belong to each component part. That the book
might end as oddly as it began, Kepler concluded it with a parody of
Catullus:

    "Et cum pocula mille mensi erîmus
    Conturbabimus illa, ne sciamus."

His new residence at Linz was not long undisturbed. He quarrelled there,
as he had done in the early part of his life at Gratz, with the Roman
Catholic party, and was excommunicated. "Judge," says he to Peter
Hoffman, "how far I can assist you, in a place where the priest and
school-inspector have combined to brand me with the public stigma of
heresy, because in every question I take that side which seems to me to
be consonant with the word of God." The particular dogma which
occasioned his excommunication, was connected with the doctrine of
transubstantiation. He published his creed in a copy of Latin verses,
preserved by his biographer Hantsch.

Before this occurrence, Kepler had been called to the diet at Ratisbon
to give his opinion on the propriety of adopting the Gregorian
reformation of the calendar, and he published a short essay, pointing
out the respective convenience of doing so, or of altering the old
Julian Calendar in some other manner. Notwithstanding the readiness of
the diet to avail themselves of his talents for the settlement of a
difficult question, the arrears of his salary were not paid much more
regularly than they had been in Rodolph's time, and he was driven to
provide himself with money by the publication of his almanac, of which
necessity he heavily and justly complained. "In order to pay the expense
of the Ephemeris for these two years, I have also written a vile
prophesying almanac, which is scarcely more respectable than begging;
unless it be because it saves the emperor's credit, who abandons me
entirely; and with all his frequent and recent orders in council, would
suffer me to perish with hunger." Kepler published this Ephemeris
annually till 1620; ten years later he added those belonging to the
years from 1620 to 1628.

In 1617 Kepler was invited into Italy, to succeed Magini as Professor of
Mathematics at Bologna. The offer tempted him; but, after mature
consideration, he rejected it, on grounds which he thus explained to
Roffini:--"By birth and spirit I am a German, imbued with German
principles, and bound by such family ties, that even if the emperor
should consent, I could not, without the greatest difficulty, remove my
dwelling-place from Germany into Italy. And although the glory of
holding so distinguished a situation among the venerable professors of
Bologna stimulates me, and there appears great likelihood of notably
increasing my fortune, as well from the great concourse to the public
lectures, as from private tuition; yet, on the other hand, that period
of my life is past which was once excited by novelty, or which might
promise itself a long enjoyment of these advantages. Besides, from a boy
up to my present years, living a German among Germans, I am accustomed
to a degree of freedom in my speech and manners, which, if persevered in
on my removal to Bologna, seems likely to draw upon me, if not danger,
at least notoriety, and might expose me to suspicion and party malice.
Notwithstanding this answer, I have yet hopes that your most honourable
invitation will be of service to me, and may make the imperial treasurer
more ready than he has hitherto been to fulfil his master's intentions
towards me. In that case I shall the sooner be able to publish the
Rudolphine Tables and the Ephemerides, of which you had the scheme so
many years back; and in this manner you and your advisers may have no
reason to regret this invitation, though for the present it seems
fruitless."

In 1619, the Emperor Matthias died, and was succeeded by Ferdinand III.,
who retained Kepler in the post he had filled under his two predecessors
on the imperial throne. Kästner, in his "History of Mathematics," has
corrected a gross error of Hantsch, in asserting that Kepler
prognosticated Matthias's death. The letter to which Hantsch refers, in
support of his statement, does indeed mention the emperor's death, but
merely as a notorious event, for the purpose of recalling a date to the
memory of his correspondent.




CHAPTER VII.

    _Kepler publishes his Harmonics--Account of his Astrological
      Opinions and Discovery of the Law of the Periods of the Planetary
      Revolutions--Sketch of Newton's proof of Kepler's Laws._


THE "Cosmographical Mystery" was written, as has been already mentioned,
when Kepler was only twenty-six, and the wildness of its theories might
be considered as due merely to the vivacity of a young man; but as if
purposely to shew that his maturer age did not renounce the creations of
his youthful fancy, he reprinted the "Mystery" in 1619, nearly at the
same time when he published his celebrated work on Harmonics; and the
extravagance of the latter publication does not at all lose in
comparison with its predecessor. It is dedicated to James I. of England,
and divided into five books: "The first, Geometrical, on the origin and
demonstration of the laws of the figures which produce harmonious
proportions;--the second, Architectonical, on figurate geometry, and the
congruence of plane and solid regular figures;--the third, properly
Harmonic, on the derivation of musical proportions from figures, and on
the nature and distinction of things relating to song, in opposition to
the old theories;--the fourth, Metaphysical, Psychological, and
Astrological, on the mental essence of harmonies, and of their kinds in
the world, especially on the harmony of rays emanating on the earth from
the heavenly bodies, and on their effect in nature, and on the sublunary
and human soul;--the fifth, Astronomical and Metaphysical, on the very
exquisite harmonies of the celestial motions, and the origin of the
excentricities in harmonious proportions."

The two first books are almost strictly, as Kepler styles them,
geometrical, relating in great measure to the inscription of regular
polygons in a circle. The following passage is curious, presenting an
analogous idea to that contained in one of the extracts already given
from the Commentaries on Mars. "The heptagon, and all other polygons and
stars beyond it, which have a prime number of sides, and all other
figures derived from them, cannot be inscribed geometrically in a
circle; although their sides have a necessary magnitude, it is equally a
matter of necessity that we remain ignorant of it. This is a question of
great importance, for on this account is it that the heptagon, and other
figures of this kind, have not been employed by God in the adornment of
the world, as the other intelligible figures are employed which have
been already explained." Kepler then introduces the algebraical
equation, on the solution of which this problem depends, and makes a
remark which is curious at this period of the history of algebra--that
the root of an equation which cannot be accurately found, may yet be
found within any degree of approximation by an expert calculator. In
conclusion he again remarks that "the side of the heptagon has no place
among scientific existences, since its formal description is impossible,
and therefore it cannot be known by the human mind, since the
possibility of description precedes the possibility of knowledge; nor is
it known even by the simple eternal act of an omniscient mind, because
its nature belongs to things which cannot be known. And yet this
scientific nonentity has some scientific properties, for if a heptagon
were described in a circle, the proportion of its sides would have
analogous proportions."

The third book is a treatise on music, in the confined and ordinary
sense in which we now use that word, and apparently a sober and rational
one, at least as nearly so as Kepler could be trusted to write on a
subject so dangerous to his discretion. All the extravagance of the work
seems reserved for the fourth book, the title of which already conveys
some notion of the nature of its contents. In this book he has collected
the substance of the astrological opinions scattered through his other
works. We shall content ourselves with merely citing his own words,
without any attempt to explain the difference between the astrology
which he believed, and that which he contemptuously rejected. The
distinctive line seems very finely drawn, and as both one and the other
are now discarded by all who enjoy the full use of their reasoning
powers, it is not of much consequence that it should be accurately
traced.

It is to be observed, that he does not in this treatise modify or recant
anything of his earlier opinions, but refers to the favourable judgment
of his contemporary philosophers as a reason for embodying them in a
regular form. "Since many very celebrated professors of philosophy and
medicine are of opinion that I have created a new and most true
philosophy, this tender plant, like all novelties, ought to be carefully
nursed and cherished, so that it may strike root in the minds of
philosophers, and not be choked by the excessive humours of vain
sophistications, or washed away by the torrents of vulgar prejudices, or
frozen by the chill of public neglect; and if I succeed in guarding it
from these dangers, I have no fear that it will be crushed by the storms
of calumny, or parched by the sun of sterling criticism."

One thing is very remarkable in Kepler's creed, that he whose candour is
so indisputable in every other part of his conduct, professed to have
been forced to adopt his astrological opinions from direct and positive
observation.--"It is now more than twenty years since I began to
maintain opinions like these on the predominant nature of the elements,
which, adopting the common name, I call sublunary. I have been driven to
this not by studying or admiring Plato, but singly and solely by
observing seasons, and noting the aspects by which they are produced. I
have seen the state of the atmosphere almost uniformly disturbed as
often as the planets are in conjunction, or in the other configurations
so celebrated among astrologers. I have noticed its tranquil state,
either when there are none or few such aspects, or when they are
transitory and of short duration. I have not formed an opinion on this
matter without good grounds, like the common herd of prophesiers, who
describe the operations of the stars as if they were a sort of deities,
the lords of heaven and earth, and producing everything at their
pleasure. They never trouble themselves to consider what means the stars
have of working any effects among us on the earth, whilst they remain in
the sky, and send down nothing to us which is obvious to the senses
except rays of light. This is the principal source of the filthy
astrological superstitions of that vulgar and childish race of dreamers,
the prognosticators."

