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Title: The Asteroids; Or Minor Planets Between Mars and Jupiter.

Author: Daniel Kirkwood

Release date: December 6, 2012 [eBook #41570]

Language: English

Credits: E-text prepared by Paul Clark, sp1nd, and the Online Distributed Proofreading Team (http://www.pgdp.net) from page images generously made available by Internet Archive (http://archive.org)

*** START OF THE PROJECT GUTENBERG EBOOK THE ASTEROIDS; OR MINOR PLANETS BETWEEN MARS AND JUPITER. ***

 

E-text prepared by Paul Clark, sp1nd,
and the Online Distributed Proofreading Team
(http://www.pgdp.net)
from page images generously made available by
Internet Archive
(http://archive.org)

 

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Transcriber's Note:

Every effort has been made to replicate this text as faithfully as possible, including non-standard spelling and punctuation. Some apparent typographical errors in the indices and names of asteroids in Tables I and II have been corrected.

 


 

 

 

[Pg 1]

THE
ASTEROIDS,
OR
MINOR PLANETS
BETWEEN
MARS AND JUPITER.

BY
DANIEL KIRKWOOD, LL.D.,
PROFESSOR EMERITUS IN THE UNIVERSITY OF INDIANA; AUTHOR OF "COMETS AND METEORS," "METEORIC ASTRONOMY," ETC.

 

 

 

PHILADELPHIA:
J. B. LIPPINCOTT COMPANY.
1888.


[Pg 2]

Copyright, 1887, by Daniel Kirkwood.


[Pg 3]

PREFACE.

The rapid progress of discovery in the zone of minor planets, the anomalous forms and positions of their orbits, the small size as well as the great number of these telescopic bodies, and their peculiar relations to Jupiter, the massive planet next exterior,—all entitle this part of the system to more particular consideration than it has hitherto received. The following essay is designed, therefore, to supply an obvious want. Its results are given in some detail up to the date of publication. Part I. presents in a popular form the leading historical facts as to the discovery of Ceres, Pallas, Juno, Vesta, and Astræa; a tabular statement of the dates and places of discovery for the entire group; a list of the names of discoverers, with the number of minor planets detected by each; and a table of the principal elements so far as computed.

In Part II. this descriptive summary is followed by questions relating to the origin of the cluster; the elimination of members from particular parts; the eccentricities and inclinations of the orbits; and the relation[Pg 4] of the zone to comets of short period. The elements are those given in the Paris Annuaire for 1887, or in recent numbers of the Circular zum Berliner Astronomischen Jahrbuch.

DANIEL KIRKWOOD.

Bloomington, Indiana, November, 1887.


[Pg 5]

CONTENTS.

PART I. PAGE
Planetary Discoveries before the Asteroids were known 9
Discovery of the First Asteroids 11
Table I.—Asteroids in the Order of their Discovery 17
Numbers found by the Respective Discoverers 23
Numbers discovered in the Different Months 25
Mode of Discovery 25
Names and Symbols 25
Magnitudes of the Asteroids 26
Orbits of the Asteroids 28
Table II.—Elements of the Asteroids 29
PART II. 
Extent of the Zone 37
Theory of Olbers 38
Small Mass of the Asteroids 38
Limits of Perihelion Distance 39
Distribution of the Asteroids in Space 40
Law of Gap Formation 42
Commensurability of Periods with that of Jupiter 43
Orders of Commensurability 44
Elimination of very Eccentric Orbits 46
Relations between certain Adjacent Orbits 47[Pg 6]
The Eccentricities 48
The Inclinations 49
Longitudes of the Perihelia and of the Ascending Nodes 50
The Periods 51
Origin of the Asteroids 52
Variability of Certain Asteroids 53
The Average Asteroid Orbit 54
The Relation of Short-Period Comets to the Zone of Asteroids 55
Appendix 59

[Pg 7]
[Pg 8]

PART I.

[Pg 9]

THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER.

1. Introductory.
PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN.

The first observer who watched the skies with any degree of care could not fail to notice that while the greater number of stars maintained the same relative places, a few from night to night were ever changing their positions. The planetary character of Mercury, Venus, Mars, Jupiter, and Saturn was thus known before the dawn of history. The names, however, of those who first distinguished them as "wanderers" are hopelessly lost. Venus, the morning and evening star, was long regarded as two distinct bodies. The discovery that the change of aspect was due to a single planet's change of position is ascribed to Pythagoras.

At the beginning of the seventeenth century but six primary planets and one satellite were known as members of the solar system. Very few, even of the learned, had then accepted the theory of Copernicus; in fact, before the invention of the telescope the evidence in its favor was not absolutely conclusive. On[Pg 10] the 7th of January, 1610, Galileo first saw the satellites of Jupiter. The bearing of this discovery on the theory of the universe was sufficiently obvious. Such was the prejudice, however, against the Copernican system that some of its opponents denied even the reality of Galileo's discovery. "Those satellites," said a Tuscan astronomer, "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, the Jews and other ancient nations, as well 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 planets this whole system falls to the ground."

No other secondary planet was discovered till March 25, 1655, when Titan, the largest satellite of Saturn, was detected by Huyghens. About two years later (December 7, 1657) the same astronomer discovered the true form of Saturn's ring; and before the close of the century (1671-1684) four more satellites, Japetus, Rhea, Tethys, and Dione, were added to the Saturnian system by the elder Cassini. Our planetary system, therefore, as known at the close of the seventeenth century, consisted of six primary and ten secondary planets.

Nearly a century had elapsed from the date of Cassini's discovery of Dione, when, on the 13th of March, 1781, Sir William Herschel enlarged the dimensions of our system by the detection of a planet—Uranus—exterior to Saturn. A few years later (1787-1794) the same distinguished observer discovered the first and second satellites of Saturn, and also the four Uranian satellites. He was the only planet discoverer of the eighteenth century.

[Pg 11]

2. Discovery of the First Asteroids.

As long ago as the commencement of the seventeenth century the celebrated Kepler observed that the respective distances of the planets from the sun formed nearly a regular progression. The series, however, by which those distances were expressed required the interpolation of a term between Mars and Jupiter,—a fact which led the illustrious German to predict the discovery of a planet in that interval. This conjecture attracted but little attention till after the discovery of Uranus, whose distance was found to harmonize in a remarkable manner with Kepler's order of progression. Such a coincidence was of course regarded with considerable interest. Towards the close of the last century Professor Bode, who had given the subject much attention, published the law of distances which bears his name, but which, as he acknowledged, is due to Professor Titius. According to this formula the distances of the planets from Mercury's orbit form a geometrical series of which the ratio is two. In other words, if we reckon the distances of Venus, the earth, etc., from the orbit of Mercury, instead of from the sun, we find that—interpolating a term between Mars and Jupiter—the distance of any member of the system is very nearly half that of the next exterior. Baron De Zach, an enthusiastic astronomer, was greatly interested in Bode's empirical scheme, and undertook to determine the elements of the hypothetical planet. In 1800 a number of astronomers met at Lilienthal, organized an astronomical society, and assigned one twenty-fourth part of the zodiac to each of twenty-four observers, in order to detect, if possible, the unseen planet. When it is remembered that at this time no primary planet had[Pg 12] been discovered within the ancient limits of the solar system, that the object to be looked for was comparatively near us, and that the so-called law of distances was purely empirical, the prospect of success, it is evident, was extremely uncertain. How long the watch, if unsuccessful, might have been continued is doubtful. The object of research, however, was fortunately brought to light before the members of the astronomical association had fairly commenced their labors.[1]

On the 1st of January, 1801, Professor Giuseppe Piazzi, of Palermo, noticed a star of the eighth magnitude, not indicated in Wollaston's catalogue. Subsequent observations soon revealed its planetary character, its mean distance corresponding very nearly with the calculations of De Zach. The discoverer called it Ceres Ferdinandea, in honor of his sovereign, the King of Naples. In this, however, he was not followed by astronomers, and the planet is now known by the name of Ceres alone. The discovery of this body was hailed by astronomers with the liveliest gratification as completing the harmony of the system. What, then, was their surprise when in the course of a few months this remarkable order was again interrupted! On the 28th of March, 1802, Dr. William Olbers, of Bremen, while examining the relative positions of the small stars along the path of Ceres, in order to find that planet with the greater facility, noticed a star of the seventh or eighth magnitude, forming with two others an equilateral triangle where he was certain no such configuration ex[Pg 13]isted a few months before. In the course of a few hours its motion was perceptible, and on the following night it had very sensibly changed its position with respect to the neighboring stars. Another planet was therefore detected, and Dr. Olbers immediately communicated his discovery to Professor Bode and Baron De Zach. In his letter to the former he suggested Pallas as the name of the new member of the system,—a name which was at once adopted. Its orbit, which was soon computed by Gauss, was found to present several striking anomalies. The inclination of its plane to that of the ecliptic was nearly thirty-five degrees,—an amount of deviation altogether extraordinary. The eccentricity also was greater than in the case of any of the old planets. These peculiarities, together with the fact that the mean distances of Ceres and Pallas were nearly the same, and that their orbits approached very near each other at the intersection of their planes, suggested the hypothesis that they are fragments of a single original planet, which, at a very remote epoch, was disrupted by some mysterious convulsion. This theory will be considered when we come to discuss the tabulated elements of the minor planets now known.

For the convenience of astronomers, Professor Harding, of Lilienthal, undertook the construction of charts of all the small stars near the orbits of Ceres and Pallas. On the evening of September 1, 1804, while engaged in observations for this purpose, he noticed a star of the eighth magnitude not mentioned in the great catalogue of Lalande. This proved to be a third member of the group of asteroids. The discovery was first announced to Dr. Olbers, who observed the planet at Bremen on the evening of September 7.

[Pg 14]

Before Ceres had been generally adopted by astronomers as the name of the first asteroid, Laplace had expressed a preference for Juno. This, however, the discoverer was unwilling to accept. Mr. Harding, like Laplace, deeming it appropriate to place Juno near Jupiter, selected the name for the third minor planet, which is accordingly known by this designation.

