The Asteroids; Or Minor Planets Between Mars and Jupiter. by Kirkwood, Daniel

Transcriber's note:

Text enclosed by underscores is in italics (_italics_).

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.

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.

Copyright, 1887, by Daniel Kirkwood.

[Illustration]

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 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.

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

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

PART I.

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 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.

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 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 existed 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.

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 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 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.

TABLE I.

_The Asteroids in the Order of their Discovery._

-----------------+----------------+---------------+------------ Asteroids. | Date of | Name of | Place of | Discovery. | Discoverer. | Discovery. -----------------+----------------+---------------+------------ 1. Ceres | 1801, Jan. 1 | Piazzi | Palermo 2. Pallas | 1802, Mar. 28 | Olbers | Bremen 3. Juno | 1804, Sept. 1 | Harding | Lilienthal 4. Vesta | 1807, Mar. 29 | Olbers | Bremen 5. Astræa | 1845, Dec. 8 | Hencke | Driessen 6. Hebe | 1847, July 1 | Hencke | Driessen 7. Iris | 1847, Aug. 14 | Hind | London 8. Flora | 1847, Oct. 18 | Hind | London 9. Metis | 1848, Apr. 26 | Graham | Markree 10. Hygeia | 1849, Apr. 12 | De Gasparis | Naples 11. Parthenope | 1850, May 11 | De Gasparis | Naples 12. Victoria | 1850, Sept. 13 | Hind | London 13. Egeria | 1850, Nov. 2 | De Gasparis | Naples 14. Irene | 1851, May 19 | Hind | London 15. Eunomia | 1851, July 29 | De Gasparis | Naples 16. Psyche | 1852, Mar. 17 | De Gasparis | Naples 17. Thetis | 1852, Apr. 17 | Luther | Bilk 18. Melpomene | 1852, June 24 | Hind | London 19. Fortuna | 1852, Aug. 22 | Hind | London 20. Massalia | 1852, Sept. 19 | De Gasparis | Naples 21. Lutetia | 1852, Nov. 15 | Goldschmidt | Paris 22. Calliope | 1852, Nov. 16 | Hind | London 23. Thalia | 1852, Dec. 15 | Hind | London 24. Themis | 1853, Apr. 5 | De Gasparis | Naples 25. Phocea | 1853, Apr. 6 | Chacornac | Marseilles 26. Proserpine | 1853, May 5 | Luther | Bilk 27. Euterpe | 1853, Nov. 8 | Hind | London 28. Bellona | 1854, Mar. 1 | Luther | Bilk 29. Amphitrite | 1854, Mar. 1 | Marth | London 30. Urania | 1854, July 22 | Hind | London 31. Euphrosyne | 1854, Sept. 1 | Ferguson | Washington 32. Pomona | 1854, Oct. 26 | Goldschmidt | Paris 33. Polyhymnia | 1854, Oct. 28 | Chacornac | Paris 34. Circe | 1855, Apr. 6 | Chacornac | Paris 35. Leucothea | 1855, Apr. 19 | Luther | Bilk 36. Atalanta | 1855, Oct. 5 | Goldschmidt | Paris 37. Fides | 1855, Oct. 5 | Luther | Bilk 38. Leda | 1856, Jan. 12 | Chacornac | Paris 39. Lætitia | 1856, Feb. 8 | Chacornac | Paris 40. Harmonia | 1856, Mar. 31 | Goldschmidt | Paris 41. Daphne | 1856, May 22 | Goldschmidt | Paris 42. Isis | 1856, May 23 | Pogson | Oxford 43. Ariadne | 1857, Apr. 15 | Pogson | Oxford 44. Nysa | 1857, May 27 | Goldschmidt | Paris 45. Eugenia | 1857, June 27 | Goldschmidt | Paris 46. Hestia | 1857, Aug. 16 | Pogson | Oxford 47. Aglaia | 1857, Sept. 15 | Luther | Bilk 48. Doris | 1857, Sept. 19 | Goldschmidt | Paris 49. Pales | 1857, Sept. 19 | Goldschmidt | Paris 