The real manner in which the configurations of the stars operate,
according to Kepler, is as follows:--"Like one who listens to a sweet
melodious song, and by the gladness of his countenance, by his voice,
and by the beating of his hand or foot attuned to the music, gives token
that he perceives and approves the harmony: just so does sublunary
nature, with the notable and evident emotion of the bowels of the earth,
bear like witness to the same feelings, especially at those times when
the rays of the planets form harmonious configurations on the
earth."--"I have been confirmed in this theory by that which might have
deterred others; I mean, by observing that the emotions do not agree
nicely with the instants of the configurations; but the earth sometimes
appears lazy and obstinate, and at another time (after important and
long-continued configurations) she becomes exasperated, and gives way to
her passion, even without the continuation of aspects. For in fact the
earth is not an animal like a dog, ready at every nod; but more like a
bull, or an elephant, slow to become angry, and so much the more furious
when incensed."

This singular doctrine must not be mistaken for one of Kepler's
favourite allegories; he actually and literally professed to believe
that the earth was an enormous living animal; and he has enumerated,
with a particularity of details into which we forbear to follow him, the
analogies he recognized between its habits and those of men and other
animals. A few samples of these may speak for the rest. "If any one who
has climbed the peaks of the highest mountains throw a stone down their
very deep clefts, a sound is heard from them; or if he throw it into one
of the mountain lakes, which beyond doubt are bottomless, a storm will
immediately arise, just as when you thrust a straw into the ear or nose
of a ticklish animal, it shakes its head, or runs shuddering away. What
so like breathing, especially of those fish who draw water into their
mouths and spout it out again through their gills, as that wonderful
tide! For although it is so regulated according to the course of the
moon, that, in the preface to my 'Commentaries on Mars,' I have
mentioned it as probable that the waters are attracted by the moon as
iron is by the loadstone; yet, if any one uphold that the earth
regulates its breathing according to the motion of the sun and moon, as
animals have daily and nightly alternations of sleep and waking, I shall
not think his philosophy unworthy of being listened to; especially if
any flexible parts should be discovered in the depths of the earth to
supply the functions of lungs or gills."

From the next extract, we must leave the reader to learn as well as he
may, how much Kepler did, and how much he did not believe on the
subject of genethliac astrology.--"Hence it is that human spirits, at
the time of celestial aspects, are particularly urged to complete the
matters which they have in hand. What the goad is to the ox, what the
spur or the rowel is to the horse, to the soldier the bell and trumpet,
an animated speech to an audience, to a crowd of rustics a performance
on the fife and bagpipes, that to all, and especially in the aggregate,
is a heavenly configuration of suitable planets; so that every single
one is excited in his thoughts and actions, and all become more ready to
unite and associate their efforts. For instance, in war you may see that
tumults, battles, fights, invasions, assaults, attacks, and panic fears,
generally happen at the time of the aspects of Mars and Mercury, Mars
and Jupiter, Mars and the Sun, Mars and Saturn, &c. In epidemic
diseases, a greater number of persons are attacked at the times of the
powerful aspects, they suffer more severely, or even die, owing to the
failure of nature in her strife with the disease, which strife (and not
the death) is occasioned by the aspect. It is not the sky which does all
these things immediately, but the faculty of the vital soul, associating
its operation with the celestial harmonies, is the principal agent in
this so-called influence of the heavens. Indeed this word influence has
so fascinated some philosophers that they prefer raving with the
senseless vulgar, to learning the truth with me. This essential property
is the principal foundation of that admirable genethliac art. For when
anything begins to have its being when that is working harmonies, the
sensible harmony of the rays of the planets has peculiar influence on
it. This then is the cause why those who are born under a season of many
aspects among the planets, generally turn out busy and industrious,
whether they accustom themselves from childhood to amass wealth, or are
born or chosen to direct public affairs, or finally, have given their
attention to study. If any one think that I might be taken as an
instance of this last class, I do not grudge him the knowledge of my
nativity. I am not checked by the reproach of boastfulness,
notwithstanding those who, by speech or conduct, condemn as folly all
kinds of writing on this subject; the idiots, the half-learned, the
inventors of titles and trappings, to throw dust in the eyes of the
people, and those whom Picus calls the plebeian theologians: among the
true lovers of wisdom, I easily clear myself of this imputation, by the
advantage of my reader; for there is no one whose nativity or whose
internal disposition and temper I can learn so well as I know my own.
Well then, Jupiter nearest the nonagesimal had passed by four degrees
the trine of Saturn; the Sun and Venus, in conjunction, were moving from
the latter towards the former, nearly in sextiles with both: they were
also removing from quadratures with Mars, to which Mercury was closely
approaching: the moon drew near the trine of the same planet, close to
the Bull's Eye, even in latitude. The 25th degree of Gemini was rising,
and the 22d of Aquarius culminating. That there was this triple
configuration on that day--namely, the sextile of Saturn and the Sun,
the sextile of Mars and Jupiter, the quadrature of Mercury and Mars, is
proved by the change of weather; for, after a frost of some days, that
very day became warmer, there was a thaw and a fall of rain.[192]

"I do not wish this single instance to be taken as a defence and proof
of all the aphorisms of astrologers, nor do I attribute to the heavens
the government of human affairs: what a vast interval still separates
these philosophical observations from that folly or madness as it should
rather be called. For, following up this example, I knew a lady[193],
born under nearly the same aspects, whose disposition, indeed, was
exceedingly restless, but who not only makes no progress in literature
(that is not strange in a woman), but troubles her whole family, and is
the cause to herself of deplorable misery. What, in my case, assisted
the aspects was--firstly, the fancy of my mother when pregnant with me,
a great admirer of her mother-in-law, my grandmother, who had some
knowledge of medicine, my grandfather's profession; a second cause is,
that I was born a male, and not a female, for astrologers have sought
in vain to distinguish sexes in the sky; thirdly, I derive from my
mother a habit of body, more fit for study than other kinds of life;
fourthly, my parents' fortune was not large, and there was no landed
property to which I might succeed and become attached; fifthly, there
were the schools, and the liberality of the magistracy towards such boys
as were apt for learning. But now if I am to speak of the result of my
studies, what I pray can I find in the sky, even remotely alluding to
it. The learned confess that several not despicable branches of
philosophy have been newly extricated or amended or brought to
perfection by me: but here my constellations were, not Mercury from the
east, in the angle of the seventh, and in quadratures with Mars, but
Copernicus, but Tycho Brahe, without whose books of observations
everything now set by me in the clearest light must have remained buried
in darkness; not Saturn predominating Mercury, but my Lords the Emperors
Rodolph and Matthias; not Capricorn, the house of Saturn, but Upper
Austria, the home of the Emperor, and the ready and unexampled bounty of
his nobles to my petition. Here is that corner, not the western one of
the horoscope, but on the Earth, whither, by permission of my imperial
master, I have betaken myself from a too uneasy court; and whence,
during these years of my life, which now tends towards its setting,
emanate these Harmonies, and the other matters on which I am engaged.

"However, it may be owing to Jupiter's ascendancy that I take greater
delight in the application of geometry to physics, than in that abstract
pursuit which partakes of the dryness of Saturn; and it is perhaps the
gibbous moon, in the bright constellation of the Bull's forehead, which
fills my mind with fantastic images."