Juno is distinguished among the first asteroids by the great eccentricity of its orbit, amounting to more than 0.25. Its least and its greatest distances from the sun are therefore to each other very nearly in the ratio of three to five. The planet consequently receives nearly three times as much light and heat in perihelion as in aphelion. It follows, also, that the half of the orbit nearest the sun is described in about eighteen months, while the remainder, or more distant half, is not passed over in much less than three years. Schroeter noticed a variation in the light of Juno, which he supposed to be produced by an axial rotation in about twenty-seven hours.

The fact that Juno was discovered not far from the point at which the orbit of Pallas approaches very near that of Ceres, was considered a strong confirmation of the hypothesis that the asteroids were produced by the explosion of a large planet; for in case this hypothesis be founded in truth, it is evident that whatever may have been the forms of the various orbits assumed by the fragments, they must all return to the point of separation. In order, therefore, to detect other members of the group, Dr. Olbers undertook a systematic examination of the two opposite regions of the heavens through which they must pass. This search was prosecuted with great industry and perseverance till ultimately crowned with success. On the 29th of March, 1807, while[Pg 15] sweeping over one of those regions through which the orbits of the known asteroids passed, a star of the sixth magnitude was observed where none had been seen at previous examinations. Its planetary character, which was immediately suspected, was confirmed by observation, its motion being detected on the very evening of its discovery. This fortunate result afforded the first instance of the discovery of two primary planets by the same observer.

The astronomer Gauss having been requested to name the new planet, fixed upon Vesta, a name universally accepted. Though the brightest of the asteroids, its apparent diameter is too small to be accurately determined, and hence its real magnitude is not well ascertained. Professor Harrington, of Ann Arbor, has estimated the diameter at five hundred and twenty miles. According to others, however, it does not exceed three hundred. If the latter be correct, the volume is about 1/20000 that of the earth. It is remarkable that notwithstanding its diminutive size it may be seen under favorable circumstances by the naked eye.

Encouraged by the discovery of Vesta (which he regarded as almost a demonstration of his favorite theory), Dr. Olbers continued his systematic search for other planetary fragments. Not meeting, however, with further success, he relinquished his observations in 1816. His failure, it may here be remarked, was doubtless owing to the fact that his examination was limited to stars of the seventh and eighth magnitudes.

The search for new planets was next resumed about 1831, by Herr Hencke, of Driessen. With a zeal and perseverance worthy of all praise, this amateur astronomer employed himself in a strict examination of the[Pg 16] heavens represented by the Maps of the Berlin Academy. These maps extend fifteen degrees on each side of the equator, and contain all stars down to the ninth magnitude and many of the tenth. Dr. Hencke rendered some of these charts still more complete by the insertion of smaller stars; or rather, "made for himself special charts of particular districts." On the evening of December 8, 1845, he observed a star of the ninth magnitude where none had been previously seen, as he knew from the fact that it was neither found on his own chart nor given on that of the Academy. On the next morning he wrote to Professors Encke and Schumacher informing them of his supposed discovery. "It is very improbable," he remarked in his letter to the latter, "that this should prove to be merely a variable star, since in my former observations of this region, which have been continued for many years, I have never detected the slightest trace of it." The new star was soon seen at the principal observatories of Europe, and its planetary character satisfactorily established. The selection of a name was left by the discoverer to Professor Encke, who chose that of Astræa.

The facts in regard to the very numerous subsequent discoveries may best be presented in a tabular form.

[Pg 17]

TABLE I.
The Asteroids in the Order of their Discovery.