50. Virginia | 1857, Oct. 4 | Ferguson | Washington 51. Nemausa | 1858, Jan. 22 | Laurent | Nismes 52. Europa | 1858, Feb. 4 | Goldschmidt | Paris 53. Calypso | 1858, Apr. 4 | Luther | Bilk 54. Alexandra | 1858, Sept. 10 | Goldschmidt | Paris 55. Pandora | 1858, Sept. 10 | Searle | Albany 56. Melete | 1857, Sept. 9 | Goldschmidt | Paris 57. Mnemosyne | 1859, Sept. 22 | Luther | Bilk 58. Concordia | 1860, Mar. 24 | Luther | Bilk 59. Olympia | 1860, Sept. 12 | Chacornac | Paris 60. Echo | 1860, Sept. 16 | Ferguson | Washington 61. Danaë | 1860, Sept. 9 | Goldschmidt | Paris 62. Erato | 1860, Sept. 14 | Foerster and | Berlin | | Lesser | 63. Ausonia | 1861, Feb. 10 | De Gasparis | Naples 64. Angelina | 1861, Mar. 4 | Tempel | Marseilles 65. Maximiliana | 1861, Mar. 8 | Tempel | Marseilles 66. Maia | 1861, Apr. 9 | Tuttle | Cambridge, U.S. 67. Asia | 1861, Apr. 17 | Pogson | Madras 68. Leto | 1861, Apr. 29 | Luther | Bilk 69. Hesperia | 1861, Apr. 29 | Schiaparelli | Milan 70. Panopea | 1861, May 5 | Goldschmidt | Paris 71. Niobe | 1861, Aug. 13 | Luther | Bilk 72. Feronia | 1862, May 29 | Peters and | Clinton | | Safford | 73. Clytie | 1862, Apr. 7 | Tuttle | Cambridge 74. Galatea | 1862, Aug. 29 | Tempel | Marseilles 75. Eurydice | 1862, Sept. 22 | Peters | Clinton 76. Freia | 1862, Oct. 21 | D'Arrest | Copenhagen 77. Frigga | 1862, Nov. 12 | Peters | Clinton 78. Diana | 1863, Mar. 15 | Luther | Bilk 79. Eurynome | 1863, Sept. 14 | Watson | Ann Arbor 80. Sappho | 1864, May 2 | Pogson | Madras 81. Terpsichore | 1864, Sept. 30 | Tempel | Marseilles 82. Alcmene | 1864, Nov. 27 | Luther | Bilk 83. Beatrix | 1865, Apr. 26 | De Gasparis | Naples 84. Clio | 1865, Aug. 25 | Luther | Bilk 85. Io | 1865, Sept. 19 | Peters | Clinton 86. Semele | 1866, Jan. 14 | Tietjen | Berlin 87. Sylvia | 1866, May 16 | Pogson | Madras 88. Thisbe | 1866, June 15 | Peters | Clinton 89. Julia | 1866, Aug. 6 | Stephan | Marseilles 90. Antiope | 1866, Oct. 1 | Luther | Bilk 91. Ægina | 1866, Nov. 4 | Borelly | Marseilles 92. Undina | 1867, July 7 | Peters | Clinton 93. Minerva | 1867, Aug. 24 | Watson | Ann Arbor 94. Aurora | 1867, Sept. 6 | Watson | Ann Arbor 95. Arethusa | 1867, Nov. 24 | Luther | Bilk 96. Ægle | 1868, Feb. 17 | Coggia | Marseilles 97. Clotho | 1868, Feb. 17 | Coggia | Marseilles 98. Ianthe | 1868, Apr. 18 | Peters | Clinton 99. Dike | 1868, May 28 | Borelly | Marseilles 100. Hecate | 1868, July 11 | Watson | Ann Arbor 101. Helena | 1868, Aug. 15 | Watson | Ann Arbor 102. Miriam | 1868, Aug. 22 | Peters | Clinton 103. Hera | 1868, Sept. 7 | Watson | Ann Arbor 104. Clymene | 1868, Sept. 13 | Watson | Ann Arbor 105. Artemis | 1868, Sept. 16 | Watson | Ann Arbor 106. Dione | 1868, Oct. 10 | Watson | Ann Arbor 107. Camilla | 1868, Nov. 17 | Pogson | Madras 108. Hecuba | 1869, Apr. 2 | Luther | Bilk 109. Felicitas | 1869, Oct. 9 | Peters | Clinton 110. Lydia | 1870, Apr. 19 | Borelly | Marseilles 111. Ate | 1870, Aug. 14 | Peters | Clinton 112. Iphigenia | 1870, Sept. 19 | Peters | Clinton 113. Amalthea | 1871, Mar. 12 | Luther | Bilk 114. Cassandra | 1871, July 23 | Peters | Clinton 115. Thyra | 1871, Aug. 6 | Watson | Ann Arbor 116. Sirona | 1871, Sept. 8 | Peters | Clinton 117. Lomia | 1871, Sept. 12 | Borelly | Marseilles 118. Peitho | 1872, Mar. 15 | Luther | Bilk 119. Althea | 1872, Apr. 3 | Watson | Ann Arbor 120. Lachesis | 1872, Apr. 10 | Borelly | Marseilles 121. Hermione | 1872, May 12 | Watson | Ann Arbor 122. Gerda | 1872, July 31 | Peters | Clinton 123. Brunhilda | 1872, July 31 | Peters | Clinton 124. Alceste | 1872, Aug. 23 | Peters | Clinton 125. Liberatrix | 1872, Sept. 11 | Prosper Henry | Paris 126. Velleda | 1872, Nov. 5 | Paul Henry | Paris 127. Johanna | 1872, Nov. 5 | Prosper Henry | Paris 128. Nemesis | 1872, Nov. 25 | Watson | Ann Arbor 129. Antigone | 1873, Feb. 5 | Peters | Clinton 130. Electra | 1873, Feb. 17 | Peters | Clinton 131. Vala | 1873, May 24 | Peters | Clinton 132. Æthra | 1873, June 13 | Watson | Ann Arbor 133. Cyrene | 1873, Aug. 16 | Watson | Ann Arbor 134. Sophrosyne | 1873, Sept. 27 | Luther | Bilk 135. Hertha | 1874, Feb. 18 | Peters | Clinton 136. Austria | 1874, Mar. 18 | Palisa | Pola 137. Melibœa | 1874, Apr. 21 | Palisa | Pola 138. Tolosa | 1874, May 19 | Perrotin | Toulouse 139. Juewa | 1874, Oct. 10 | Watson | Pekin 140. Siwa | 1874, Oct. 13 | Palisa | Pola 141. Lumen | 1875, Jan. 13 | Paul Henry | Paris 142. Polana | 1875, Jan. 28 | Palisa | Pola 143. Adria | 1875, Feb. 23 | Palisa | Pola 144. Vibilia | 1875, June 3 | Peters | Clinton 145. Adeona | 1875, June 3 | Peters | Clinton 146. Lucina | 1875, June 8 | Borelly | Marseilles 147. Protogenea | 1875, July 10 | Schulhof | Vienna 148. Gallia | 1875, Aug. 7 | Prosper Henry | Paris 149. Medusa | 1875, Sept. 21 | Perrotin | Toulouse 150. Nuwa | 1875, Oct. 18 | Watson | Ann Arbor 151. Abundantia | 1875, Nov. 1 | Palisa | Pola 152. Atala | 1875, Nov. 2 | Paul Henry | Paris 153. Hilda | 1875, Nov. 2 | Palisa | Pola 154. Bertha | 1875, Nov. 4 | Prosper Henry | Paris 155. Scylla | 1875, Nov. 8 | Palisa | Pola 156. Xantippe | 1875, Nov. 22 | Palisa | Pola 157. Dejanira | 1875, Dec. 1 | Borelly | Marseilles 158. Coronis | 1876, Jan. 4 | Knorre | Berlin 159. Æmilia | 1876, Jan. 26 | Paul Henry | Paris 160. Una | 1876, Feb. 20 | Peters | Clinton 161. Athor | 1876, Apr. 19 | Watson | Ann Arbor 162. Laurentia | 1876, Apr. 21 | Prosper Henry | Paris 163. Erigone | 1876, Apr. 26 | Perrotin | Toulouse 164. Eva | 1876, July 12 | Paul Henry | Paris 165. Loreley | 1876, Aug. 9 | Peters | Clinton 166. Rhodope | 1876, Aug. 15 | Peters | Clinton 167. Urda | 1876, Aug. 28 | Peters | Clinton 168. Sibylla | 1876, Sept. 27 | Watson | Ann Arbor 169. Zelia | 1876, Sept. 28 | Prosper Henry | Paris 170. Maria | 1877, Jan. 10 | Perrotin | Toulouse 171. Ophelia | 1877, Jan. 13 | Borelly | Marseilles 172. Baucis | 1877, Feb. 5 | Borelly | Marseilles 173. Ino | 1877, Aug. 1 | Borelly | Marseilles 174. Phædra | 1877, Sept. 2 | Watson | Ann Arbor 175. Andromache | 1877, Oct. 1 | Watson | Ann Arbor 176. Idunna | 1877, Oct. 14 | Peters | Clinton 177. Irma | 1877, Nov. 5 | Paul Henry | Paris 178. Belisana | 1877, Nov. 6 | Palisa | Pola 179. Clytemnestra| 1877, Nov. 11 | Watson | Ann Arbor 180. Garumna | 1878, Jan. 29 | Perrotin | Toulouse 181. Eucharis | 1878, Feb. 2 | Cottenot | Marseilles 182. Elsa | 1878, Feb. 7 | Palisa | Pola 183. Istria | 1878, Feb. 8 | Palisa | Pola 184. Deiopea | 1878, Feb. 28 | Palisa | Pola 185. Eunice | 1878, Mar. 1 | Peters | Clinton 186. Celuta | 1878, Apr. 6 | Prosper Henry | Paris 187. Lamberta | 1878, Apr. 11 | Coggia | Marseilles 188. Menippe | 1878, June 18 | Peters | Clinton 189. Phthia | 1878, Sept. 9 | Peters | Clinton 190. Ismene | 1878, Sept. 22 | Peters | Clinton 191. Kolga | 1878, Sept. 30 | Peters | Clinton 192. Nausicaa | 1879, Feb. 17 | Palisa | Pola 193. Ambrosia | 1879, Feb. 28 | Coggia | Marseilles 194. Procne | 1879, Mar. 21 | Peters | Clinton 195. Euryclea | 1879, Apr. 22 | Palisa | Pola 196. Philomela | 1879, May 14 | Peters | Clinton 197. Arete | 