The most remarkable thing contained in the 5th Book, is the announcement
of the celebrated law connecting the mean distances of the planets with
the periods of their revolution about the Sun. This law is expressed in
mathematical language, by saying that the squares of the times vary as
the cubes of the distances.[194] Kepler's rapture on detecting it was
unbounded, as may be seen from the exulting rhapsody with which he
announced it. "What I prophecied two-and-twenty years ago, as soon as I
discovered the five solids among the heavenly orbits--what I firmly
believed long before I had seen Ptolemy's 'Harmonics'--what I had
promised my friends in the title of this book, which I named before I
was sure of my discovery--what, sixteen years ago, I urged as a thing to
be sought--that for which I joined Tycho Brahe, for which I settled in
Prague, for which I have devoted the best part of my life to
astronomical contemplations, at length I have brought to light, and have
recognized its truth beyond my most sanguine expectations. Great as is
the absolute nature of Harmonics with all its details, as set forth in
my third book, it is all found among the celestial motions, not indeed
in the manner which I imagined, (that is not the least part of my
delight,) but in another very different, and yet most perfect and
excellent. It is now eighteen months since I got the first glimpse of
light, three months since the dawn, very few days since the unveiled
sun, most admirable to gaze on, burst out upon me. Nothing holds me; I
will indulge in my sacred fury; I will triumph over mankind by the
honest confession, that I have stolen the golden vases of the
Egyptians[195], to build up a tabernacle for my God far away from the
confines of Egypt. If you forgive me, I rejoice; if you are angry, I can
bear it: the die is cast, the book is written; to be read either now or
by posterity, I care not which: it may well wait a century for a reader,
as God has waited six thousand years for an observer."

He has told, with his usual particularity, the manner and precise moment
of the discovery. "Another part of my 'Cosmographical Mystery,'
suspended twenty-two years ago, because it was then undetermined, is
completed and introduced here, after I had discovered the true intervals
of the orbits, by means of Brahe's observations, and had spent the
continuous toil of a long time in investigating the true proportion of
the periodic times to the orbits,

    Sera quidem respexit inertem,
    Respexit tamen, et longo post tempore venit.

If you would know the precise moment, the first idea came across me on
the 8th March of this year, 1618; but chancing to make a mistake in the
calculation, I rejected it as false. I returned again to it with new
force on the 15th May, and it has dissipated the darkness of my mind by
such an agreement between this idea and my seventeen years' labour on
Brahe's observations, that at first I thought I must be dreaming, and
had taken my result for granted in my first assumptions. But the fact is
perfect, the fact is certain, that the proportion existing between the
periodic times of any two planets is exactly the sesquiplicate
proportion of the mean distances of the orbits."

There is high authority for not attempting over anxiously to understand
the rest of the work. Delambre sums it up as follows:--"In the music of
the celestial bodies it appears that Saturn and Jupiter take the bass,
Mars the tenor, the Earth and Venus the counter-tenor, and Mercury the
treble." If the patience of this indefatigable historian gave way, as he
confesses, in the perusal, any further notice of it here may be well
excused. Kepler became engaged, in consequence of this publication, in
an angry controversy with the eccentric Robert Fludd, who was at least
Kepler's match in wild extravagance and mysticism, if far inferior to
him in genius. It is diverting to hear each reproaching the other with
obscurity.

In the "Epitome of the Copernican Astronomy," which Kepler published
about the same time, we find the manner in which he endeavoured to
deduce the beautiful law of periodic times, from his principles of
motion and radiation of whirling forces. This work is in fact a summary
of all his astronomical opinions, drawn up in a popular style in the
form of question and answer. We find there a singular argument against
believing, as some did, that each planet is carried round by an angel,
for in that case, says Kepler, "the orbits would be perfectly circular;
but the elliptic form, which we find in them, rather smacks of the
nature of the lever and material necessity."

The investigation of the relation between the periodic times and
distances of the planets is introduced by a query whether or not they
are to be considered heavy. The answer is given in the following
terms:--"Although none of the celestial globes are heavy, in the sense
in which we say on earth that a stone is heavy, nor light as fire is
light with us, yet have they, by reason of their materiality, a natural
inability to move from place to place: they have a natural inertness or
quietude, in consequence of which they remain still in every situation
where they are placed alone.

"_P._ Is it then the sun, which by its turning carries round the
planets? How can the sun do this, having no hands to seize the planet at
so great a distance, and force it round along with itself?--Its bodily
virtue, sent forth in straight lines into the whole space of the world,
serves instead of hands; and this virtue, being a corporeal species,
turns with the body of the sun like a very rapid vortex, and travels
over the whole of that space which it fills as quickly as the sun
revolves in its very confined space round the centre.

"_P._ Explain what this virtue is, and belonging to what class of
things?--As there are two bodies, the mover and the moved, so are there
two powers by which the motion is obtained. The one is passive, and
rather belonging to matter, namely, the resemblance of the body of the
planet to the body of the sun in its corporeal form, and so that part of
the planetary body is friendly, the opposite part hostile to the sun.
The other power is active, and bearing more relation to form, namely,
the body of the sun has a power of attracting the planet by its friendly
part, of repelling it by the hostile part, and finally, of retaining it
if it be placed so that neither the one nor the other be turned directly
towards the sun.

"_P._ How can it be that the whole body of the planet should be like or
cognate to the body of the sun, and yet part of the planet friendly,
part hostile to the sun?--Just as when one magnet attracts another, the
bodies are cognate; but attraction takes place only on one side,
repulsion on the other.

"_P._ Whence, then, arises that difference of opposite parts in the same
body?--In magnets the diversity arises from the situation of the parts
with respect to the whole. In the heavens the matter is a little
differently arranged, for the sun does not, like the magnet, possess
only on one side, but in all the parts of its substance, this active and
energetic faculty of attracting, repelling, or retaining the planet. So
that it is probable that the centre of the solar body corresponds to one
extremity or pole of the magnet, and its whole surface to the other
pole.

"_P._ If this were so, all the planets would be restored[196] in the
same time with the sun?--True, if this were all: but it has been said
already that, besides this carrying power of the sun, there is also in
the planets a natural inertness to motion, which causes that, by reason
of their material substance, they are inclined to remain each in its
place. The carrying power of the sun, and the impotence or material
inertness of the planet, are thus in opposition. Each shares the
victory; the sun moves the planet from its place, although in some
degree it escapes from the chains with which it was held by the sun, and
so is taken hold of successively by every part of this circular virtue,
or, as it may be called, solar circumference, namely, by the parts which
follow those from which it has just extricated itself.

"_P._ But how does one planet extricate itself more than another from
this violence--First, because the virtue emanating from the sun has the
same degree of weakness at different distances, as the distances or the
width of the circles described on these distances.[197] This is the
principal reason. Secondly, the cause is partly in the greater or less
inertness or resistance of the planetary globes, which reduces the
proportions to one-half; but of this more hereafter.

"_P._ How can it be that the virtue emanating from the sun becomes
weaker at a greater distance? What is there to hurt or weaken
it?--Because that virtue is corporeal, and partaking of quantity, which
can be spread out and rarefied. Then, since there is as much virtue
diffused in the vast orb of Saturn as is collected in the very narrow
one of Mercury, it is very rare and therefore weak in Saturn's orbit,
very dense and therefore powerful at Mercury.

"_P._ You said, in the beginning of this inquiry into motion, that the
periodic times of the planets are exactly in the sesquiplicate
proportion of their orbits or circles: pray what is the cause of
this?--Four causes concur for lengthening the periodic time. First, the
length of the path; secondly, the weight or quantity of matter to be
carried; thirdly, the degree of strength of the moving virtue; fourthly,
the bulk or space into which is spread out the matter to be moved. The
circular paths of the planets are in the simple ratio of the distances;
the weights or quantities of matter in different planets are in the
subduplicate ratio of the same distances, as has been already proved; so
that with every increase of distance, a planet has more matter, and
therefore is moved more slowly, and accumulates more time in its
revolution, requiring already as it did more time by reason of the
length of the way. The third and fourth causes compensate each other in
a comparison of different planets: the simple and subduplicate
proportion compound the sesquiplicate proportion, which therefore is the
ratio of the periodic times."