Asteroids.Date of
Discovery.
Name of
Discoverer.
Place of
Discovery.
1. Ceres1801, Jan. 1PiazziPalermo
2. Pallas1802, Mar. 28OlbersBremen
3. Juno1804, Sept. 1HardingLilienthal
4. Vesta1807, Mar. 29OlbersBremen
5. Astræa1845, Dec. 8HenckeDriessen
6. Hebe1847, July 1HenckeDriessen
7. Iris1847, Aug. 14HindLondon
8. Flora1847, Oct. 18HindLondon
9. Metis1848, Apr. 26GrahamMarkree
10. Hygeia1849, Apr. 12De GasparisNaples
11. Parthenope1850, May 11De GasparisNaples
12. Victoria1850, Sept. 13HindLondon
13. Egeria1850, Nov. 2De GasparisNaples
14. Irene1851, May 19HindLondon
15. Eunomia1851, July 29De GasparisNaples
16. Psyche1852, Mar. 17De GasparisNaples
17. Thetis1852, Apr. 17LutherBilk
18. Melpomene1852, June 24HindLondon
19. Fortuna1852, Aug. 22HindLondon
20. Massalia1852, Sept. 19De GasparisNaples
21. Lutetia1852, Nov. 15GoldschmidtParis
22. Calliope1852, Nov. 16HindLondon
23. Thalia1852, Dec. 15HindLondon
24. Themis1853, Apr. 5De GasparisNaples
25. Phocea1853, Apr. 6ChacornacMarseilles
26. Proserpine1853, May 5LutherBilk
27. Euterpe1853, Nov. 8HindLondon
28. Bellona1854, Mar. 1LutherBilk
29. Amphitrite1854, Mar. 1MarthLondon
30. Urania1854, July 22HindLondon
31. Euphrosyne1854, Sept. 1FergusonWashington
32. Pomona1854, Oct. 26GoldschmidtParis
33. Polyhymnia1854, Oct. 28ChacornacParis
34. Circe1855, Apr. 6ChacornacParis
35. Leucothea1855, Apr. 19LutherBilk
36. Atalanta1855, Oct. 5GoldschmidtParis
37. Fides1855, Oct. 5LutherBilk
38. Leda1856, Jan. 12ChacornacParis
39. Lætitia1856, Feb. 8ChacornacParis
40. Harmonia1856, Mar. 31GoldschmidtParis
41. Daphne1856, May 22GoldschmidtParis
42. Isis1856, May 23PogsonOxford
43. Ariadne1857, Apr. 15PogsonOxford[Pg 18]
44. Nysa1857, May 27GoldschmidtParis
45. Eugenia1857, June 27GoldschmidtParis
46. Hestia1857, Aug. 16PogsonOxford
47. Aglaia1857, Sept. 15LutherBilk
48. Doris1857, Sept. 19GoldschmidtParis
49. Pales1857, Sept. 19GoldschmidtParis
50. Virginia1857, Oct. 4FergusonWashington
51. Nemausa1858, Jan. 22LaurentNismes
52. Europa1858, Feb. 4GoldschmidtParis
53. Calypso1858, Apr. 4LutherBilk
54. Alexandra1858, Sept. 10GoldschmidtParis
55. Pandora1858, Sept. 10SearleAlbany
56. Melete1857, Sept. 9GoldschmidtParis
57. Mnemosyne1859, Sept. 22LutherBilk
58. Concordia1860, Mar. 24LutherBilk
59. Olympia1860, Sept. 12ChacornacParis
60. Echo1860, Sept. 16FergusonWashington
61. Danaë1860, Sept. 9GoldschmidtParis
62. Erato1860, Sept. 14Foerster and LesserBerlin
63. Ausonia1861, Feb. 10De GasparisNaples
64. Angelina1861, Mar. 4TempelMarseilles
65. Maximiliana1861, Mar. 8TempelMarseilles
66. Maia1861, Apr. 9TuttleCambridge, U.S.
67. Asia1861, Apr. 17PogsonMadras
68. Leto1861, Apr. 29LutherBilk
69. Hesperia1861, Apr. 29SchiaparelliMilan
70. Panopea1861, May 5GoldschmidtParis
71. Niobe1861, Aug. 13LutherBilk
72. Feronia1862, May 29Peters and SaffordClinton
73. Clytie1862, Apr. 7TuttleCambridge
74. Galatea1862, Aug. 29TempelMarseilles
75. Eurydice1862, Sept. 22PetersClinton
76. Freia1862, Oct. 21D'ArrestCopenhagen
77. Frigga1862, Nov. 12PetersClinton
78. Diana1863, Mar. 15LutherBilk
79. Eurynome1863, Sept. 14WatsonAnn Arbor
80. Sappho1864, May 2PogsonMadras
81. Terpsichore1864, Sept. 30TempelMarseilles
82. Alcmene1864, Nov. 27LutherBilk
83. Beatrix1865, Apr. 26De GasparisNaples
84. Clio1865, Aug. 25LutherBilk
85. Io1865, Sept. 19PetersClinton
86. Semele1866, Jan. 14TietjenBerlin
87. Sylvia1866, May 16PogsonMadras
88. Thisbe1866, June 15PetersClinton
89. Julia1866, Aug. 6StephanMarseilles
90. Antiope1866, Oct. 1LutherBilk
91. Ægina1866, Nov. 4BorellyMarseilles
92. Undina1867, July 7PetersClinton[Pg 19]
93. Minerva1867, Aug. 24WatsonAnn Arbor
94. Aurora1867, Sept. 6WatsonAnn Arbor
95. Arethusa1867, Nov. 24LutherBilk
96. Ægle1868, Feb. 17CoggiaMarseilles
97. Clotho1868, Feb. 17CoggiaMarseilles
98. Ianthe1868, Apr. 18PetersClinton
99. Dike1868, May 28BorellyMarseilles
100. Hecate1868, July 11WatsonAnn Arbor
101. Helena1868, Aug. 15WatsonAnn Arbor
102. Miriam1868, Aug. 22PetersClinton
103. Hera1868, Sept. 7WatsonAnn Arbor
104. Clymene1868, Sept. 13WatsonAnn Arbor
105. Artemis1868, Sept. 16WatsonAnn Arbor
106. Dione1868, Oct. 10WatsonAnn Arbor
107. Camilla1868, Nov. 17PogsonMadras
108. Hecuba1869, Apr. 2LutherBilk
109. Felicitas1869, Oct. 9PetersClinton
110. Lydia1870, Apr. 19BorellyMarseilles
111. Ate1870, Aug. 14PetersClinton
112. Iphigenia1870, Sept. 19PetersClinton
113. Amalthea1871, Mar. 12LutherBilk
114. Cassandra1871, July 23PetersClinton
115. Thyra1871, Aug. 6WatsonAnn Arbor
116. Sirona1871, Sept. 8PetersClinton
117. Lomia1871, Sept. 12BorellyMarseilles
118. Peitho1872, Mar. 15LutherBilk
119. Althea1872, Apr. 3WatsonAnn Arbor
120. Lachesis1872, Apr. 10BorellyMarseilles
121. Hermione1872, May 12WatsonAnn Arbor
122. Gerda1872, July 31PetersClinton
123. Brunhilda1872, July 31PetersClinton
124. Alceste1872, Aug. 23PetersClinton
125. Liberatrix1872, Sept. 11Prosper HenryParis
126. Velleda1872, Nov. 5Paul HenryParis
127. Johanna1872, Nov. 5Prosper HenryParis
128. Nemesis1872, Nov. 25WatsonAnn Arbor
129. Antigone1873, Feb. 5PetersClinton
130. Electra1873, Feb. 17PetersClinton
131. Vala1873, May 24PetersClinton
132. Æthra1873, June 13WatsonAnn Arbor
133. Cyrene1873, Aug. 16WatsonAnn Arbor
134. Sophrosyne1873, Sept. 27LutherBilk
135. Hertha1874, Feb. 18PetersClinton
136. Austria1874, Mar. 18PalisaPola
137. Melibœa1874, Apr. 21PalisaPola
138. Tolosa1874, May 19PerrotinToulouse
139. Juewa1874, Oct. 10WatsonPekin
140. Siwa1874, Oct. 13PalisaPola
141. Lumen1875, Jan. 13Paul HenryParis[Pg 20]
142. Polana1875, Jan. 28PalisaPola
143. Adria1875, Feb. 23PalisaPola
144. Vibilia1875, June 3PetersClinton
145. Adeona1875, June 3PetersClinton
146. Lucina1875, June 8BorellyMarseilles
147. Protogenea1875, July 10SchulhofVienna
148. Gallia1875, Aug. 7Prosper HenryParis
149. Medusa1875, Sept. 21PerrotinToulouse
150. Nuwa1875, Oct. 18WatsonAnn Arbor
151. Abundantia1875, Nov. 1PalisaPola
152. Atala1875, Nov. 2Paul HenryParis
153. Hilda1875, Nov. 2PalisaPola
154. Bertha1875, Nov. 4Prosper HenryParis
155. Scylla1875, Nov. 8PalisaPola
156. Xantippe1875, Nov. 22PalisaPola
157. Dejanira1875, Dec. 1BorellyMarseilles
158. Coronis1876, Jan. 4KnorreBerlin
159. Æmilia1876, Jan. 26Paul HenryParis
160. Una1876, Feb. 20PetersClinton
161. Athor1876, Apr. 19WatsonAnn Arbor
162. Laurentia1876, Apr. 21Prosper HenryParis
163. Erigone1876, Apr. 26PerrotinToulouse
164. Eva1876, July 12Paul HenryParis
165. Loreley1876, Aug. 9PetersClinton
166. Rhodope1876, Aug. 15PetersClinton
167. Urda1876, Aug. 28PetersClinton
168. Sibylla1876, Sept. 27WatsonAnn Arbor
169. Zelia1876, Sept. 28Prosper HenryParis
170. Maria1877, Jan. 10PerrotinToulouse
171. Ophelia1877, Jan. 13BorellyMarseilles
172. Baucis1877, Feb. 5BorellyMarseilles
173. Ino1877, Aug. 1BorellyMarseilles
174. Phædra1877, Sept. 2WatsonAnn Arbor
175. Andromache1877, Oct. 1WatsonAnn Arbor
176. Idunna1877, Oct. 14PetersClinton
177. Irma1877, Nov. 5Paul HenryParis
178. Belisana1877, Nov. 6PalisaPola
179. Clytemnestra1877, Nov. 11WatsonAnn Arbor
180. Garumna1878, Jan. 29PerrotinToulouse
181. Eucharis1878, Feb. 2CottenotMarseilles
182. Elsa1878, Feb. 7PalisaPola
183. Istria1878, Feb. 8PalisaPola
184. Deiopea1878, Feb. 28PalisaPola
185. Eunice1878, Mar. 1PetersClinton
186. Celuta1878, Apr. 6Prosper HenryParis
187. Lamberta1878, Apr. 11CoggiaMarseilles
188. Menippe1878, June 18PetersClinton
189. Phthia1878, Sept. 9PetersClinton
190. Ismene1878, Sept. 22PetersClinton[Pg 21]
191. Kolga1878, Sept. 30PetersClinton
192. Nausicaa1879, Feb. 17PalisaPola
193. Ambrosia1879, Feb. 28CoggiaMarseilles
194. Procne1879, Mar. 21PetersClinton
195. Euryclea1879, Apr. 22PalisaPola
196. Philomela1879, May 14PetersClinton
197. Arete1879, May 21PalisaPola
198. Ampella1879, June 13BorellyMarseilles
199. Byblis1879, July 9PetersClinton
200. Dynamene1879, July 27PetersClinton
201. Penelope1879, Aug. 7PalisaPola
202. Chryseis1879, Sept. 11PetersClinton
203. Pompeia1879, Sept. 25PetersClinton
204. Callisto1879, Oct. 8PalisaPola
205. Martha1879, Oct. 13PalisaPola
206. Hersilia1879, Oct. 13PetersClinton
207. Hedda1879, Oct. 17PalisaPola
208. Lachrymosa1879, Oct. 21PalisaPola
209. Dido1879, Oct. 22PetersClinton
210. Isabella1879, Nov. 12PalisaPola
211. Isolda1879, Dec. 10PalisaPola
212. Medea1880, Feb. 6PalisaPola
213. Lilæa1880, Feb. 16PetersClinton
214. Aschera1880, Feb. 26PalisaPola
215. Œnone1880, Apr. 7KnorreBerlin
216. Cleopatra1880, Apr. 10PalisaPola
217. Eudora1880, Aug. 30CoggiaMarseilles
218. Bianca1880, Sept. 4PalisaPola
219. Thusnelda1880, Sept. 20PalisaPola
220. Stephania1881, May 19PalisaVienna
221. Eos1882, Jan. 18PalisaVienna
222. Lucia1882, Feb. 9PalisaVienna
223. Rosa1882, Mar. 9PalisaVienna
224. Oceana1882, Mar. 30PalisaVienna
225. Henrietta1882, Apr. 19PalisaVienna
226. Weringia1882, July 19PalisaVienna
227. Philosophia1882, Aug. 12Paul HenryParis
228. Agathe1882, Aug. 19PalisaVienna
229. Adelinda1882, Aug. 22PalisaVienna
230. Athamantis1882, Sept. 3De BallBothcamp
231. Vindobona1882, Sept. 10PalisaVienna
232. Russia1883, Jan. 31PalisaVienna
233. Asterope1883, May 11BorellyMarseilles
234. Barbara1883, Aug. 13PetersClinton
235. Caroline1883, Nov. 29PalisaVienna
236. Honoria1884, Apr. 26PalisaVienna
237. Cœlestina1884, June 27PalisaVienna
238. Hypatia1884, July 1KnorreBerlin
239. Adrastea1884, Aug. 18PalisaVienna[Pg 22]
240. Vanadis1884, Aug. 27BorellyMarseilles
241. Germania1884, Sept. 12LutherDusseldorf
242. Kriemhild1884, Sept. 22PalisaVienna
243. Ida1884, Sept. 29PalisaVienna
244. Sita1884, Oct. 14PalisaVienna
245. Vera1885, Feb. 6PogsonMadras
246. Asporina1885, Mar. 6BorellyMarseilles
247. Eukrate1885, Mar. 14LutherDusseldorf
248. Lameia1885, June 5PalisaVienna
249. Ilse1885, Aug. 17PetersClinton
250. Bettina1885, Sept. 3PalisaVienna
251. Sophia1885, Oct. 4PalisaVienna
252. Clementina1885, Oct. 27PerrotinNice
253. Mathilde1885, Nov. 12PalisaVienna
254. Augusta1886, Mar. 31PalisaVienna
255. Oppavia1886, Mar. 31PalisaVienna
256. Walpurga1886, Apr. 3PalisaVienna
257. Silesia1886, Apr. 5PalisaVienna
258. Tyche1886, May 4LutherDusseldorf
259. Aletheia1886, June 28PetersClinton
260. Huberta1886, Oct. 3PalisaVienna
261. Prymno1886, Oct. 31PetersClinton
262. Valda1886, Nov. 3PalisaVienna
263. Dresda1886, Nov. 3PalisaVienna
264. Libussa1886, Dec. 17PetersClinton
265. Anna1887, Feb. 25PalisaVienna
266. Aline1887, May 17PalisaVienna
267. Tirza1887, May 27CharloisNice
268.1887, June 9BorellyMarseilles
269.1887, Sept. 21PalisaVienna
270.1887, Oct. 8PetersClinton
271.1887, Oct. 16KnorreBerlin

[Pg 23]

3. Remarks on Table I.

The numbers discovered by the thirty-five observers are respectively as follows:

Palisa 60
Peters 47
Luther 23
Watson 22
Borelly 15
Goldschmidt 14
Hind 10
De Gasparis 9
Pogson 8
Paul Henry 7
Prosper Henry 7
Chacornac 6
Perrotin 6
Coggia 5
Knorre 4
Tempel 4
Ferguson 3
Olbers 2
Hencke 2
Tuttle 2
Foerster (with Lesser) 1
Safford (with Peters) 1
and Messrs. Charlois, Cottenot, D'Arrest, De Ball, Graham, Harding, Laurent, Piazzi, Schiaparelli, Schulhof, Stephan, Searle, and Tietjen, each 1

Before arrangements had been made for the telegraphic transmission of discoveries between Europe and America, or even between the observatories of Europe, the same planet was sometimes independently discovered by different observers. For example, Virginia was found by Ferguson, at Washington, on October 4, 1857,[Pg 24] and by Luther, at Bilk, fifteen days later. In all cases, however, credit has been given to the first observer.