1879, May 21 | Palisa | Pola 198. Ampella | 1879, June 13 | Borelly | Marseilles 199. Byblis | 1879, July 9 | Peters | Clinton 200. Dynamene | 1879, July 27 | Peters | Clinton 201. Penelope | 1879, Aug. 7 | Palisa | Pola 202. Chryseis | 1879, Sept. 11 | Peters | Clinton 203. Pompeia | 1879, Sept. 25 | Peters | Clinton 204. Callisto | 1879, Oct. 8 | Palisa | Pola 205. Martha | 1879, Oct. 13 | Palisa | Pola 206. Hersilia | 1879, Oct. 13 | Peters | Clinton 207. Hedda | 1879, Oct. 17 | Palisa | Pola 208. Lachrymosa | 1879, Oct. 21 | Palisa | Pola 209. Dido | 1879, Oct. 22 | Peters | Clinton 210. Isabella | 1879, Nov. 12 | Palisa | Pola 211. Isolda | 1879, Dec. 10 | Palisa | Pola 212. Medea | 1880, Feb. 6 | Palisa | Pola 213. Lilæa | 1880, Feb. 16 | Peters | Clinton 214. Aschera | 1880, Feb. 26 | Palisa | Pola 215. Œnone | 1880, Apr. 7 | Knorre | Berlin 216. Cleopatra | 1880, Apr. 10 | Palisa | Pola 217. Eudora | 1880, Aug. 30 | Coggia | Marseilles 218. Bianca | 1880, Sept. 4 | Palisa | Pola 219. Thusnelda | 1880, Sept. 20 | Palisa | Pola 220. Stephania | 1881, May 19 | Palisa | Vienna 221. Eos | 1882, Jan. 18 | Palisa | Vienna 222. Lucia | 1882, Feb. 9 | Palisa | Vienna 223. Rosa | 1882, Mar. 9 | Palisa | Vienna 224. Oceana | 1882, Mar. 30 | Palisa | Vienna 225. Henrietta | 1882, Apr. 19 | Palisa | Vienna 226. Weringia | 1882, July 19 | Palisa | Vienna 227. Philosophia | 1882, Aug. 12 | Paul Henry | Paris 228. Agathe | 1882, Aug. 19 | Palisa | Vienna 229. Adelinda | 1882, Aug. 22 | Palisa | Vienna 230. Athamantis | 1882, Sept. 3 | De Ball | Bothcamp 231. Vindobona | 1882, Sept. 10 | Palisa | Vienna 232. Russia | 1883, Jan. 31 | Palisa | Vienna 233. Asterope | 1883, May 11 | Borelly | Marseilles 234. Barbara | 1883, Aug. 13 | Peters | Clinton 235. Caroline | 1883, Nov. 29 | Palisa | Vienna 236. Honoria | 1884, Apr. 26 | Palisa | Vienna 237. Cœlestina | 1884, June 27 | Palisa | Vienna 238. Hypatia | 1884, July 1 | Knorre | Berlin 239. Adrastea | 1884, Aug. 18 | Palisa | Vienna 240. Vanadis | 1884, Aug. 27 | Borelly | Marseilles 241. Germania | 1884, Sept. 12 | Luther | Dusseldorf 242. Kriemhild | 1884, Sept. 22 | Palisa | Vienna 243. Ida | 1884, Sept. 29 | Palisa | Vienna 244. Sita | 1884, Oct. 14 | Palisa | Vienna 245. Vera | 1885, Feb. 6 | Pogson | Madras 246. Asporina | 1885, Mar. 6 | Borelly | Marseilles 247. Eukrate | 1885, Mar. 14 | Luther | Dusseldorf 248. Lameia | 1885, June 5 | Palisa | Vienna 249. Ilse | 1885, Aug. 17 | Peters | Clinton 250. Bettina | 1885, Sept. 3 | Palisa | Vienna 251. Sophia | 1885, Oct. 4 | Palisa | Vienna 252. Clementina | 1885, Oct. 27 | Perrotin | Nice 253. Mathilde | 1885, Nov. 12 | Palisa | Vienna 254. Augusta | 1886, Mar. 31 | Palisa | Vienna 255. Oppavia | 1886, Mar. 31 | Palisa | Vienna 256. Walpurga | 1886, Apr. 3 | Palisa | Vienna 257. Silesia | 1886, Apr. 5 | Palisa | Vienna 258. Tyche | 1886, May 4 | Luther | Dusseldorf 259. Aletheia | 1886, June 28 | Peters | Clinton 260. Huberta | 1886, Oct. 3 | Palisa | Vienna 261. Prymno | 1886, Oct. 31 | Peters | Clinton 262. Valda | 1886, Nov. 3 | Palisa | Vienna 263. Dresda | 1886, Nov. 3 | Palisa | Vienna 264. Libussa | 1886, Dec. 17 | Peters | Clinton 265. Anna | 1887, Feb. 25 | Palisa | Vienna 266. Aline | 1887, May 17 | Palisa | Vienna 267. Tirza | 1887, May 27 | Charlois | Nice 268. | 1887, June 9 | Borelly | Marseilles 269. | 1887, Sept. 21 | Palisa | Vienna 270. | 1887, Oct. 8 | Peters | Clinton 271. | 1887, Oct. 16 | Knorre | Berlin -----------------+----------------+---------------+------------