Three of the four suppositions here made by Kepler to explain the
beautiful law he had detected, are now indisputably known to be false.
Neither the weights nor the sizes of the different planets observe the
proportions assigned by him, nor is the force by which they are retained
in their orbits in any respect similar in its effects to those
attributed by him to it. The wonder which might naturally be felt that
he should nevertheless reach the desired conclusion, will be
considerably abated on examining the mode in which he arrived at and
satisfied himself of the truth of these three suppositions. It has been
already mentioned that his notions on the existence of a whirling force
emanating from the sun, and decreasing in energy at increased distances,
are altogether inconsistent with all the experiments and observations we
are able to collect. His reason for asserting that the sizes of the
different planets are proportional to their distances from the sun, was
simply because he chose to take for granted that either their
solidities, surfaces, or diameters, must necessarily be in that
proportion, and of the three, the solidities appeared to him least
liable to objection. The last element of his precarious reasoning rested
upon equally groundless assumptions. Taking as a principle, that where
there is a number of different things they must be different in every
respect, he declared that it was quite unreasonable to suppose all the
planets of the same density. He thought it indisputable that they must
be rarer as they were farther from the sun, "and yet not in the
proportion of their distances, for thus we should sin against the law of
variety in another way, and make the quantity of matter (according to
what he had just said of their bulk) the same in all. But if we assume
the ratio of the quantities of matter to be half that of the distances,
we shall observe the best mean of all; for thus Saturn will be half as
heavy again as Jupiter, and Jupiter half again as dense as Saturn. And
the strongest argument of all is, that unless we assume this proportion
of the densities, the law of the periodic times will not answer." This
is the _proof_ alluded to, and it is clear that by such reasoning any
required result might be deduced from any given principles.

It may not be uninstructive to subjoin a sketch of the manner in which
Newton established the same celebrated results, starting from principles
of motion diametrically opposed to Kepler's, and it need scarcely be
added, reasoning upon them in a manner not less different. For this
purpose, a very few prefatory remarks will be found sufficient.

The different motions seen in nature are best analysed and classified by
supposing that every body in motion, if left to itself, will continue to
move forward at the same rate in a straight line, and by considering all
the observed deviations from this manner of moving, as exceptions and
disturbances occasioned by some external cause. To this supposed cause
is generally given the name of Force, and it is said to be the first law
of motion, that, unless acted on by some force, every body at rest
remains at rest, and every body in motion proceeds uniformly in a
straight line. Many employ this language, without perceiving that it
involves a definition of force, on the admission of which, it is reduced
to a truism. We see common instances of force in a blow, or a pull from
the end of a string fastened to the body: we shall also have occasion
presently to mention some forces where no visible connexion exists
between the moving body and that towards which the motion takes place,
and from which the force is said to proceed.

[Illustration:

  _c_           C
  +-------------+
   \           / \
    \         /   \
     \       /     \
      \     /       \
       \   /         \
        \ /           \
         +-------------+
         B             C' ]

A second law of motion, founded upon experiment, is this: if a body have
motion communicated to it in two directions, by one of which motions
alone it would have passed through a given space in a given time, as for
instance, through BC´ in one second, and by the other alone through any
other space B_c_ in the same time, it will, when both are given to it at
the same instant, pass in the same time (in the present instance in one
second) through BC the diagonal of the parallelogram of which BC´ and
B_c_ are sides.

[Illustration:

                  / S \
                 / /|\ \
                / / | \ \
               / /  |  \ \
              / /   |   \ \
             / /    |    \ \
            / /     |     \ \
   --------+-+------+------+-+
           A B      C      D E ]

Let a body, acted upon by no force, be moving along the line AE; that
means, according to what has been said, let it pass over the equal
straight lines AB, BC, CD, DE, &c., in equal times. If we take any point
S not in the line AE, and join AS, BS, &c., the triangles ASB, BSC, &c.
are also equal, having a common altitude and standing on equal bases, so
that if a string were conceived reaching from S to the moving body
(being lengthened or shortened in each position to suit its distance
from S), this string, as the body moved along AE, would sweep over equal
triangular areas in equal times.

[Illustration]

Let us now examine how far these conclusions will be altered if the body
from time to time is forced towards S. We will suppose it moving
uniformly from A to B as before, no matter for the present how it got to
A, or into the direction AB. If left to itself it would, in an equal
time (say 1´´) go through BC´ in the same straight line with and equal
to AB. But just as it reaches B, and is beginning to move along BC´, let
it be suddenly pulled towards S with a motion which, had it been at
rest, would have carried it in the same time, 1´´ through any other
space B_c_. According to the second law of motion, its direction during
this 1´´, in consequence of the two motions combined, will be along BC,
the diagonal of the parallelogram of which BC´, B_c_, are sides. In
this case, as this figure is drawn, BC, though passed in the same time,
is longer than AB; that is to say, the body is moving quicker than at
first. How is it with the triangular areas, supposed as before to be
swept by a string constantly stretched between S and the body? It will
soon be seen that these still remain equal, notwithstanding the change
of direction, and increased swiftness. For since CC´ is parallel to
B_c_, the triangles SCB, SC´B are equal, being on the same base SB, and
between the same parallels SB, CC´, and SC´B is equal to SBA as before,
therefore SCB, SBA are equal. The body is now moving uniformly (though
quicker than along AB) along BC. As before, it would in a time equal to
the time of passing along BC, go through an equal space CD´ in the same
straight line. But if at C it has a second pull towards S, strong enough
to carry it to _d_ in the same time, its direction will change a second
time to CD, the diagonal of the parallelogram, whose sides are CD´,
C_d_; and the circumstances being exactly similar to those at the first
pull, it is shewn in the same manner that the triangular area SDC = SCB
= SBA.

Thus it appears, that in consequence of these intermitting pulls towards
S, the body may be moving round, sometimes faster, sometimes slower, but
that the triangles formed by any of the straight portions of its path
(which are all described in equal times), and the lines joining S to the
ends of that portion, are all equal. The path it will take depends of
course, in other respects, upon the frequency and strength of the
different pulls, and it might happen, if they were duly proportionate,
that when at H, and moving off in the direction HA´, the pull H_a_
might be such as just to carry the body back to A, the point from which
it started, and with such a motion, that after one pull more, A_b_, at
A, it might move along AB as it did at first. If this were so, the body
would continue to move round in the same polygonal path, alternately
approaching and receding from S, as long as the same pulls were repeated
in the same order, and at the same intervals.

It seems almost unnecessary to remark, that the same equality which
subsists between any two of these triangular areas subsists also between
an equal number of them, from whatever part of the path taken; so that,
for instance, the four paths AB, BC, CD, DE, corresponding to the four
areas ASB, BSC, CSD, DSE, that is, to the area ABCDES, are passed in the
same time as the four EF, FG, GH, HA, corresponding to the equal area
EFGHAS. Hence it may be seen, if the whole time of revolution from A
round to A again be called a year, that in half a year the body will
have got to E, which in the present figure is more than half way round,
and so of any other periods.

The more frequently the pulls are supposed to recur, the more frequently
will the body change its direction; and if the pull were supposed
constantly exerted in the direction towards S, the body would move in a
curve round S, for no three successive positions of it could be in a
straight line. Those who are not familiar with the methods of measuring
curvilinear spaces must here be contented to observe, that the law
holds, however close the pulls are brought together, and however closely
the polygon is consequently made to resemble a curve: they may, if they
please, consider the minute portions into which the curve is so divided,
as differing insensibly from little rectilinear triangles, any equal
number of which, according to what has been said above, wherever taken
in the curve, would be swept in equal times. The theorem admits, in this
case also, a rigorous proof; but it is not easy to make it entirely
satisfactory, without entering into explanations which would detain us
too long from our principal subject.

The proportion in which the pull is strong or weak at different
distances from the central spot, is called "_the law of the central or
centripetal force_," and it may be observed, that after assuming the
laws of motion, our investigations cease to have anything hypothetical
or experimental in them; and that if we wish, according to these
principles of motion, to determine the law of force necessary to make a
body move in a curve of any required form, or conversely to discover the
form of the curve described, in consequence of any assumed law of force,
the inquiry is purely geometrical, depending upon the nature and
properties of geometrical quantities only. This distinction between what
is hypothetical, and what necessary truth, ought never to be lost sight
of.