Hersilia, the two hundred and sixth of the group, was lost before sufficient observations were obtained for determining its elements. It was not rediscovered till December 14, 1884. Menippe, the one hundred and eighty-eighth, was also lost soon after its discovery in 1878. It has not been seen for more than nine years, and considerable uncertainty attaches to its estimated elements.

Of the two hundred and seventy-one members now known (1887), one hundred and ninety-one have been discovered in Europe, seventy-four in America, and six in Asia. The years of most successful search, together with the number discovered in each, were:

  Asteroids.
187920
187517
186812
187812

And six has been the average yearly number since the commencement of renewed effort in 1845. All the larger members of the group have, doubtless, been discovered. It seems not improbable, however, that an indefinite number of very small bodies belonging to the zone remain to be found. The process of discovery is becoming more difficult as the known number increases. The astronomer, for instance, who may discover number two hundred and seventy-two must know the simultaneous positions of the two hundred and seventy-one previously detected before he can decide whether he has picked up a new planet or merely rediscovered an old one. The numbers discovered in the several months are as follows:

[Pg 25]

January 13
February 23
March 19
April 35
May 21
June 13
July 14
August 28
September 46
October 28
November 26
December 5

This obvious disparity is readily explained. The weather is favorable for night watching in April and September; the winter months are too cold for continuous observations; and the small numbers in June and July may be referred to the shortness of the nights.

4. Mode of Discovery.

The astronomer who would undertake the search for new asteroids must supply himself with star-charts extending some considerable distance on each side of the ecliptic, and containing all telescopic stars down to the thirteenth or fourteenth magnitude. The detection of a star not found in the chart of a particular section will indicate its motion, and hence its planetary character. The construction of such charts has been a principal object in the labors of Dr. Peters, at Clinton, New York. In fact, his discovery of minor planets has in most instances been merely an incidental result of his larger and more important work.

NAMES AND SYMBOLS.

The fact that the names of female deities in the Greek and Roman mythologies had been given to the first asteroids suggested a similar course in the selection of names after the new epoch of discovery in 1845. While conformity to this rule has been the general aim[Pg 26] of discoverers, the departures from it have been increasingly numerous. The twelfth asteroid, discovered in London, was named Victoria, in honor of the reigning sovereign; the twentieth and twenty-fifth, detected at Marseilles,[2] received names indicative of the place of their discovery; Lutetia, the first found at Paris, received its name for a similar purpose; the fifty-fourth was named Alexandra, for Alexander von Humboldt; the sixty-seventh, found by Pogson at Madras, was named Asia, to commemorate the fact that it was the first discovered on that continent. We find, also, Julia, Bertha, Xantippe, Zelia, Maria, Isabella, Martha, Dido, Cleopatra, Barbara, Ida, Augusta, and Anna. Why these were selected we will not stop to inquire.

As the number of asteroids increased it was found inconvenient to designate them individually by particular signs, as in the case of the old planets. In 1849, Dr. B. A. Gould proposed to represent them by the numbers expressing their order of discovery enclosed in a small circle. This method was at once very generally adopted.

5. Magnitudes of the Asteroids.

The apparent diameter of the largest is less than one-second of arc. They are all too small, therefore, to be accurately measured by astronomical instruments. From photometric observations, however, Argelander,[3] Stone,[4] and Pickering[5] have formed estimates of the diameters,[Pg 27] the results giving probably close approximations to the true magnitudes. According to these estimates the diameter of the largest, Vesta, is about three hundred miles, that of Ceres about two hundred, and those of Pallas and Juno between one and two hundred. The diameters of about thirty are between fifty and one hundred miles, and those of all others less than fifty; the estimates for Menippe and Eva giving twelve and thirteen miles respectively. The diameter of the former is to that of the earth as one to six hundred and sixty-four; and since spheres are to each other as the cubes of their diameters, it would require two hundred and ninety millions of such asteroids to form a planet as large as our globe. In other words, if the earth be represented by a sphere one foot in diameter, the magnitude of Menippe on the same scale would be that of a sand particle whose diameter is one fifty-fifth of an inch. Its surface contains about four hundred and forty square miles,—an area equal to a county twenty-one miles square. The surface attractions of two planets having the same density are to each other as their diameters. A body, therefore, weighing two hundred pounds at the earth's surface would on the surface of the asteroid weigh less than five ounces. At the earth's surface a weight falls sixteen feet the first second, at the surface of Menippe it would fall about one-fourth of an inch. A person might leap from its surface to a height of several hundred feet, in which case he could not return in much less than an hour. "But of such speculations," Sir John Herschel remarks, "there is no end."

The number of these planetules between the orbits of Mars and Jupiter in all probability can never be known. It was estimated by Leverrier that the quantity of mat[Pg 28]ter contained in the group could not be greater than one-fourth of the earth's mass. But this would be equal to five thousand planets, each as large as Vesta, to seventy-two millions as large as Menippe, or to four thousand millions of five miles in diameter. In short, the existence of an indefinite number too small for detection by the most powerful glasses is by no means improbable. The more we study this wonderful section of the solar system, the more mystery seems to envelop its origin and constitution.

6. The Orbits of the Asteroids.

The form, magnitude, and position of a planet's orbit are determined by the following elements:

1. The semi-axis major, or mean distance, denoted by the symbol a.

2. The eccentricity, e.

3. The longitude of the perihelion, π.

4. The longitude of the ascending node, ☊.

5. The inclination, or the angle contained between the plane of the orbit and that of the ecliptic, i.

And in order to compute a planet's place in its orbit for any given time we must also know

6. Its period, P, and

7. Its mean longitude, l, at a given epoch.

These elements, except the last, are given for all the asteroids, so far as known, in Table II. In column first the number denoting the order of discovery is attached to each name.

[Pg 29]

TABLE II.
Elements of the Asteroids.