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, 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. 1879 20 1875 17 1868 12 1878 12

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:

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 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, 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 matter 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.

TABLE II.

_Elements of the Asteroids._

-----------------+--------+---------+--------+----------+----------+-------- Name | _a_ | _P_ | _e_ | _π_ | ☊ | _i_ -----------------+--------+---------+--------+----------+----------+-------- 149. Medusa | 2.1327 | 1137.7d | 0.1194 | 246° 37´ | 342° 13´ | 1° 6´ 244. Sita | 2.1765 | 1172.8 | 0.1370 | 13 8 | 208 37 | 2 50 228. Agathe | 2.2009 | 1192.6 | 0.2405 | 329 23 | 313 18 | 2 33 8. Flora | 2.2014 | 1193.3 | 0.1567 | 32 54 | 110 18 | 5 53 43. Ariadne | 2.2033 | 1194.5 | 0.1671 | 277 58 | 264 35 | 3 28 254. Augusta | 2.2060 | 1196.8 | 0.1227 | 260 47 | 28 9 | 4 36 72. Feronia | 2.2661 | 1246.0 | 0.1198 | 307 58 | 207 49 | 5 24 40. Harmonia | 2.2673 | 1247.0 | 0.0466 | 0 54 | 93 35 | 4 16 207. Hedda | 2.2839 | 1260.7 | 0.0301 | 217 2 | 28 51 | 3 49 136. Austria | 2.2863 | 1262.7 | 0.0849 | 316 6 | 186 7 | 9 33 18. Melpomene | 2.2956 | 1270.4 | 0.2177 | 15 6 | 150 4 | 10 9 80. Sappho | 2.2962 | 1270.9 | 0.2001 | 355 18 | 218 44 | 8 37 261. Prymno | 2.3062 | 1278.4 | 0.0794 | 179 35 | 96 33 | 3 38 12. Victoria | 2.3342 | 1302.7 | 0.2189 | 301 39 | 235 35 | 8 23 27. Euterpe | 2.3472 | 1313.5 | 0.1739 | 87 59 | 93 51 | 1 36 219. Thusnelda | 2.3542 | 1319.4 | 0.2247 | 340 34 | 200 44 | 10 47 163. Erigone | 2.3560 | 1320.9 | 0.1567 | 93 46 | 159 2 | 4 42 169. Zelia | 2.3577 | 1322.3 | 0.1313 | 326 20 | 354 38 | 5 31 4. Vesta | 2.3616 | 1325.6 | 0.0884 | 250 57 | 103 29 | 7 8 186. Celuta | 2.3623 | 1326.2 | 0.1512 | 327 24 | 14 34 | 13 6 84. Clio | 2.3629 | 1326.7 | 0.2360 | 339 20 | 327 28 | 9 22 51. Nemausa | 2.3652 | 1328.6 | 0.0672 | 174 43 | 175 52 | 9 57 220. Stephania | 2.3666 | 1329.8 | 0.2653 | 332 53 | 258 24 | 7 35 30. Urania | 2.3667 | 1329.9 | 0.1266 | 31 46 | 308 12 | 2 6 105. Artemis | 2.3744 | 1336.4 | 0.1749 | 242 38 | 188 3 | 21 31 113. Amalthea | 2.3761 | 1337.8 | 0.0874 | 198 44 | 123 11 | 5 2 115. Thyra | 2.3791 | 1340.3 | 0.1939 | 43 2 | 309 5 | 11 35 161. Athor | 2.3792 | 1340.5 | 0.1389 | 310 40 | 18 27 | 9 3 172. Baucis | 2.3794 | 1340.6 | 0.1139 | 329 23 | 331 50 | 10 2 249. Ilse | 2.3795 | 1340.6 | 0.2195 | 14 17 | 334 49 | 9 40 230. Athamantis | 2.3842 | 1344.6 | 0.0615 | 17 31 | 239 33 | 9 26 7. Iris | 2.3862 | 1346.4 | 0.2308 | 41 23 | 259 48 | 5 28 9. Metis | 2.3866 | 1346.7 | 0.1233 | 71 4 | 68 32 | 5 36 234. Barbara | 2.3873 | 1347.3 | 0.2440 | 333 26 | 144 9 | 15 22 60. Echo | 2.3934 | 1352.4 | 0.1838 | 98 36 | 192 5 | 3 35 63. Ausonia | 2.3979 | 1356.3 | 0.1239 | 270 25 | 337 58 | 5 48 25. Phocea | 2.4005 | 1358.5 | 0.2553 | 302 48 | 208 27 | 21 35 192. Nausicaa | 2.4014 | 1359.3 | 0.2413 | 343 19 | 160 46 | 6 50 20. Massalia | 2.4024 | 1365.8 | 0.1429 | 99 7 | 206 36 | 0 41 265. Anna | 2.4096 | 1366.2 | 0.2628 | 226 18 | 335 26 | 25 24 182. Elsa | 2.4157 | 1371.4 | 0.1852 | 51 52 | 106 30 | 2 0 142. Polana | 2.4194 | 1374.5 | 0.1322 | 219 54 | 317 34 | 2 14 67. Asia | 2.4204 | 1375.4 | 0.1866 | 306 35 | 202 47 | 5 59 44. Nysa | 2.4223 | 1377.0 | 0.1507 | 111 57 | 131 11 | 3 42 6. Hebe | 2.4254 | 1379.3 | 0.2034 | 15 16 | 138 43 | 10 47 83. Beatrix | 2.4301 | 1383.6 | 0.0859 | 191 46 | 27 32 | 5 0 135. Hertha | 2.4303 | 1383.8 | 0.2037 | 320 11 | 344 3 | 2 19 131. Vala | 2.4318 | 1385.1 | 0.0683 | 222 50 | 65 15 | 4 58 112. Iphigenia | 2.4335 | 1386.6 | 0.1282 | 338 9 | 324 3 | 2 37 21. Lutetia | 2.4354 | 1388.2 | 0.1621 | 327 4 | 80 28 | 3 5 118. Peitho | 2.4384 | 1390.8 | 0.1608 | 77 36 | 47 30 | 7 48 126. Velleda | 2.4399 | 1392.1 | 0.1061 | 347 46 | 23 7 | 2 56 42. Isis | 2.4401 | 1392.2 | 0.2256 | 317 58 | 84 28 | 8 35 19. Fortuna | 2.4415 | 1394.4 | 0.1594 | 31 3 | 211 27 | 1 33 79. Eurynome | 2.4436 | 1395.2 | 0.1945 | 44 22 | 206 44 | 4 37 138. Tolosa | 2.4492 | 1400.0 | 0.1623 | 311 39 | 54 52 | 3 14 189. Phthia | 2.4505 | 1401.1 | 0.0356 | 6 50 | 203 22 | 5 10 11. Parthenope | 2.4529 | 1403.2 | 0.0994 | 318 2 | 125 11 | 4 37 178. Belisana | 2.4583 | 1407.8 | 0.1266 | 278 0 | 50 17 | 2 5 198. Ampella | 2.4595 | 1408.9 | 0.2266 | 354 46 | 268 45 | 9 20 248. Lameia | 2.4714 | 1419.1 | 0.0656 | 248 40 | 246 34 | 4 1 17. Thetis | 2.4726 | 1420.1 | 0.1293 | 261 37 | 125 24 | 5 36 46. Hestia | 2.5265 | 1466.8 | 0.1642 | 354 14 | 181 31 | 2 17 89. Julia | 2.5510 | 1488.2 | 0.1805 | 353 13 | 311 42 | 16 11 232. Russia | 2.5522 | 1489.3 | 0.1754 | 200 25 | 152 30 | 6 4 29. Amphitrite | 2.5545 | 1491.3 | 0.0742 | 56 23 | 356 41 | 6 7 170. Maria | 2.5549 | 1491.7 | 0.0639 | 95 47 | 301 20 | 14 23 262. Valda | 2.5635 | 1496.4 | 0.2172 | 61 42 | 38 40 | 7 46 258. Tyche | 2.5643 | 1499.8 | 0.1966 | 15 42 | 208 4 | 14 50 134. Sophrosyne | 2.5647 | 1500.3 | 0.1165 | 67 33 | 346 22 | 11 36 264. Libussa | 2.5672 | 1502.4 | 0.0925 | 0 7 | 50 23 | 10 29 193. Ambrosia | 2.5758 | 1510.0 | 0.2854 | 70 52 | 351 15 | 11 39 13. Egeria | 2.5765 | 1510.6 | 0.0871 | 120 10 | 43 12 | 16 32 5. Astræa | 2.5786 | 1512.4 | 0.1863 | 134 57 | 141 28 | 5 19 119. Althea | 2.5824 | 1515.7 | 0.0815 | 11 29 | 203 57 | 5 45 157. Dejanira | 2.5828 | 1516.1 | 0.2105 | 107 24 | 62 31 | 12 2 101. Helena | 2.5849 | 1518.0 | 0.1386 | 327 15 | 343 46 | 10 11 32. Pomona | 2.5873 | 1520.1 | 0.0830 | 193 22 | 220 43 | 5 29 91. Ægina | 2.5895 | 1522.1 | 0.1087 | 80 22 | 11 7 | 2 8 14. Irene | 2.5896 | 1522.1 | 0.1627 | 180 19 | 86 48 | 9 8 111. Ate | 2.5927 | 1524.8 | 0.1053 | 108 42 | 306 13 | 4 57 151. Abundantia | 2.5932 | 1525.3 | 0.0356 | 173 55 | 38 48 | 6 30 56. Melete | 2.6010 | 1532.2 | 0.2340 | 294 50 | 194 1 | 8 2 132. Æthra | 2.6025 | 1533.5 | 0.3799 | 152 24 | 260 2 | 25 0 214. Aschera | 2.6111 | 1541.1 | 0.0316 | 115 55 | 342 30 | 3 27 70. Panopea | 2.6139 | 1543.6 | 0.1826 | 299 49 | 48 18 | 11 38 194. Procne | 2.6159 | 1545.4 | 0.2383 | 319 33 | 159 19 | 18 24 53. Calypso | 2.6175 | 1546.8 | 0.2060 | 92 52 | 143 58 | 5 7 78. Diana | 2.6194 | 1548.5 | 0.2088 | 121 42 | 333 58 | 8 40 124. Alceste | 2.6297 | 1557.6 | 0.0784 | 245 42 | 188 26 | 2 56 23. Thalia | 2.6306 | 1558.4 | 0.2299 | 123 58 | 67 45 | 10 14 164. Eva | 2.6314 | 1559.1 | 0.3471 | 359 32 | 77 28 | 24 25 15. Eunomia | 2.6437 | 1570.0 | 0.1872 | 27 52 | 188 26 | 2 56 37. Fides | 2.6440 | 1570.3 | 0.1758 | 66 26 | 8 21 | 3 7 66. Maia | 2.6454 | 1571.6 | 0.1750 | 48 8 | 8 17 | 3 6 224. Oceana | 2.6465 | 1572.6 | 0.0455 | 270 51 | 353 18 | 5 52 253. Mathilde | 2.6469 | 1572.9 | 0.2620 | 333 39 | 180 3 | 6 37 50. Virginia | 2.6520 | 1577.4 | 0.2852 | 10 9 | 173 45 | 2 48 144. Vibilia | 2.6530 | 1578.4 | 0.2348 | 7 9 | 76 47 | 4 48 85. Io | 2.6539 | 1579.2 | 0.1911 | 322 35 | 203 56 | 11 53 26. Proserpine | 2.6561 | 1581.1 | 0.0873 | 236 25 | 45 55 | 3 36 233. Asterope | 2.6596 | 1584.3 | 0.1010 | 344 36 | 222 25 | 7 39 102. Miriam | 2.6619 | 1586.3 | 0.3035 | 354 39 | 211 58 | 5 4 240. Vanadis | 2.6638 | 1588.0 | 0.2056 | 51 53 | 114 54 | 2 6 73. Clytie | 2.6652 | 1589.3 | 0.0419 | 57 55 | 7 51 | 2 24 218. Bianca | 2.6653 | 1589.3 | 0.1155 | 230 14 | 170 50 | 15 13 141. Lumen | 2.6666 | 1590.5 | 0.2115 | 13 43 | 319 7 | 11 57 77. Frigga | 2.6680 | 1591.8 | 0.1318 | 58 47 | 2 0 | 2 28 3. Juno | 2.6683 | 1592.0 | 0.2579 | 54 50 | 170 53 | 13 1 97. Clotho | 2.6708 | 1594.3 | 0.2550 | 65 32 | 160 37 | 11 46 75. Eurydice | 2.6720 | 1595.3 | 0.3060 | 335 33 | 359 56 | 5 1 145. Adeona | 2.6724 | 1595.4 | 0.1406 | 117 53 | 77 41 | 12 38 204. Callisto | 2.6732 | 1596.4 | 0.1752 | 257 45 | 205 40 | 8 19 114. Cassandra | 2.6758 | 1598.8 | 0.1401 | 153 6 | 164 24 | 4 55 201. Penelope | 2.6764 | 1599.3 | 0.1818 | 334 21 | 157 5 | 5 44 64. Angelina | 2.6816 | 1603.9 | 0.1271 | 125 36 | 311 4 | 1 19 98. Ianthe | 2.6847 | 1606.7 | 0.1920 | 148 52 | 354 7 | 15 32 34. Circe | 2.6864 | 1608.3 | 0.1073 | 148 41 | 184 46 | 5 27 123. Brunhilda | 2.6918 | 1613.2 | 0.1150 | 72 57 | 308 28 | 6 27 166. Rhodope | 2.6927 | 1613.9 | 0.2140 | 30 51 | 129 33 | 12 2 109. Felicitas | 2.6950 | 1616.0 | 0.3002 | 56 1 | 4 56 | 8 3 246. Asporina | 2.6994 | 1619.9 | 0.1065 | 255 54 | 162 35 | 15 39 58. Concordia | 2.7004 | 1620.8 | 0.0426 | 189 10 | 161 20 | 5 2 103. Hera | 2.7014 | 1621.8 | 0.0803 | 321 3 | 136 18 | 5 24 54. Alexandra | 2.7095 | 1629.1 | 0.2000 | 295 39 | 313 45 | 11 47 226. Weringia | 2.7118 | 1631.2 | 0.2048 | 284 46 | 135 18 | 15 50 59. Olympia | 2.7124 | 1631.7 | 0.1189 | 17 33 | 170 26 | 8 37 146. Lucina | 2.7189 | 1637.5 | 0.0655 | 227 34 | 84 16 | 13 6 45. Eugenia | 2.7205 | 1639.0 | 0.0811 | 232 5 | 147 57 | 6 35 210. Isabella | 2.7235 | 1641.7 | 0.1220 | 44 22 | 32 58 | 5 18 187. Lamberta | 2.7272 | 1645.0 | 0.2391 | 214 4 | 22 13 | 10 43 180. Garumna | 2.7286 | 1646.3 | 0.1722 | 125 56 | 314 42 | 0 54 160. Una | 2.7287 | 1646.4 | 0.0624 | 55 57 | 9 22 | 3 51 140. Siwa | 2.7316 | 1649.0 | 0.2160 | 300 33 | 107 2 | 3 12 110. Lydia | 2.7327 | 1650.0 | 0.0770 | 336 49 | 57 10 | 6 0 185. Eunice | 2.7372 | 1654.1 | 0.1292 | 16 32 | 153 50 | 23 17 203. Pompeia | 2.7376 | 1654.5 | 0.0588 | 42 51 | 348 37 | 3 13 200. Dynamene | 2.7378 | 1654.6 | 0.1335 | 46 38 | 325 26 | 6 56 197. Arete | 2.7390 | 1655.8 | 0.1621 | 324 51 | 82 6 | 8 48 206. Hersilia | 2.7399 | 1656.5 | 0.0389 | 95 44 | 145 16 | 3 46 255. Oppavia | 2.7402 | 1656.6 | 0.0728 | 169 15 | 14 6 | 9 33 247. Eukrate | 2.7412 | 1657.7 | 0.2387 | 53 44 | 0 20 | 25 7 38. Leda | 2.7432 | 1659.6 | 0.1531 | 101 20 | 296 27 | 6 57 125. Liberatrix | 2.7437 | 1660.0 | 0.0798 | 273 29 | 169 35 | 4 38 173. Ino | 2.7446 | 1660.8 | 0.2047 | 13 28 | 148 34 | 14 15 36. Atalanta | 2.7452 | 1661.3 | 0.3023 | 42 44 | 359 14 | 18 42 128. Nemesis | 2.7514 | 1666.9 | 0.1257 | 16 34 | 76 31 | 6 16 93. Minerva | 2.7537 | 1669.0 | 0.1405 | 274 44 | 5 4 | 8 37 127. Johanna | 2.7550 | 1670.3 | 0.0659 | 122 37 | 31 46 | 8 17 71. Niobe | 2.7558 | 1671.0 | 0.1732 | 221 17 | 316 30 | 23 19 213. Lilæa | 2.7563 | 1671.4 | 0.1437 | 281 4 | 122 17 | 6 47 55. Pandora | 2.7604 | 1675.1 | 0.1429 | 10 36 | 10 56 | 7 14 237. Cœlestina | 2.7607 | 1675.5 | 0.0738 | 282 49 | 84 33 | 9 46 143. Adria | 2.7619 | 1676.6 | 0.0729 | 222 27 | 333 42 | 11 30 82. Alcmene | 2.7620 | 1676.6 | 0.2228 | 131 45 | 26 57 | 2 51 116. Sirona | 2.7669 | 1681.1 | 0.1433 | 152 47 | 64 26 | 3 35 1. Ceres | 2.7673 | 1681.4 | 0.0763 | 149 38 | 80 47 | 10 37 88. Thisbe | 2.7673 | 1681.5 | 0.1632 | 308 34 | 277 54 | 16 11 215. Œnone | 2.7679 | 1682.0 | 0.0390 | 346 24 | 25 25 | 1 44 2. Pallas | 2.7680 | 1682.1 | 0.2408 | 122 12 | 172 45 | 34 44 39. Lætitia | 2.7680 | 1682.1 | 0.1142 | 3 8 | 157 15 | 10 22 41. Daphne | 2.7688 | 1682.8 | 0.2674 | 220 33 | 179 8 | 15 58 177. Irma | 2.7695 | 1683.5 | 0.2370 | 22 6 | 349 17 | 1 27 148. Gallia | 2.7710 | 1684.8 | 0.1855 | 36 7 | 145 13 | 25 21 267. Tirza | 2.7742 | 1687.6 | 0.0986 | 264 5 | 73 59 | 6 2 74. Galatea | 2.7770 | 1690.3 | 0.2392 | 8 