As the object of the present treatise is not to teach geometry, we shall
describe, in very general terms, the manner in which Newton, who was
the first who systematically extended the laws of motion to the heavenly
bodies, identified their results with the two remaining laws of Kepler.
His "Principles of Natural Philosophy" contain general propositions with
regard to any law of centripetal force, but that which he supposed to be
the true one in our system, is expressed in mathematical language, by
saying that the centripetal force varies inversely as the square of the
distance, which means, that if the force at any distance be taken for
the unit of force, at half that distance, it is two times twice, or four
times as strong; at one-third the distance, three times thrice, or nine
times as strong, and so for other distances. He shewed the probability
of this law in the first instance by comparing the motion of the moon
with that of heavy bodies at the surface of the earth. Taking LP to
represent part of the moon's orbit described in one minute, the line PM
between the orbit and the tangent at L would shew the space through
which the central force at the earth (assuming the above principles of
motion to be correct) would draw the moon. From the known distance and
motion of the moon, this line PM is found to be about sixteen feet. The
distance of the moon is about sixty times the radius of the earth, and
therefore if the law of the central force in this instance were such as
has been supposed, the force at the earth's surface would be 60 times
60, or 3600 times stronger, and at the earth's surface, the central
force would make a body fall through 3600 times 16 feet in one minute.
Galileo had already taught that the spaces through which a body would be
made to fall, by the constant action of the same unvarying force, would
be proportional to the squares of the times during which the force was
exerted, and therefore according to these laws, a body at the earth's
surface ought (since there are sixty seconds in a minute) to fall
through 16 feet in one second, which was precisely the space previously
established by numerous experiments.

[Illustration]

With this confirmation of the supposition, Newton proceeded to the
purely geometrical calculation of the law of centripetal[198] force
necessary to make a moving body describe an ellipse round its focus,
which Kepler's observations had established to be the form of the orbits
of the planets round the sun. The result of the inquiry shewed that this
curve required the same law of the force, varying inversely as the
square of the distance, which therefore of course received additional
confirmation. His method of doing this may, perhaps, be understood by
referring to the last figure but one, in which C_d_, for instance,
representing the space fallen from any point C towards S, in a given
time, and the area CSD being proportional to the corresponding time, the
space through which the body would have fallen at C in any other time
(which would be greater, by Galileo's law, in proportion to the squares
of the times), might be represented by a quantity varying directly as
C_d_, and inversely in the duplicate proportion of the triangular area
CSD, that is to say, proportional to C_d_/(SC × D_k_)², if D_k_ be drawn
from D perpendicular on SC. If this polygon represent an ellipse, so
that CD represents a small arc of the curve, of which S is the focus, it
is found by the nature of that curve, that C_d_/(D_k_)² is the same at
all points of the curve, so that the law of variation of the force in
the same ellipse is represented solely by 1/(SC)². If C_d_, &c. are
drawn so that C_d_/(D_k_)² is not the same at every point, the curve
ceases to be an ellipse whose focus is at S, as Newton has shewn in the
same work. The line to which (Dk)²/Cd is found to be equal, is one drawn
through the focus at right angles to the longest axis of the ellipse
till it meets the curve;--this line is called the _latus rectum_, and is
a third proportional to the two principal axes.

Kepler's third law follows as an immediate consequence of this
determination; for, according to what has been already shown, the time
of revolution round the whole ellipse, or, as it is commonly called,
the periodic time, bears the same ratio to the unit of time as the whole
area of the ellipse does to the area described in that unit. The area of
the whole ellipse is proportional in different ellipses to the rectangle
contained by the two principal axes, and the area described in an unit
of time is proportional to SC × D_k_, that is to say, is in the
subduplicate ratio of SC² × D_k_², or D_k_²/C_d_, when the force varies
inversely as the square of the distance SC; and in the ellipse, as we
have said already, this is equal to a third proportional to the
principal axes; consequently the periodic times in different ellipses,
which are proportional to the whole areas of the ellipses directly, and
the areas described in the unit of time inversely, are in the compound
ratio of the rectangle of the axes directly, and subduplicately as a
third proportional to the axes inversely; that is to say, the squares of
these times are proportional to the cubes of the longest axes, which is
Kepler's law.


FOOTNOTES:

[192] This mode of verifying configurations, though something of the
boldest, was by no means unusual. On a former occasion Kepler, wishing
to cast the nativity of his friend Zehentmaier, and being unable to
procure more accurate information than that he was born about three
o'clock in the afternoon of the 21st of October, 1751, supplied the
deficiency by a record of fevers and accidents at known periods of his
life, from which he deduced a more exact horoscope.

[193] Kepler probably meant his own mother, whose horoscope he in many
places declared to be nearly the same as his own.

[194] See Preliminary Treatise, p. 13.

[195] In allusion to the Harmonics of Ptolemy.

[196] This is a word borrowed from the Ptolemaic astronomy, according to
which the sun and planets are hurried from their places by the daily
motion of the _primum mobile_, and by their own peculiar motion seek to
regain or be restored to their former places.

[197] In other parts of his works, Kepler assumes the diminution to be
proportional to the circles themselves, not to the diameters.

[198] In many curves, as in the circle and ellipse, there is a point to
which the name of centre is given, on account of peculiar properties
belonging to it: but the term "centripetal force" always refers to the
place towards which the force is directed, whether or not situated in
the centre of the curve.




CHAPTER VIII.

    _The Epitome prohibited at Rome--Logarithmic Tables--Trial of
      Catharine Kepler--Kepler invited to England--Rudolphine
      Tables--Death--Conclusion._


KEPLER'S "Epitome," almost immediately on its appearance, enjoyed the
honour of being placed by the side of the work of Copernicus, on the
list of books prohibited by the congregation of the Index at Rome. He
was considerably alarmed on receiving this intelligence, anticipating
that it might occasion difficulties in publishing his future writings.
His words to Remus, who had communicated the news to him, are as
follows:--"I learn from your letter, for the first time, that my book is
prohibited at Rome and Florence. I particularly beg of you, to send me
the exact words of the censure, and that you will inform me whether that
censure would be a snare for the author, if he were caught in Italy, or
whether, if taken, he would be enjoined a recantation. It is also of
consequence for me to know whether there is any chance of the same
censure being extended into Austria. For if this be so, not only shall I
never again find a printer there, but also the copies which the
bookseller has left in Austria at my desire will be endangered, and the
ultimate loss will fall upon me. It will amount to giving me to
understand, that I must cease to profess Astronomy, after I have grown
old in the belief of these opinions, having been hitherto gainsayed by
no one,--and, in short, I must give up Austria itself, if room is no
longer to be left in it for philosophical liberty." He was, however,
tranquillized, in a great degree, by the reply of his friend, who told
him that "the book is only prohibited as contrary to the decree
pronounced by the holy office two years ago. This has been partly
occasioned by a Neapolitan monk (Foscarini), who was spreading these
notions by publishing them in Italian, whence were arising dangerous
consequences and opinions: and besides, Galileo was at the same time
pleading his cause at Rome with too much violence. Copernicus has been
corrected in the same manner for some lines, at least in the beginning
of his first book. But by obtaining a permission, they may be read (and,
as I suppose, this "Epitome" also) by the learned and skilful in this
science, both at Rome and throughout all Italy. There is therefore no
ground for your alarm, either in Italy or Austria; only keep yourself
within bounds, and put a guard upon your own passions."

We shall not dwell upon Kepler's different works on comets, beyond
mentioning that they were divided, on the plan of many of his other
publications, into three parts, Astronomical, Physical, and
Astrological. He maintained that comets move in straight lines, with a
varying degree of velocity. Later theories have shewn that they obey the
same laws of motion as the planets, differing from them only in the
extreme excentricity of their orbits. In the second book, which contains
the Physiology of Comets, there is a passing remark that comets come out
from the remotest parts of ether, as whales and monsters from the depth
of the sea; and the suggestion is thrown out that perhaps comets are
something of the nature of silkworms, and are wasted and consumed in
spinning their own tails.

Among his other laborious employments, Kepler yet found time to
calculate tables of logarithms, he having been one of the first in
Germany to appreciate the full importance of the facilities they afford
to the numerical calculator. In 1618 he wrote to his friend Schickhard:
"There is a Scottish Baron (whose name has escaped my memory), who has
made a famous contrivance, by which all need of multiplication and
division is supplied by mere addition and subtraction; and he does it
without sines. But even he wants a table of tangents[199], and the
variety, frequency, and difficulty of the additions and subtractions, in
some cases, is greater than the labour of multiplying and dividing."