NameaPeπi
149. Medusa2.13271137.7d0.1194 246°37´ 342°13´ 1°6´
244. Sita2.17651172.80.1370 138 20837 250
228. Agathe2.20091192.60.2405 32923 31318 233
8. Flora2.20141193.30.1567 3254 11018 553
43. Ariadne2.20331194.50.1671 27758 26435 328
254. Augusta2.20601196.80.1227 26047 289 436
72. Feronia2.26611246.00.1198 30758 20749 524
40. Harmonia2.26731247.00.0466 054 9335 416
207. Hedda2.28391260.70.0301 2172 2851 349
136. Austria2.28631262.70.0849 3166 1867 933
18. Melpomene2.29561270.40.2177 156 1504 109
80. Sappho2.29621270.90.2001 35518 21844 837
261. Prymno2.30621278.40.0794 17935 9633 338
12. Victoria2.33421302.70.2189 30139 23535 823
27. Euterpe2.34721313.50.1739 8759 9351 136
219. Thusnelda2.35421319.40.2247 34034 20044 1047
163. Erigone2.35601320.90.1567 9346 1592 442
169. Zelia2.35771322.30.1313 32620 35438 531
4. Vesta2.36161325.60.0884 25057 10329 78
186. Celuta2.36231326.20.1512 32724 1434 136
84. Clio2.36291326.70.2360 33920 32728 922
51. Nemausa2.36521328.60.0672 17443 17552 957
220. Stephania2.36661329.80.2653 33253 25824 735
30. Urania2.36671329.90.1266 3146 30812 26
105. Artemis2.37441336.40.1749 24238 1883 2131
113. Amalthea2.37611337.80.0874 19844 12311 52
115. Thyra2.37911340.30.1939 432 3095 1135
161. Athor2.37921340.50.1389 31040 1827 93
172. Baucis2.37941340.60.1139 32923 33150 102
249. Ilse2.37951340.60.2195 1417 33449 940
230. Athamantis2.38421344.60.0615 1731 23933 926
7. Iris2.38621346.40.2308 4123 25948 528
9. Metis2.38661346.70.1233 714 6832 536
234. Barbara2.38731347.30.2440 33326 1449 1522
60. Echo2.39341352.40.1838 9836 1925 335
63. Ausonia2.39791356.30.1239 27025 33758 548
25. Phocea2.40051358.50.2553 30248 20827 2135
192. Nausicaa2.40141359.30.2413 34319 16046 650
20. Massalia2.40241365.80.1429 997 20636 041
265. Anna2.40961366.20.2628 22618 33526 2524
182. Elsa2.41571371.40.1852 5152 10630 20
142. Polana2.41941374.50.1322 21954 31734 214
67. Asia2.42041375.40.1866 30635 20247 559
44. Nysa2.42231377.00.1507 11157 13111 342[Pg 30]
6. Hebe2.42541379.30.2034 1516 13843 1047
83. Beatrix2.43011383.60.0859 19146 2732 50
135. Hertha2.43031383.80.2037 32011 3443 219
131. Vala2.43181385.10.0683 22250 6515 458
112. Iphigenia2.43351386.60.1282 3389 3243 237
21. Lutetia2.43541388.20.1621 3274 8028 35
118. Peitho2.43841390.80.1608 7736 4730 748
126. Velleda2.43991392.10.1061 34746 237 256
42. Isis2.44011392.20.2256 31758 8428 835
19. Fortuna2.44151394.40.1594 313 21127 133
79. Eurynome2.44361395.20.1945 4422 20644 437
138. Tolosa2.44921400.00.1623 31139 5452 314
189. Phthia2.45051401.10.0356 650 20322 510
11. Parthenope2.45291403.20.0994 3182 12511 437
178. Belisana2.45831407.80.1266 2780 5017 25
198. Ampella2.45951408.90.2266 35446 26845 920
248. Lameia2.47141419.10.0656 24840 24634 41
17. Thetis2.47261420.10.1293 26137 12524 536
46. Hestia2.52651466.80.1642 35414 18131 217
89. Julia2.55101488.20.1805 35313 31142 1611
232. Russia2.55221489.30.1754 20025 15230 64
29. Amphitrite2.55451491.30.0742 5623 35641 67
170. Maria2.55491491.70.0639 9547 30120 1423
262. Valda2.56351496.40.2172 6142 3840 746
258. Tyche2.56431499.80.1966 1542 2084 1450
134. Sophrosyne2.56471500.30.1165 6733 34622 1136
264. Libussa2.56721502.40.0925 07 5023 1029
193. Ambrosia2.57581510.00.2854 7052 35115 1139
13. Egeria2.57651510.60.0871 12010 4312 1632
5. Astræa2.57861512.40.1863 13457 14128 519
119. Althea2.58241515.70.0815 1129 20357 545
157. Dejanira2.58281516.10.2105 10724 6231 122
101. Helena2.58491518.00.1386 32715 34346 1011
32. Pomona2.58731520.10.0830 19322 22043 529
91. Ægina2.58951522.10.1087 8022 117 28
14. Irene2.58961522.10.1627 18019 8648 98
111. Ate2.59271524.80.1053 10842 30613 457
151. Abundantia2.59321525.30.0356 17355 3848 630
56. Melete2.60101532.20.2340 29450 1941 82
132. Æthra2.60251533.50.3799 15224 2602 250
214. Aschera2.61111541.10.0316 11555 34230 327
70. Panopea2.61391543.60.1826 29949 4818 1138
194. Procne2.61591545.40.2383 31933 15919 1824
53. Calypso2.61751546.80.2060 9252 14358 57
78. Diana2.61941548.50.2088 12142 33358 840
124. Alceste2.62971557.60.0784 24542 18826 256
23. Thalia2.63061558.40.2299 12358 6745 1014
164. Eva2.63141559.10.3471 35932 7728 2425
15. Eunomia2.64371570.00.1872 2752 18826 256
37. Fides2.64401570.30.1758 6626 821 37[Pg 31]
66. Maia2.64541571.60.1750 488 817 36
224. Oceana2.64651572.60.0455 27051 35318 552
253. Mathilde2.64691572.90.2620 33339 1803 637
50. Virginia2.65201577.40.2852 109 17345 248
144. Vibilia2.65301578.40.2348 79 7647 448
85. Io2.65391579.20.1911 32235 20356 1153
26. Proserpine2.65611581.10.0873 23625 4555 336
233. Asterope2.65961584.30.1010 34436 22225 739
102. Miriam2.66191586.30.3035 35439 21158 54
240. Vanadis2.66381588.00.2056 5153 11454 26
73. Clytie2.66521589.30.0419 5755 751 224
218. Bianca2.66531589.30.1155 23014 17050 1513
141. Lumen2.66661590.50.2115 1343 3197 1157
77. Frigga2.66801591.80.1318 5847 20 228
3. Juno2.66831592.00.2579 5450 17053 131
97. Clotho2.67081594.30.2550 6532 16037 1146
75. Eurydice2.67201595.30.3060 33533 35956 51
145. Adeona2.67241595.40.1406 11753 7741 1238
204. Callisto2.67321596.40.1752 25745 20540 819
114. Cassandra2.67581598.80.1401 1536 16424 455
201. Penelope2.67641599.30.1818 33421 1575 544
64. Angelina2.68161603.90.1271 12536 3114 119
98. Ianthe2.68471606.70.1920 14852 3547 1532
34. Circe2.68641608.30.1073 14841 18446 527
123. Brunhilda2.69181613.20.1150 7257 30828 627
166. Rhodope2.69271613.90.2140 3051 12933 122
109. Felicitas2.69501616.00.3002 561 456 83
246. Asporina2.69941619.90.1065 25554 16235 1539
58. Concordia2.70041620.80.0426 18910 16120 52
103. Hera2.70141621.80.0803 3213 13618 524
54. Alexandra2.70951629.10.2000 29539 31345 1147
226. Weringia2.71181631.20.2048 28446 13518 1550
59. Olympia2.71241631.70.1189 1733 17026 837
146. Lucina2.71891637.50.0655 22734 8416 136
45. Eugenia2.72051639.00.0811 2325 14757 635
210. Isabella2.72351641.70.1220 4422 3258 518
187. Lamberta2.72721645.00.2391 2144 2213 1043
180. Garumna2.72861646.30.1722 12556 31442 054
160. Una2.72871646.40.0624 5557 922 351
140. Siwa2.73161649.00.2160 30033 1072 312
110. Lydia2.73271650.00.0770 33649 5710 60
185. Eunice2.73721654.10.1292 1632 15350 2317
203. Pompeia2.73761654.50.0588 4251 34837 313
200. Dynamene2.73781654.60.1335 4638 32526 656
197. Arete2.73901655.80.1621 32451 826 848
206. Hersilia2.73991656.50.0389 9544 14516 346
255. Oppavia2.74021656.60.0728 16915 146 933
247. Eukrate2.74121657.70.2387 5344 020 257
38. Leda2.74321659.60.1531 10120 29627 657
125. Liberatrix2.74371660.00.0798 27329 16935 438[Pg 32]
173. Ino2.74461660.80.2047 1328 14834 1415
36. Atalanta2.74521661.30.3023 4244 35914 1842
128. Nemesis2.75141666.90.1257 1634 7631 616
93. Minerva2.75371669.00.1405 27444 54 837
127. Johanna2.75501670.30.0659 12237 3146 817
71. Niobe2.75581671.00.1732 22117 31630 2319
213. Lilæa2.75631671.40.1437 2814 12217 647
55. Pandora2.76041675.10.1429 1036 1056 714
237. Cœlestina2.76071675.50.0738 28249 8433 946
143. Adria2.76191676.60.0729 22227 33342 1130
82. Alcmene2.76201676.60.2228 13145 2657 251
116. Sirona2.76691681.10.1433 15247 6426 335
1. Ceres2.76731681.40.0763 14938 8047 1037
88. Thisbe2.76731681.50.1632 30834 27754 1611
215. Œnone2.76791682.00.0390 34624 2525 144
2. Pallas2.76801682.10.2408 12212 17245 3444
39. Lætitia2.76801682.10.1142 38 15715 1022
41. Daphne2.76881682.80.2674 22033 1798 1558
177. Irma2.76951683.50.2370 226 34917 127
148. Gallia2.77101684.80.1855 367 14513 2521
267. Tirza2.77421687.60.0986 2645 7359 62
74. Galatea2.77701690.30.2392 818 19751 40
205. Martha2.77711690.40.1752 2154 21212 1040
139. Juewa2.77931692.40.1773 16434 221 1057
28. Bellona2.77971692.70.1491 1241 14437 922
68. Leto2.78051693.50.1883 34514 451 758
216. Cleopatra2.79641708.00.2492 32815 21549 132
99. Dike2.79661708.30.2384 24036 4144 1353
236. Honoria2.79931710.70.1893 35659 18627 737
183. Istria2.80241713.40.3530 450 14246 2633
266. Aline2.80781718.50.1573 2352 23618 1320
188. Menippe2.82111730.70.2173 30938 24144 1121
167. Urda2.85331760.40.0340 2964 16628 211
81. Terpsichore2.85801764.80.2080 491 225 755
174. Phædra2.86001766.60.1492 25312 32849 129
243. Ida2.86101767.50.0419 7122 32621 110
242. Kriemhild2.86231768.70.1219 1231 20757 1117
129. Antigone2.86781773.90.2126 2424 13737 1210
217. Eudora2.86901774.90.3068 31441 16410 1019
158. Coronis2.87141777.20.0545 5656 28130 10
33. Polyhymnia2.87511780.70.3349 34259 919 156
195. Euryclea2.87901784.20.0471 11548 757 71
235. Caroline2.87951784.70.0595 26829 6635 94
47. Aglaia2.88191786.90.1317 31240 4020 51
208. Lachrymosa2.89261796.90.0149 12752 543 148
191. Kolga2.89671800.80.0876 2321 15947 1129
22. Calliope2.90901801.00.0193 6243 447 145
155. Scylla2.91271815.70.2559 821 4252 144
238. Hypatia2.91631819.00.0946 3218 18426 1228
231. Vindobona2.91921821.70.1537 25323 35249 510[Pg 33]
16. Psyche2.92101823.40.1392 159 15036 34
179. Clytemnestra2.97111870.60.1133 35539 25313 747
239. Adrastea2.97361873.00.2279 261 18134 64
69. Hesperia2.97791877.00.1712 10819 18712 828
150. Nuwa2.97851877.50.1307 35527 20735 29
61. Danaë2.98551884.20.1615 3444 33411 1814
117. Lomia2.99071889.10.0229 4846 34939 1458
35. Leucothea2.99231890.60.2237 20225 35549 812
263. Dresda3.01201909.30.3051 30849 21756 127
221. Eos3.01341910.70.1028 33058 14235 1051
162. Laurentia3.02411920.80.1726 14552 3815 64
156. Xantippe3.03751933.70.2637 15558 24611 729
241. Germania3.03811934.00.1013 3407 27228 530
256. Walpurga3.04501940.80.1180 24017 18335 1244
211. Isolda3.04641942.20.1541 7412 26529 351
96. Ægle3.04971945.30.1405 16310 32250 167
257. Silesia3.05721952.50.2555 5416 3431 441
133. Cyrene3.05781953.00.1398 24713 3218 714
95. Arethusa3.07121965.90.1447 3258 24417 1254
202. Chryseis3.07771972.10.0959 12946 13747 848
268. ——3.08521973.90.1285 18448 12153 225
100. Hecate3.09041984.30.1639 3083 12812 623
49. Pales3.09081984.70.2330 3115 29040 38
223. Rosa3.09401987.90.1186 10248 490 159
52. Europa3.09551988.00.1098 10657 12940 727
245. Vera3.09851992.10.1950 2529 6237 510
86. Semele3.10151995.10.2193 2910 8745 447
159. Æmilia3.10892002.20.1034 10122 1359 64
48. Doris3.11272005.90.0649 7033 18455 631
196. Philomela3.11372006.80.0118 30919 7324 716
130. Electra3.11452007.70.2132 2034 1466 2257
212. Medea3.11572008.80.1013 5618 31516 416
120. Lachesis3.12112014.00.0475 2140 34251 71
181. Eucharis3.12262015.40.2205 9525 14445 1838
62. Erato3.12412016.90.1756 390 12546 212
222. Lucia3.12632019.00.1453 2582 8011 211
137. Melibœa3.12642019.10.2074 30758 20422 1322
165. Loreley3.12692019.60.0734 22350 3046 1012
251. Sophia3.13152024.10.1243 777 1576 1020
24. Themis3.13572028.10.1242 1448 3549 049
152. Atala3.13622028.60.0862 8423 4129 1212
10. Hygeia3.13662029.10.1156 2372 28538 349
259. Aletheia3.13692029.30.1176 24145 8832 1040
227. Philosophia3.13932031.60.2131 22623 33052 916
147. Protogenea3.13932031.60.0247 2538 25116 154
171. Ophelia3.14322035.40.1168 14359 10110 234
209. Dido3.14362035.90.0637 25733 20 715
31. Euphrosyne3.14682039.00.2228 9326 3131 2627
90. Antiope3.14752039.70.1645 30115 7129 217
104. Clymene3.15072042.70.1579 5932 4332 254[Pg 34]
57. Mnemosyne3.15102043.00.1145 5325 2002 1512
250. Bettina3.15242044.30.1302 8728 2612 1254
252. Clementina3.15522047.10.0837 3558 20819 102
94. Aurora3.16022052.00.0827 4846 49 84
106. Dione3.16702058.60.1788 2557 6314 438
199. Byblis3.17772069.00.1687 26120 8952 1522
92. Undina3.18512076.30.1024 33127 10252 957
184. Deiopea3.18832079.40.0725 16922 33618 112
176. Idunna3.19062081.60.1641 2034 20113 2231
154. Bertha3.19762088.50.0788 19047 3735 2059
108. Hecuba3.21132101.00.1005 17349 35217 424
122. Gerda3.21772108.20.0415 20345 17843 136
168. Sibylla3.37652266.20.0707 1126 20947 433
225. Henrietta3.40072277.80.2661 29913 20045 2045
229. Adelinda3.41292302.90.1562 3327 3049 211
76. Freia3.41402304.10.1700 9049 2125 23
260. Huberta3.42122311.50.1113 31322 16848 618
65. Maximiliana3.42702317.20.1097 26036 15850 329
121. Hermione3.45352344.20.1255 35750 7646 736
87. Sylvia3.48332374.50.0922 33348 7549 1055
107. Camilla3.48472376.00.0756 11553 17618 954
175. Andromache3.50712399.00.3476 2930 2335 346
190. Ismene3.94712864.30.1634 10539 1770 67
153. Hilda3.95232869.90.1721 28547 22820 755