Kepler dedicated his "Ephemeris" for 1620 to the author of this
celebrated invention, Baron Napier, of Merchistoun; and in 1624,
published what he called "Chilias Logarithmorum," containing the
Napierian logarithms of the quotients of 100,000 divided by the first
ten numbers, then proceeding by the quotients of every ten to 100, and
by hundreds to 100,000. In the supplement published the following year,
is a curious notice of the manner in which this subtle contrivance was
at first received: "In the year 1621, when I had gone into Upper
Austria, and had conferred everywhere with those skilled in mathematics,
on the subject of Napier's logarithms, I found that those whose prudence
had increased, and whose readiness had diminished, through age, were
hesitating whether to adopt this new sort of numbers, instead of a table
of sines; because they said it was disgraceful to a professor of
mathematics to exult like a child at some compendious method of working,
and meanwhile to admit a form of calculation, resting on no legitimate
proof, and which at some time might entangle us in error, when we least
feared it. They complained that Napier's demonstration rested on a
fiction of geometrical motion, too loose and slippery for a sound method
of reasonable demonstration to be founded on it.[200] "This led me
forthwith to conceive the germ of a legitimate demonstration, which
during that same winter I attempted, without reference to lines or
motion, or flow, or any other which I may call sensible quality.

"Now to answer the question; what is the use of logarithms? Exactly what
ten years ago was announced by their author, Napier, and which may be
told in these words.--Wheresoever in common arithmetic, and in the Rule
of Three, come two numbers to be multiplied together, there the sum of
the logarithms is to be taken; where one number is to be divided by
another, the difference; and the number corresponding to this sum or
difference, as the case may be, will be the required product or
quotient. This, I say, is the use of logarithms. But in the same work in
which I gave the demonstration of the principles, I could not satisfy
the unfledged arithmetical chickens, greedy of facilities, and gaping
with their beaks wide open, at the mention of this use, as if to bolt
down every particular gobbet, till they are crammed with my
precepticles."

The year 1622 was marked by the catastrophe of a singular adventure
which befell Kepler's mother, Catharine, then nearly seventy years old,
and by which he had been greatly harassed and annoyed during several
years. From her youth she had been noted for a rude and passionate
temper, which on the present occasion involved her in serious
difficulties. One of her female acquaintance, whose manner of life had
been by no means unblemished, was attacked after a miscarriage by
violent headaches, and Catharine, who had often taken occasion to sneer
at her notorious reputation, was accused with having produced these
consequences, by the administration of poisonous potions. She repelled
the charge with violence, and instituted an action of scandal against
this person, but was unlucky (according to Kepler's statement) in the
choice of a young doctor, whom she employed as her advocate. Considering
the suit to be very instructive, he delayed its termination during five
years, until the judge before whom it was tried was displaced. He was
succeeded by another, already indisposed against Catharine Kepler, who
on some occasion had taunted him with his sudden accession to wealth
from a very inferior situation. Her opponent, aware of this advantage,
turned the tables on her, and in her turn became the accuser. The end
of the matter was, that in July, 1620, Catharine was imprisoned, and
condemned to the torture. Kepler was then at Linz, but as soon as he
learned his mother's danger, hurried to the scene of trial. He found the
charges against her supported only by evidence which never could have
been listened to, if her own intemperate conduct had not given advantage
to her adversaries. He arrived in time to save her from the question,
but she was not finally acquitted and released from prison till November
in the following year. Kepler then returned to Linz, leaving behind him
his mother, whose spirit seemed in no degree broken by the unexpected
turn in the course of her litigation. She immediately commenced a new
action for costs and damages against the same antagonist, but this was
stopped by her death, in April 1622, in her seventy-fifth year.

In 1620 Kepler was visited by Sir Henry Wotton, the English ambassador
at Venice, who finding him, as indeed he might have been found at every
period of his life, oppressed by pecuniary difficulties, urged him to go
over to England, where he assured him of a welcome and honourable
reception; but Kepler could not resolve upon the proposed journey,
although in his letters he often returned to the consideration of it. In
one of them, dated a year later, he says, "The fires of civil war are
raging in Germany--they who are opposed to the honour of the empire are
getting the upper hand--everything in my neighbourhood seems abandoned
to flame and destruction. Shall I then cross the sea, whither Wotton
invites me? I, a German? a lover of firm land? who dread the confinement
of an island? who presage its dangers, and must drag along with me my
little wife and flock of children? Besides my son Louis, now thirteen
years old, I have a marriageable daughter, a two-year old son by my
second marriage, an infant daughter, and its mother but just recovering
from her confinement." Six years later, he says again,--"As soon as the
Rudolphine Tables are published, my desire will be to find a place where
I can lecture on them to a considerable assembly; if possible, in
Germany; if not, why then in Italy, France, the Netherlands, or England,
provided the salary is adequate for a traveller."

In the same year in which he received this invitation an affront was put
upon Kepler by his early patrons, the States of Styria, who ordered all
the copies of his "Calendar," for 1624, to be publicly burnt. Kepler
declares that the reason of this was, that he had given precedence in
the title-page to the States of Upper Ens, in whose service he then was,
above Styria. As this happened during his absence in Wirtemberg, it was
immediately coupled by rumour with his hasty departure from Linz: it was
said that he had incurred the Emperor's displeasure, and that a large
sum was set upon his head. At this period Matthias had been succeeded by
Ferdinand III., who still continued to Kepler his barren title of
imperial mathematician.

In 1624 Kepler went to Vienna, in the hopes of getting money to complete
the Rudolphine Tables, but was obliged to be satisfied with the sum of
6000 florins and with recommendatory letters to the States of Suabia,
from whom he also collected some money due to the emperor. On his return
he revisited the University of Tubingen, where he found his old
preceptor, Mästlin, still alive, but almost worn out with old age.
Mästlin had well deserved the regard Kepler always appears to have
entertained for him; he had treated him with great liberality whilst at
the University, where he refused to receive any remuneration for his
instruction. Kepler took every opportunity of shewing his gratitude;
even whilst he was struggling with poverty he contrived to send his old
master a handsome silver cup, in acknowledging the receipt of which
Mästlin says,--"Your mother had taken it into her head that you owed me
two hundred florins, and had brought fifteen florins and a chandelier
towards reducing the debt, which I advised her to send to you. I asked
her to stay to dinner, which she refused: however, we handselled your
cup, as you know she is of a thirsty temperament."

The publication of the Rudolphine Tables, which Kepler always had so
much at heart, was again delayed, notwithstanding the recent grant, by
the disturbances arising out of the two parties into which the
Reformation had divided the whole of Germany. Kepler's library was
sealed up by desire of the Jesuits, and nothing but his connexion with
the Imperial Court secured to him his own personal indemnity. Then
followed a popular insurrection, and the peasantry blockaded Linz, so
that it was not until 1627 that these celebrated tables finally made
their appearance, the earliest calculated on the supposition that the
planets move in elliptic orbits. Ptolemy's tables had been succeeded by
the "Alphonsine," so called from Alphonso, King of Castile, who, in the
thirteenth century, was an enlightened patron of astronomy. After the
discoveries of Copernicus, these again made way for the Prussian, or
Prutenic tables, calculated by his pupils Reinhold and Rheticus. These
remained in use till the observations of Tycho Brahe showed their
insufficiency, and Kepler's new theories enabled him to improve upon
them. The necessary types for these tables were cast at Kepler's own
expense. They are divided into four parts, the first and third
containing a variety of logarithmic and other tables, for the purpose of
facilitating astronomical calculations. In the second are tables of the
elements of the sun, moon, and planets. The fourth gives the places of
1000 stars as determined by Tycho, and also at the end his table of
refractions, which appears to have been different for the sun, moon, and
stars. Tycho Brahe assumed the horizontal refraction of the sun to be 7´
30´´, of the moon 8´, and of the other stars 3´. He considered all
refraction of the atmosphere to be insensible above 45° of altitude, and
even at half that altitude in the case of the fixed stars. A more
detailed account of these tables is here obviously unsuitable: it will
be sufficient to say merely, that if Kepler had done nothing in the
course of his whole life but construct these, he would have well earned
the title of a most useful and indefatigable calculator.

Some copies of these tables have prefixed to them a very remarkable map,
divided by hour lines, the object of which is thus explained:--

"The use of this nautical map is, that if at a given hour the place of
the moon is known by its edge being observed to touch any known star, or
the edges of the sun, or the shadow of the earth; and if that place
shall (if necessary) be reduced from apparent to real by clearing it of
parallax; and if the hour at Uraniburg be computed by the Rudolphine
tables, when the moon occupied that true place, the difference will show
the observer's meridian, whether the picture of the shores be accurate
or not, for by this means it may come to be corrected."

This is probably one of the earliest announcements of the method of
determining longitudes by occultations; the imperfect theory of the moon
long remained a principal obstacle to its introduction in practice.
Another interesting passage connected with the same object may be
introduced here. In a letter to his friend Cruger, dated in 1616, Kepler
says: "You propose a method of observing the distances of places by
sundials and automata. It is good, but needs a very accurate practice,
and confidence in those who have the care of the clocks. Let there be
only one clock, and let it be transported; and in both places let
meridian lines be drawn with which the clock may be compared when
brought. The only doubt remaining is, whether a greater error is likely
from the unequal tension in the automaton, and from its motion, which
varies with the state of the air, or from actually measuring the
distances. For if we trust the latter, we can easily determine the
longitudes by observing the differences of the height of the pole."

In an Appendix to the Rudolphine Tables, or, as Kepler calls it, "an
alms doled out to the nativity casters," he has shown how they may use
his tables for their astrological predictions. Everything in his hands
became an allegory; and on this occasion he says,--"Astronomy is the
daughter of Astrology, and this modern Astrology, again, is the daughter
of Astronomy, bearing something of the lineaments of her grandmother;
and, as I have already said, this foolish daughter, Astrology, supports
her wise but needy mother, Astronomy, from the profits of a profession
not generally considered creditable."

Soon after the publication of these tables, the Grand Duke of Tuscany
sent him a golden chain; and if we remember the high credit in which
Galileo stood at this time in Florence, it does not seem too much to
attribute this honourable mark of approbation to his representation of
the value of Kepler's services to astronomy. This was soon followed by a
new and final change in his fortunes. He received permission from the
emperor to attach himself to the celebrated Duke of Friedland, Albert
Wallenstein, one of the most remarkable men in the history of that
time. Wallenstein was a firm believer in astrology, and the reception
Kepler experienced by him was probably due, in great measure, to his
reputation in that art. However that may be, Kepler found in him a more
munificent patron than any one of his three emperors; but he was not
destined long to enjoy the appearance of better fortune. Almost the last
work which he published was a commentary on the letter addressed, by the
missionary Terrentio, from China, to the Jesuits at Ingolstadt. The
object of this communication was to obtain from Europe means for
carrying into effect a projected scheme for improving the Chinese
calendar. In this essay Kepler maintains the opinion, which has been
discussed with so much warmth in more modern times, that the pretended
ancient observations of the Chinese were obtained by computing them
backwards from a much more recent date. Wallenstein furnished him with
an assistant for his calculations, and with a printing press; and
through his influence nominated him to the professorship in the
University of Rostoch, in the Duchy of Mecklenburg. His claims on the
imperial treasury, which amounted at this time to 8000 crowns, and which
Ferdinand would gladly have transferred to the charge of Wallenstein,
still remained unsatisfied. Kepler made a last attempt to obtain them at
Ratisbon, where the imperial meeting was held, but without success. The
fatigue and vexation occasioned by his fruitless journey brought on a
fever, which unexpectedly put an end to his life, in the early part of
November, 1630, in his fifty-ninth year. His old master, Mästlin,
survived him for about a year, dying at the age of eighty-one.

Kepler left behind him two children by his first wife, Susanna and
Louis; and three sons and two daughters, Sebald, Cordelia, Friedman,
Hildebert, and Anna Maria, by his widow. Susanna married, a few months
before her father's death, a physician named Jacob Bartsch, the same who
latterly assisted Kepler in preparing his "Ephemeris." He died very
shortly after Kepler himself. Louis studied medicine, and died in 1663,
whilst practising as a physician at Konigsberg. The other children died
young.

Upon Kepler's death the Duke of Friedland caused an inventory to be
taken of his effects, when it appeared that near 24,000 florins were due
to him, chiefly on account of his salary from the emperor. His daughter
Susanna, Bartsch's widow, managed to obtain a part of these arrears by
refusing to give up Tycho Brahe's observations till her claims were
satisfied. The widow and younger children were left in very straightened
circumstances, which induced Louis, Kepler's eldest son, to print, for
their relief, one of his father's works, which had been left by him
unpublished. It was not without much reluctance, in consequence of a
superstitious feeling which he did not attempt to conceal or deny.
Kepler himself, and his son-in-law, Bartsch, had been employed in
preparing it for publication at the time of their respective deaths; and
Louis confessed that he did not approach the task without apprehension
that he was incurring some risk of a similar fate. This little rhapsody
is entitled a "Dream on Lunar Astronomy;" and was intended to illustrate
the appearances which would present themselves to an astronomer living
upon the moon.

The narrative in the dream is put into the mouth of a personage, named
Duracoto, the son of an Icelandic enchantress, of the name of
Fiolxhildis. Kepler tells us that he chose the last name from an old map
of Europe in his house, in which Iceland was called Fiolx: Duracoto
seemed to him analogous to the names he found in the history of
Scotland, the neighbouring country. Fiolxhildis was in the habit of
selling winds to mariners, and used to collect herbs to use in her
incantations on the sides of Mount Hecla, on the Eve of St. John.
Duracoto cut open one of his mother's bags, in punishment of which she
sold him to some traders, who brought him to Denmark, where he became
acquainted with Tycho Brahe. On his return to Iceland, Fiolxhildis
received him kindly, and was delighted with the progress he had made in
astronomy. She then informed him of the existence of certain spirits, or
demons, from whom, although no traveller herself, she acquired a
knowledge of other countries, and especially of a very remarkable
country, called Livania. Duracoto requesting further information, the
necessary ceremonies were performed for invoking the demon; Duracoto and
his mother enveloped their heads in their clothing, and presently "the
screaking of a harsh dissonant voice began to speak in the Icelandic
tongue." The island of Livania is situated in the depths of ether, at
the distance of about 250000 miles; the road thence or thither is very
seldom open, and even when it is passable, mankind find the journey a
most difficult and dangerous one. The demon describes the method
employed by his fellow spirits to convey such travellers as are thought
fit for the undertaking: "We bring no sedentary people into our company,
no corpulent or delicate persons; but we pick out those who waste their
life in the continual use of post-horses, or who sail frequently to the
Indies; who are accustomed to live upon biscuit, garlic, dried fish, and
such abominable feeding. Those withered old hags are exactly fit for us,
of whom the story is familiar that they travel immense distances by
night on goats, and forks, and old petticoats. The Germans do not suit
us at all; but we do not reject the dry Spaniards." This extract will
probably be sufficient to show the style of the work. The inhabitants of
Livania are represented to be divided into two classes, the Privolvans
and Subvolvans, by whom are meant those supposed to live in the
hemisphere facing the earth, which is called the Volva, and those on the
opposite half of the moon: but there is nothing very striking in the
account given of the various phenomena as respects these two classes. In
some notes which were added some time after the book was first written,
are some odd insights into Kepler's method of composing. Fiolxhildis had
been made to invoke the dæmon with twenty-one characters; Kepler
declares, in a note, that he cannot remember why he fixed on this
number, "except because that is the number of letters in _Astronomia
Copernicana_, or because there are twenty-one combinations of the
planets, two together, or because there are twenty-one different throws
upon two dice." The dream is abruptly terminated by a storm, in which,
says Kepler, "I suddenly waked; the Demon, Duracoto, and Fiolxhildis
were gone, and instead of their covered heads, I found myself rolled up
among the blankets."

Besides this trifle, Kepler left behind him a vast mass of unpublished
writings, which came at last into the hands of his biographer, Hantsch.
In 1714, Hantsch issued a prospectus for publishing them by
subscription, in twenty-two folio volumes. The plan met no
encouragement, and nothing was published but a single folio volume of
letters to and from Kepler, which seem to have furnished the principal
materials for the memoir prefixed to them. After various unavailing
attempts to interest different learned bodies in their appearance, the
manuscripts were purchased for the library at St. Petersburg, where
Euler, Lexell, and Kraft, undertook to examine them, and select the most
interesting parts for publication. The result of this examination does
not appear.