[Pg 35]
[Pg 36]

PART II.

[Pg 37]

DISCUSSION OF THE FACTS IN TABLE II.

1. Extent of the Zone.

In Table II. the unit of column a is the earth's mean distance from the sun, or ninety-three million miles. On this scale the breadth of the zone is 1.8196. Or, if we estimate the breadth from the perihelion of Æthra (1.612) to the aphelion of Andromache (4.726), it is 3.114,—more than three times the radius of the earth's orbit. A very remarkable characteristic of the group is the interlacing or intertwining of orbits. "One fact," says D'Arrest, "seems above all to confirm the idea of an intimate relation between all the minor planets; it is, that if their orbits are figured under the form of material rings, these rings will be found so entangled that it would be possible, by means of one among them taken at hazard, to lift up all the rest."[6] Our present knowledge of this wide and complicated cluster is the result of a vast amount, not only of observations, but also of mathematical labor. In view, however, of the perturbations of these bodies by the larger planets, and especially by Jupiter, it is easy to see that the discussion[Pg 38] of their motions must present a field of investigation practically boundless.

While the known minor planets were but few in number the theory of Olbers in regard to their origin seemed highly probable; it has, however, been completely disproved by more recent discoveries. The breadth of the zone being now greater than the distance of Mars from the sun, it is no more probable that the asteroids were produced by the disruption of a single planet than that Mercury, Venus, the earth, and Mars originated in a similar manner.

2. The Small Mass of the Asteroids.

In taking a general view of the solar system we cannot fail to be struck by the remarkable fact that Jupiter, whose mass is much greater than that of all other planets united, should be immediately succeeded by a region so nearly destitute of matter as the zone of asteroids. Leverrier inferred from the motion of Mars's perihelion that the mass of Jupiter is at least twelve hundred times greater than that of all the planets in the asteroid ring. The fact is suggestive of Jupiter's dominating energy in the evolution of the asteroid system. We find also something analogous among the satellites of Jupiter, Saturn, and Uranus. Jupiter's third satellite, the largest of the number, is nearly four times greater than the second. Immediately within the orbit of Titan, the largest satellite of Saturn, occurs a wide hiatus, and the volume of the next interior satellite is to that of Titan in the ratio of one to twenty-one. In the Uranian system the widest interval between adjacent orbits is just within the orbit of the bright satellite, Titania.

[Pg 39]

The foregoing facts suggest the inquiry, What effect would be produced by a large planet on interior masses abandoned by a central spheroid? As the phenomena in all instances would be of the same nature, we will consider a single case,—that of Jupiter and the asteroids.

The powerful mass of the exterior body would produce great perturbations of the neighboring small planets abandoned at the solar equator. The disturbed orbits, in some cases, would thus attain considerable eccentricity, so that the matter moving in them would, in perihelion, be brought in contact with the equatorial parts of the central body, and thus become reunited with it.[7] The extreme rarity of the zone between Mars and Jupiter, regarded as a single ring, is thus accounted for in accordance with known dynamical laws.

3. The Limits of Perihelion Distance.

It is sufficiently obvious that whenever the perihelion distance of a planet or comet is less than the sun's radius, a collision must occur as the moving body approaches the focus of its path. The great comet of 1843 passed so near the sun as almost to graze its surface. With a perihelion distance but very slightly less, it would have been precipitated into the sun and incorporated with its mass. In former epochs, when the dimensions of the sun were much greater than at present, this falling of comets into the central orb of the system must have been a comparatively frequent occurrence. Again, if Mercury's orbit had its present eccentricity when the radius[Pg 40] of the solar spheroid was twenty-nine million miles, the planet at its nearest approach to the centre of its motion must have passed through the outer strata of the central body. In such case a lessening of the planet's mean distance would be a necessary consequence. We thus see that in the formation of the solar system the eccentricity of an asteroidal orbit could not increase beyond a moderate limit without the planet's return to the solar mass. The bearing of these views on the arrangement of the minor planets will appear in what follows.

4. Was the Asteroid Zone originally Stable?—Distribution of the Members in Space.

One of the most interesting discoveries of the eighteenth century was Lagrange's law securing the stability of the solar system. This celebrated theorem, however, is not to be understood in an absolute or unlimited sense. It makes no provision against the effect of a resisting medium, or against the entrance of cosmic matter from without. It does not secure the stability of all periodic comets nor of the meteor streams revolving about the sun. In the early stages of the system's development the matter moving in unstable orbits may have been, and probably was, much more abundant than at present. But even now, are we justified in concluding that all known asteroids have stable orbits? For the major planets the secular variations of eccentricity have been calculated, but for the orbits between Mars and Jupiter these limits are unknown. With an eccentricity of 0.252 (less than that of many asteroids), the distance of Hilda's aphelion would be greater than that of Jupiter's perihelion. It seems possible, therefore, that certain[Pg 41] minor planets may have their orbits much changed by Jupiter's disturbing influence.[8]

Whoever looks at a table of asteroids arranged in their order of discovery will find only a perplexing mass of figures. Whether we regard their distances, their inclinations, or the forms of their orbits, the elements of the members are without any obvious connection. Nor is the confusion lessened when the orbits are drawn and presented to the eye. In fact, the crossing and recrossing of so many ellipses of various forms merely increase the entanglement. But can no order be traced in all this complexity? Are there no breaks or vacant spaces within the zone's extreme limits? Has Jupiter's influence been effective in fixing the position and arrangement of the cluster? Such are some of the questions demanding our attention. If "the universe is a book written for man's reading," patient study may resolve the problem contained in these mysterious leaves.

Simultaneously with the discovery of new members in the cluster of minor planets, near the middle of the century, occurred the resolution of the great nebula in Orion. This startling achievement by Lord Rosse's telescope was the signal for the abandonment of the nebular hypothesis by many of its former advocates. To the present writer, however, the partial resolution of a single nebula seemed hardly a sufficient reason for its summary rejection. The question then arose whether any probable test of Laplace's theory could be found in[Pg 42] the solar system itself. The train of thought was somewhat as follows: Several new members have been found in the zone of asteroids; its dimensions have been greatly extended, so that we can now assign no definite limits either to the ring itself or to the number of its planets; if the nebular hypothesis be true, the sun, after Jupiter's separation, extended successively to the various decreasing distances of the several asteroids; the eccentricities of these bodies are generally greater than those of the old planets; this difference is probably due to the disturbing force of Jupiter; the zone includes several distances at which the periods of asteroids would be commensurable with that of Jupiter; in such case the conjunctions of the minor with the major planet would occur in the same parts of its path, the disturbing effects would accumulate, and the eccentricity would become very marked; such bodies in perihelion would return to the sun, and hence blanks or chasms would be formed in particular parts of the zone. On the other hand, if the nebular hypothesis was not true, the occurrence of these gaps was not to be expected. Having thus pointed out a prospective test of the theory, it was announced with some hesitation that those parts of the asteroid zone in which a simple relation of commensurability would obtain between the period of a minor planet and that of Jupiter are distinguished as gaps or chasms similar to the interval in Saturn's ring.

The existence of these blanks was thus predicted in theory before it was established as a fact of observation. When the law was first publicly stated in 1866, but ten asteroids had been found with distances greater than three times that of the earth. The number of such now known is sixty-five. For more than a score of[Pg 43] years the progress of discovery has been watched with lively interest, and the one hundred and eighty new members of the group have been found moving in harmony with this law of distribution.[9]

COMMENSURABILITY OF PERIODS.

When we say that an asteroid's period is commensurable with that of Jupiter, we mean that a certain whole number of the former is equal to another whole number of the latter. For instance, if a minor planet completes two revolutions to Jupiter's one, or five to Jupiter's two, the periods are commensurable. It must be remarked, however, that Jupiter's effectiveness in disturbing the motion of a minor planet depends on the order of commensurability. Thus, if the ratio of the less to the greater period is expressed by the fraction 12, where the difference between the numerator and the denominator is one, the commensurability is of the first order; 13 is of the second; 25, of the third, etc. The difference between the terms of the ratio indicates the frequency of conjunctions while Jupiter is completing the number of revolutions expressed by the numerator. The distance 3.277, corresponding to the ratio 12, is the only case of the first order in the entire ring; those of the second order, answering to 13 and 35, are 2.50 and 3.70. These orders of commensurability may be thus arranged in a tabular form, the radius of the earth's orbit being the unit of distance:

[Pg 44]

Order.Ratio.Distance.
First123.277
Second13, 35

2.50
3.70
Third25, 47, 58

2.82
3.58
3.80
Fourth37, 59, 711

2.95
3.51
3.85

Do these parts of the ring present discontinuities? and, if so, can they be ascribed to a chance distribution? Let us consider them in order.

I.—The Distance 3.277.

At this distance an asteroid's conjunctions with Jupiter would all occur at the same place, and its perturbations would be there repeated at intervals equal to Jupiter's period (11.86 y.). Now, when the asteroids are arranged in the order of their mean distances (as in Table II.) this part of the zone presents a wide chasm. The space between 3.218 and 3.376 remains, hitherto a perfect blank, while the adjacent portions of equal breadth, interior and exterior, contain fifty-four minor planets. The probability that this distribution is not the result of chance is more than three hundred billions to one.

The breadth of this chasm is one-twentieth part of its distance from the sun, or one-eleventh part of the breadth of the entire zone.

II.—The Second Order of Commensurability.—The Distances 2.50 and 3.70.

At the former of these distances an asteroid's period would be one-third of Jupiter's, and at the latter, three-[Pg 45]fifths. That part of the zone included between the distances 2.30 and 2.70 contains one hundred and ten intervals, exclusive of the maximum at the critical distance 2.50. This gap—between Thetis and Hestia—is not only much greater than any other of this number, but is more than sixteen times greater than their average. The distance 3.70 falls in the wide hiatus interior to the orbit of Ismene.

III.—Chasms corresponding to the Third Order.—The Distances 2.82, 3.58, and 3.80.

As the order of commensurability becomes less simple, the corresponding breaks in the zone are less distinctly marked. In the present case conjunctions with Jupiter would occur at angular intervals of 120°. The gaps, however, are still easily perceptible. Between the distances 2.765 and 2.808 we find twenty minor planets. In the next exterior space of equal breadth, containing the distance 2.82, there is but one. This is No. 188, Menippe, whose elements are still somewhat uncertain. The space between 2.851 and 2.894—that is, the part of equal extent immediately beyond the gap—contains thirteen asteroids. The distances 3.58 and 3.80 are in the chasm between Andromache and Ismene.

IV.—The Distances 2.95, 3.51,[10] and 3.85, corresponding to the Fourth Order of Commensurability.

The first of these distances is in the interval between Psyche and Clytemnestra; the second and third, in that exterior to Andromache.

[Pg 46]

The nine cases considered are the only ones in which the conjunctions with Jupiter would occur at less than five points of an asteroid's orbit. Higher orders of commensurability may perhaps be neglected. It will be seen, however, that the distances 2.25, 2.70, 3.03, and 3.23, corresponding to the ratios of the fifth order, 27, 38, 49, and 6/11, still afford traces of Jupiter's influence. The first is in the interval between Augusta and Feronia; the last falls in the same gap with 3.277; and the second and third are in breaks less distinctly marked. It may also be worthy of notice that the rather wide interval between Prymno and Victoria is where ten periods of a minor planet would be equal to three of Jupiter. The distance of Medusa is somewhat uncertain.

The FACT of the existence of well-defined gaps in the designated parts of the ring has been clearly established. But the theory of probability applied in a single instance gives, as we have seen, but one chance in 300,000,000,000 that the distribution is accidental. This improbability is increased many millions of times when we include all the gaps corresponding to simple cases of commensurability. We conclude, therefore, that those discontinuities cannot be referred to a chance arrangement. What, then, was their physical cause? and what has become of the eliminated asteroids?

[Pg 47]

What was said in regard to the limits of perihelion distance may suggest a possible answer to these interesting questions. The doctrine of the sun's gradual contraction is now accepted by a majority of astronomers. According to this theory the solar radius at an epoch not relatively remote was twice what it is at present. At anterior stages it was 0.4, 1.0, 2.0,[11] etc. At the first mentioned the comets of 1843 and 1668, as well as several others, could not have been moving in their present orbits, since in perihelion they must have plunged into the sun. At the second, Encke's comet and all others with perihelia within Mercury's orbit would have shared a similar fate. At the last named all asteroids with perihelion distances less than two would have been re-incorporated with the central mass. As the least distance of Æthra is but 1.587, its orbit could not have had its present form and dimensions when the radius of the solar nebula was equal to the aphelion distance of Mars (1.665).

It is easy to see, therefore, that in those parts of the ring where Jupiter would produce extraordinary disturbance the formation of chasms would be very highly probable.

5. Relations between certain Adjacent Orbits.

The distances, periods, inclinations, and eccentricities of Hilda and Ismene, the outermost pair of the group, are very nearly identical. It is a remarkable fact, however, that the longitudes of their perihelia differ by almost exactly 180°. Did they separate at nearly the[Pg 48] same time from opposite sides of the solar nebula? Other adjacent pairs having a striking similarity between their orbital elements are Sirona and Ceres, Fides and Maia, Fortuna and Eurynome, and perhaps a few others. Such coincidences can hardly be accidental. Original asteroids, soon after their detachment from the central body, may have been separated by the sun's unequal attraction on their parts. Such divisions have occurred in the world of comets, why not also in the cluster of minor planets?

6. The Eccentricities.

The least eccentric orbit in the group is that of Philomela (196); the most eccentric that of Æthra (132). Comparing these with the orbit of the second comet of 1867 we have

The eccentricity of Philomela = 0.01
""" Æthra = 0.38
""" Comet II. 1867 (ret. in 1885) = 0.41

The orbit of Æthra, it is seen, more nearly resembles the last than the first. It might perhaps be called the connecting-link between planetary and cometary orbits.

The average eccentricity of the two hundred and sixty-eight asteroids whose orbits have been calculated is 0.1569. As with the orbits of the old planets, the eccentricities vary within moderate limits, some increasing, others diminishing. The average, however, will probably remain very nearly the same. An inspection of the table shows that while but one orbit is less eccentric than the earth's, sixty-nine depart more from[Pg 49] the circular form than the orbit of Mercury. These eccentricities seem to indicate that the forms of the asteroidal orbits were influenced by special causes. It may be worthy of remark that the eccentricity does not appear to vary with the distance from the sun, being nearly the same for the interior members of the zone as for the exterior.

7. The Inclinations.

The inclinations in Table II. are thus distributed:

From 0° to 4°70
" 4° to 8°83
" 8° to 12°59
" 12° to 16°32
" 16° to 20°8
" 20° to 24°8
" 24° to 28°7
" 28° to 32°0
above 32°1

One hundred and fifty-four, considerably more than half, have inclinations between 3° and 11°, and the mean of the whole number is about 8°,—slightly greater than the inclination of Mercury, or that of the plane of the sun's equator. The smallest inclination, that of Massalia, is 0° 41´, and the largest, that of Pallas, is about 35°. Sixteen minor planets, or six per cent. of the whole number, have inclinations exceeding 20°. Does any relation obtain between high inclinations and great eccentricities? These elements in the cases named above are as follows:

[Pg 50]

Asteroid.Inclination.Eccentricity.
Pallas 34°42´ 0.238
Istria 2630 0.353
Euphrosyne 2629 0.228
Anna 2524 0.263
Gallia 2521 0.185
Æthra 250 0.380
Eukrate 2457 0.236
Eva 2425 0.347
Niobe 2319 0.173
Eunice 2317 0.129
Electra 2255 0.208
Idunna 2231 0.164
Phocea 2135 0.255
Artemis 2131 0.175
Bertha 2059 0.085
Henrietta 2047 0.260

This comparison shows the most inclined orbits to be also very eccentric; Bertha and Eunice being the only exceptions in the foregoing list. On the other hand, however, we find over fifty asteroids with eccentricities exceeding 0.20 whose inclinations are not extraordinary. The dependence of the phenomena on a common cause can, therefore, hardly be admitted. At least, the forces which produced the great eccentricity failed in a majority of cases to cause high inclinations.

8. Longitudes of the Perihelia.

The perihelia of the asteroidal orbits are very unequally distributed; one hundred and thirty-six—a majority of the whole number determined—being within the 120° from longitude 290° 50´ to 59° 50´. The maximum occurs between 30° and 60°, where thirty-five perihelia are found in 30° of longitude.

[Pg 51]

9. Distribution of the Ascending Nodes.

An inspection of the column containing the longitudes of the ascending nodes, in Table II., indicates two well-marked maxima, each extending about sixty degrees, in opposite parts of the heavens.

I.  From 310° to 10°, containing 61  ascending nodes.
II.  " 120° to 180°,"59 ""
  Making in 120°120 ""

A uniform distribution would give 89. An arc of 84°—from 46° to 130°—contains the ascending nodes of all the old planets. This arc, it will be noticed, is not coincident with either of the maxima found for the asteroids.

10. The Periods.

Since, according to Kepler's third law, the periods of planets depend upon their mean distances, the clustering tendency found in the latter must obtain also in the former. This marked irregularity in the order of periods is seen below.