Kepler's body was buried in St. Peter's churchyard at Ratisbon, and a
simple inscription was placed on his tombstone. This appears to have
been destroyed not long after, in the course of the wars which still
desolated the country. In 1786, a proposal was made to erect a marble
monument to his memory, but nothing was done. Kästner, on whose
authority it is mentioned, says upon this, rather bitterly, that it
matters little whether or not Germany, having almost refused him bread
during his life, should, a century and a half after his death, offer him
a stone.

Delambre mentions, in his History of Astronomy, that this design was
resumed in 1803 by the Prince Bishop of Constance, and that a monument
has been erected in the Botanical Garden at Ratisbon, near the place of
his interment. It is built in the form of a temple, surmounted by a
sphere; in the centre is placed a bust of Kepler, in Carrara marble.
Delambre does not mention the original of the bust; but says it is not
unlike the figure engraved in the frontispiece of the Rudolphine Tables.
That frontispiece consists of a portico of ten pillars, supporting a
cupola covered with astronomical emblems. Copernicus, Tycho Brahe,
Ptolemy, Hipparchus, and other astronomers, are seen among them. In one
of the compartments of the common pedestal is a plan of the observatory
at Uraniburg; in another, a printing press; in a third is the figure of
a man, meant for Kepler, seated at a table. He is identified by the
titles of his works, which are round him; but the whole is so small as
to convey very little idea of his figure or countenance. The only
portrait known of Kepler was given by him to his assistant Gringallet,
who presented it to Bernegger; and it was placed by the latter in the
library at Strasburg. Hantsch had a copy taken for the purpose of
engraving it, but died before it was completed. A portrait of Kepler is
engraved in the seventh part of Boissard's Bibliotheca Chalcographica.
It is not known whence this was taken, but it may, perhaps, be a copy of
that which was engraved by desire of Bernegger in 1620. The likeness is
said not to have been well preserved. "His heart and genius," says
Kästner, "are faithfully depicted in his writings; and that may console
us, if we cannot entirely trust his portrait." In the preceding pages,
it has been endeavoured to select such passages from his writings as
might throw the greatest light on his character, with a subordinate
reference only to the importance of the subjects treated. In conclusion,
it may be well to support the opinion which has been ventured on the
real nature of his triumphs, and on the danger of attempting to follow
his method in the pursuit of truth, by the judgment pronounced by
Delambre, as well on his failures as on his success. "Considering these
matters in another point of view, it is not impossible to convince
ourselves that Kepler may have been always the same. Ardent, restless,
burning to distinguish himself by his discoveries, he attempted
everything; and having once obtained a glimpse of one, no labour was too
hard for him in following or verifying it. All his attempts had not the
same success, and, in fact, that was impossible. Those which have failed
seem to us only fanciful; those which have been more fortunate appear
sublime. When in search of that which really existed, he has sometimes
found it; when he devoted himself to the pursuit of a chimera, he could
not but fail; but even there he unfolded the same qualities, and that
obstinate perseverance that must triumph over all difficulties but those
which are insurmountable."[201]


_List of Kepler's published Works._

  Ein Calender                               _Gratz_, 1594
  Prodromus Dissertat. Cosmograph.           _Tubingæ_, 1596, 4to.
  De fundamentis Astrologiæ                  _Pragæ_, 1602, 4to.
  Paralipomena ad Vitellionem                _Francofurti_, 1604, 4to.
  Epistola de Solis deliquio                 1605
  De stellâ novâ                             _Pragæ_, 1606, 4to.
  Vom Kometen                                _Halle_, 1608, 4to.
  Antwort an Röslin                          _Pragæ_, 1609, 4to.
  Astronomia Nova                            _Pragæ_, 1609, fol.
  Tertius interveniens                       _Frankfurt_, 1610, 4to.
  Dissertatio cum Nuncio Sidereo             _Francofurti_, 1610, 4to.
  Strena, seu De dive sexangulâ              _Frankfurt_, 1611, 4to.
  Dioptrica                                  _Francofurti_, 1611, 4to.
  Vom Geburts Jahre des Heylandes            _Strasburg_, 1613, 4to.
  Respons. ad epist S. Calvisiii             _Francofurti_, 1614, 4to.
  Eclogæ Chronicæ                            _Frankfurt_, 1615, 4to.
  Nova Stereometria                          _Lincii_, 1615, 4to.
  Ephemerides 1617-1620                      _Lincii_, 1616, 4to.
  Epitomes Astron. Copern. Libri i. ii. iii. _Lentiis_, 1618, 8vo.
  De Cometis                                 _Aug. Vindelic._ 1619, 4to.
  Harmonice Mundi                            _Lincii_, 1619, fol.
  Kanones Pueriles                           _Ulmæ_, 1620
  Epitomes Astron. Copern. Liber iv.         _Lentiis_, 1622, 8vo.
  Epitomes Astron. Copern. Libri v. vi. vii. _Francofurti_, 1622, 8vo.
  Discurs von der grossen Conjunction        _Linz._ 1623, 4to.
  Chilias Logarithmorum                      _Marpurgi_, 1624, fol.
  Supplementum                               _Lentiis_, 1625, 4to.
  Hyperaspistes                              _Francofurti_, 1625, 8vo.
  Tabulæ Rudolphinæ                          _Ulmæ_, 1627, fol.
  Resp. ad epist. J. Bartschii               _Sagani_, 1629, 4to.
  De anni 1631 phænomenis                    _Lipsæ_, 1629, 4to.
  Terrentii epistolium cum commentatiunculâ  _Sagani_, 1630, 4to.
  Ephemerides.                               _Sagani_, 1630, 4to.

  Somnium                                    _Francofurti_, 1634, 4to.
  Tabulæ mannales                            _Argentorati_, 1700, 12mo.


FOOTNOTES:

[199] The meaning of this passage is not very clear: Kepler evidently
had seen and used logarithms at the time of writing this letter; yet
there is nothing in the method to justify this expression,--"_At tamen
opus est ipsi Tangentium canone._"

[200] This was the objection originally made to Newton's "Fluxions," and
in fact, Napier's idea of logarithms is identical with that method of
conceiving quantities. This may be seen at once from a few of his
definitions,

    1 Def. A line is said to increase uniformly, when the point by which
    it is described passes through equal intervals, in equal times.

    2 Def. A line is said to diminish to a shorter one proportionally,
    when the point passing along it cuts off in equal times segments
    proportional to the remainder.

    6 Def. The logarithm of any sine is the number most nearly denoting
    the line, which has increased uniformly, whilst the radius has
    diminished to that sine proportionally, the initial velocity being
    the same in both motions. (Mirifici logarithmorum canonis
    descriptio, Edinburgi 1614.)

This last definition contains what we should now call the differential
equation between a number and the logarithm of its reciprocal.

[201] Histoire del'Astronomie Moderne, Paris, 1821.




Transcriber's Notes.

Corrections.

The first line indicates the original, the second the correction.


Life of Galileo Galilei

p. 20:

  success very inadeqnate to the zeal
  success very inadequate to the zeal

p. 20:

 "New method of Guaging,
 "New method of Gauging,

p. 23:

  the knowlege, if it existed
  the knowledge, if it existed

p. 30, note:

  to represent terrestial objects correctly.
  to represent terrestrial objects correctly.

p. 64:

  the palace of the Archishop Piccolomini
  the palace of the Archbishop Piccolomini

p. 68:

  that ladies ringlets
  that ladies' ringlets

p. 69:

  For hitherto I have never happened to see the terrestial earth
  For hitherto I have never happened to see the terrestrial earth

p. 106:

  80   1    50, _for_ any _read_ an indefinitely small.
  80   2    44, _for_ any _read_ an indefinitely small.


Life of Kepler

p. 6:

  Now, inscribe in the Earth an icosaedron, the circle inscribed in it
  will be Venus.

  Now, inscribe in the Earth an icosahedron, the circle inscribed in
  it will be Venus.

  Inscribe an octaedron in Venus, the circle inscribed in it will be
  Mercury.

  Inscribe an octahedron in Venus, the circle inscribed in it will be
  Mercury.

p. 32:

  Butthere are no such means
  But there are no such means

p. 48:

  the compound ratio of the rectangle of the axes directly, and
  subduplicatly

  the compound ratio of the rectangle of the axes directly, and
  subduplicately

p. 52:

  and was in-intended to illustrate the appearances
  and was intended to illustrate the appearances








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