Between 1100 and 1200 days 6 periods.
" 1200 " 1300 " 7 "
" 1300 " 1400 " 43 "
" 1400 " 1500 " 13 "
" 1500 " 1600 " 46 "
" 1600 " 1700 " 54 "
" 1700 " 1800 " 20 "
" 1800 " 1900 " 13 "
" 1900 " 2000 " 19 "
" 2000 " 2100 " 33 "
" 2100 " 2200 " 2 "
" 2200 " 2300 " 2 "
" 2300 " 2400 " 8 "
" 2400 " 2800 " 0 "
" 2800 " 2900 " 2 "

[Pg 52] The period of Hilda (153) is more than two and a half times that of Medusa (149). This is greater than the ratio of Saturn's period to that of Jupiter. The maximum observed between 2000 and 2100 days corresponds to the space immediately interior to chasm I. on a previous page, that between 1300 and 1400 to the space interior to the second, and that between 1500 and 1700 to the part of the zone within the fourth gap. The table presents quite numerous instances of approximate equality; in forty-three cases the periods differing less than twenty-four hours. It is impossible to say, however, whether any two of these periods are exactly equal. In cases of a very close approach two asteroids, notwithstanding their small mass, may exert upon each other quite sensible perturbations.

11. Origin of the Asteroids.

But four minor planets had been discovered when Laplace issued his last edition of the "Système du Monde." The author, in his celebrated seventh note in the second volume of that work, explained the origin of these bodies by assuming that the primitive ring from which they were formed, instead of collecting into a single sphere, as in the case of the major planets, broke up into four distinct masses. But the form and extent of the cluster as now known, as well as the observed facts bearing on the constitution of Saturn's ring, seem to require a modification of Laplace's theory. Throughout the greater part of the interval between Mars and Jupiter an almost continuous succession of small planetary masses—not nebulous rings—appears to have been abandoned at the solar equator. The entire cluster,[Pg 53] distributed throughout a space whose outer radius exceeds the inner by more than two hundred millions of miles, could not have originated, as supposed by Laplace, in a single nebulous zone the different parts of which revolved with the same angular velocity. The following considerations may furnish a suggestion in regard to the mode in which these bodies were separated from the equator of the solar nebula.

(a) The perihelion distance of Jupiter is 4.950, while the aphelion distance of Hilda is 4.623. If, therefore, the sun once extended to the latter, the central attraction of its mass on an equatorial particle was but five times greater than Jupiter's perihelion influence on the same. It is easy to see, then, that this "giant planet" would produce enormous tidal elevations in the solar mass.

(b) The centrifugal force would be greatest at the crest of this tidal wave.

(c) Three periods of solar revolution were then about equal to two periods of Jupiter. The disturbing influence of the planet would therefore be increased at each conjunction with this protuberance. The ultimate separation (not of a ring but) of a planetary mass would be the probable result of these combined and accumulating forces.

12. Variability of Certain Asteroids.

Observations of some minor planets have indicated a variation of their apparent magnitudes. Frigga, discovered by Dr. Peters in 1862, was observed at the next opposition in 1864; but after this it could not be[Pg 54] found till 1868, when it was picked up by Professor Tietjen. From the latter date its light seems again to have diminished, as all efforts to re-observe it were unsuccessful till 1879. According to Dr. Peters, the change in brightness during the period of observation in that year was greater than that due to its varying distance. No explanation of such changes has yet been offered. It has been justly remarked, however, that "the length of the period of the fluctuation does not allow of our connecting it with the rotation of the planet."

13. The Average Asteroid Orbit.

At the meeting of the American Association for the Advancement of Science in 1884, Professor Mark W. Harrington, of Ann Arbor, Michigan, presented a paper in which the elements of the asteroid system were considered on the principle of averages. Two hundred and thirty orbits, all that had then been determined, were employed in the discussion. Professor Harrington supposes two planes to intersect the ecliptic at right angles; one passing through the equinoxes and the other through the solstices. These planes will intersect the asteroidal orbits, each in four points, and "the mean intersection at each solstice and equinox may be considered a point in the average orbit."

In 1883 the Royal Academy of Denmark offered its gold medal for a statistical examination of the orbits of the small planets considered as parts of a ring around the sun. The prize was awarded in 1885 to M. Svedstrup, of Copenhagen. The results obtained by these astronomers severally are as follows:

[Pg 55]

 Harrington.Svedstrup.
Longitude of perihelion 14°39´ 101°48´
Longitude of ascending node 11356 13327
Inclination 10 66
Eccentricity 0.0448 0.0281
Mean distance 2.7010 2.6435

These elements, with the exception of the first, are in reasonable harmony.

14. The Relation of Short-Period Comets to the Zone of Asteroids.

Did comets originate within the solar system, or do they enter it from without? Laplace assigned them an extraneous origin, and his view is adopted by many eminent astronomers. With all due respect to the authority of great names, the present writer has not wholly abandoned the theory that some comets of short period are specially related to the minor planets. According to M. Lehmann-Filhès, the eccentricity of the third comet of 1884, before its last close approach to Jupiter, was only 0.2787.[12] This is exceeded by that of twelve known minor planets. Its mean distance before this great perturbation was about 4.61, and six of its periods were nearly equal to five of Jupiter's,—a commensurability of the first order. According to Hind and Krueger, the great transformation of its orbit by Jupiter's influence occurred in May, 1875. It had previously[Pg 56] been an asteroid too remote to be seen even in perihelion. This body was discovered by M. Wolf, at Heidelberg, September 17, 1884. Its present period is about six and one-half years.

The perihelion distance of the comet 1867 II. at its return in 1885 was 2.073; its aphelion is 4.897; so that its entire path, like those of the asteroids, is included between the orbits of Mars and Jupiter. Its eccentricity, as we have seen, is little greater than that of Æthra, and its period, inclination, and longitude of the ascending node are approximately the same with those of Sylvia, the eighty-seventh minor planet. In short, this comet may be regarded as an asteroid whose elements have been considerably modified by perturbation.

It has been stated that the gap at the distance 3.277 is the only one corresponding to the first order of commensurability. The distance 3.9683, where an asteroid's period would be two-thirds of Jupiter's, is immediately beyond the outer limit of the cluster as at present known; the mean distance of Hilda being 3.9523. The discovery of new members beyond this limit is by no means improbable. Should a minor planet at the mean distance 3.9683 attain an eccentricity of 0.3—and this is less than that of eleven now known—its aphelion would be more remote than the perihelion of Jupiter. Such an orbit might not be stable. Its form and extent might be greatly changed after the manner of Lexell's comet. Two well-known comets, Faye's and Denning's, have periods approximately equal to two-thirds of Jupiter's. In like manner the periods of D'Arrest's and Biela's comets correspond to the hiatus at 3.51, and that of 1867 II. to that at 3.277.

Of the thirteen telescopic comets whose periods cor[Pg 57]respond to mean distances within the asteroid zone, all have direct motion; all have inclinations similar to those of the minor planets; and their eccentricities are generally less than those of other known comets. Have these facts any significance in regard to their origin?


[Pg 58]
[Pg 59]

APPENDIX.

NOTE A.
THE POSSIBLE EXISTENCE OF ASTEROIDS IN UNDISCOVERED RINGS.

If Jupiter's influence was a factor in the separation of planetules at the sun's equator, may not similar clusters exist in other parts of our system? The hypothesis is certainly by no means improbable. For anything we know to the contrary a group may circulate between Jupiter and Saturn; such bodies, however, could not be discovered—at least not by ordinary telescopes—on account of their distance. The Zodiacal Light, it has been suggested, may be produced by a cloud of indefinitely small particles related to the planets between the sun and Mars. The rings of Saturn are merely a dense asteroidal cluster; and, finally, the phenomena of luminous meteors indicate the existence of small masses of matter moving with different velocities in interstellar space.

NOTE B.
THE ORIGIN AND STRUCTURE OF COSMICAL RINGS.

The general theory of cosmical rings and of their arrangement in sections or clusters with intervening chasms may be briefly stated in the following propositions:

[Pg 60]

I.

Whenever the separating force of a primary body on a secondary or satellite is greater than the central attraction of the latter on its superficial stratum, the satellite, if either gaseous or liquid, will be transformed into a ring.

Examples.—Saturn's ring, and the meteoric rings of April 20, August 10, November 14, and November 27.

See Payne's Sidereal Messenger, April, 1885.

II.

When a cosmical body is surrounded by a ring of considerable breadth, and has also exterior satellites at such distances that a simple relation of commensurability would obtain between the periods of these satellites and those of certain particles of the ring, the disturbing influence of the former will produce gaps or intervals in the ring so disturbed.

See "Meteoric Astronomy," Chapter XII.; also the Proceedings of the American Philosophical Society, October 6, 1871; and the Sidereal Messenger for February, 1884; where the papers referred to assign a physical cause for the gaps in Saturn's ring.

THE END.

FOOTNOTES:

[1] The discoverer, Piazzi, was not, as has been so often affirmed, one of the astronomers to whom the search had been especially committed.

[2] Massalia was discovered by De Gasparis, at Naples, Sept. 19, 1852, and independently, the next night, by Chacornac, at Marseilles. The name was given by the latter.

[3] Astr. Nach., No. 932.

[4] Monthly Notices, vol. xxvii.

[5] Annals of the Obs. of Harv. Coll., 1879.

[6] This ingenious idea may be readily extended. The least distance of Æthra is less than the present aphelion distance of Mars; and the maximum aphelion distance of the latter exceeds the perihelion distance of several known asteroids. Moreover, if we represent the orbits of the major planets, and also those of the comets of known periods, by material rings, it is easy to see that the major as well as the minor planets are all linked together in the manner suggested by D'Arrest.

[7] The effects of Jupiter's disturbing influence will again be resumed.

[8] Not only nebulæ are probably unstable, but also many of the sidereal systems. The Milky Way itself was so regarded by Sir William Herschel.

[9] Menippe, No. 188, is placed in one of the gaps by its calculated elements; but the fact that it has not been seen since the year of its discovery, 1878, indicates a probable error in its elements.

[10] The minor planet Andromache, immediately interior to the critical distance 3.51, has elements somewhat remarkable. With two exceptions, Æthra (132) and Istria (183), it has the greatest eccentricity (0.3571),—nearly equal to that of the comet 1867 II. at its last return. Its perihelion distance is 2.2880, its aphelion 4.7262; hence the distance from the perihelion to the aphelion of its orbit is greater than its least distance from the sun, and it crosses the orbits of all members of the group so far as known; its least distance from the sun being considerably less than the aphelion of Medusa, and its greatest exceeding the aphelion of Hilda.

[11] The unit being the sun's distance from the earth.

[12] Annuaire, 1886.