18 | 197 51 | 4 0 205. Martha | 2.7771 | 1690.4 | 0.1752 | 21 54 | 212 12 | 10 40 139. Juewa | 2.7793 | 1692.4 | 0.1773 | 164 34 | 2 21 | 10 57 28. Bellona | 2.7797 | 1692.7 | 0.1491 | 124 1 | 144 37 | 9 22 68. Leto | 2.7805 | 1693.5 | 0.1883 | 345 14 | 45 1 | 7 58 216. Cleopatra | 2.7964 | 1708.0 | 0.2492 | 328 15 | 215 49 | 13 2 99. Dike | 2.7966 | 1708.3 | 0.2384 | 240 36 | 41 44 | 13 53 236. Honoria | 2.7993 | 1710.7 | 0.1893 | 356 59 | 186 27 | 7 37 183. Istria | 2.8024 | 1713.4 | 0.3530 | 45 0 | 142 46 | 26 33 266. Aline | 2.8078 | 1718.5 | 0.1573 | 23 52 | 236 18 | 13 20 188. Menippe | 2.8211 | 1730.7 | 0.2173 | 309 38 | 241 44 | 11 21 167. Urda | 2.8533 | 1760.4 | 0.0340 | 296 4 | 166 28 | 2 11 81. Terpsichore | 2.8580 | 1764.8 | 0.2080 | 49 1 | 2 25 | 7 55 174. Phædra | 2.8600 | 1766.6 | 0.1492 | 253 12 | 328 49 | 12 9 243. Ida | 2.8610 | 1767.5 | 0.0419 | 71 22 | 326 21 | 1 10 242. Kriemhild | 2.8623 | 1768.7 | 0.1219 | 123 1 | 207 57 | 11 17 129. Antigone | 2.8678 | 1773.9 | 0.2126 | 242 4 | 137 37 | 12 10 217. Eudora | 2.8690 | 1774.9 | 0.3068 | 314 41 | 164 10 | 10 19 158. Coronis | 2.8714 | 1777.2 | 0.0545 | 56 56 | 281 30 | 1 0 33. Polyhymnia | 2.8751 | 1780.7 | 0.3349 | 342 59 | 9 19 | 1 56 195. Euryclea | 2.8790 | 1784.2 | 0.0471 | 115 48 | 7 57 | 7 1 235. Caroline | 2.8795 | 1784.7 | 0.0595 | 268 29 | 66 35 | 9 4 47. Aglaia | 2.8819 | 1786.9 | 0.1317 | 312 40 | 40 20 | 5 1 208. Lachrymosa | 2.8926 | 1796.9 | 0.0149 | 127 52 | 5 43 | 1 48 191. Kolga | 2.8967 | 1800.8 | 0.0876 | 23 21 | 159 47 | 11 29 22. Calliope | 2.9090 | 1801.0 | 0.0193 | 62 43 | 4 47 | 1 45 155. Scylla | 2.9127 | 1815.7 | 0.2559 | 82 1 | 42 52 | 14 4 238. Hypatia | 2.9163 | 1819.0 | 0.0946 | 32 18 | 184 26 | 12 28 231. Vindobona | 2.9192 | 1821.7 | 0.1537 | 253 23 | 352 49 | 5 10 16. Psyche | 2.9210 | 1823.4 | 0.1392 | 15 9 | 150 36 | 3 4 179. Clytemnestra| 2.9711 | 1870.6 | 0.1133 | 355 39 | 253 13 | 7 47 239. Adrastea | 2.9736 | 1873.0 | 0.2279 | 26 1 | 181 34 | 6 4 69. Hesperia | 2.9779 | 1877.0 | 0.1712 | 108 19 | 187 12 | 8 28 150. Nuwa | 2.9785 | 1877.5 | 0.1307 | 355 27 | 207 35 | 2 9 61. Danaë | 2.9855 | 1884.2 | 0.1615 | 344 4 | 334 11 | 18 14 117. Lomia | 2.9907 | 1889.1 | 0.0229 | 48 46 | 349 39 | 14 58 35. Leucothea | 2.9923 | 1890.6 | 0.2237 | 202 25 | 355 49 | 8 12 263. Dresda | 3.0120 | 1909.3 | 0.3051 | 308 49 | 217 56 | 1 27 221. Eos | 3.0134 | 1910.7 | 0.1028 | 330 58 | 142 35 | 10 51 162. Laurentia | 3.0241 | 1920.8 | 0.1726 | 145 52 | 38 15 | 6 4 156. Xantippe | 3.0375 | 1933.7 | 0.2637 | 155 58 | 246 11 | 7 29 241. Germania | 3.0381 | 1934.0 | 0.1013 | 340 7 | 272 28 | 5 30 256. Walpurga | 3.0450 | 1940.8 | 0.1180 | 240 17 | 183 35 | 12 44 211. Isolda | 3.0464 | 1942.2 | 0.1541 | 74 12 | 265 29 | 3 51 96. Ægle | 3.0497 | 1945.3 | 0.1405 | 163 10 | 322 50 | 16 7 257. Silesia | 3.0572 | 1952.5 | 0.2555 | 54 16 | 34 31 | 4 41 133. Cyrene | 3.0578 | 1953.0 | 0.1398 | 247 13 | 321 8 | 7 14 95. Arethusa | 3.0712 | 1965.9 | 0.1447 | 32 58 | 244 17 | 12 54 202. Chryseis | 3.0777 | 1972.1 | 0.0959 | 129 46 | 137 47 | 8 48 268. ---- | 3.0852 | 1973.9 | 0.1285 | 184 48 | 121 53 | 2 25 100. Hecate | 3.0904 | 1984.3 | 0.1639 | 308 3 | 128 12 | 6 23 49. Pales | 3.0908 | 1984.7 | 0.2330 | 31 15 | 290 40 | 3 8 223. Rosa | 3.0940 | 1987.9 | 0.1186 | 102 48 | 49 0 | 1 59 52. Europa | 3.0955 | 1988.0 | 0.1098 | 106 57 | 129 40 | 7 27 245. Vera | 3.0985 | 1992.1 | 0.1950 | 25 29 | 62 37 | 5 10 86. Semele | 3.1015 | 1995.1 | 0.2193 | 29 10 | 87 45 | 4 47 159. Æmilia | 3.1089 | 2002.2 | 0.1034 | 101 22 | 135 9 | 6 4 48. Doris | 3.1127 | 2005.9 | 0.0649 | 70 33 | 184 55 | 6 31 196. Philomela | 3.1137 | 2006.8 | 0.0118 | 309 19 | 73 24 | 7 16 130. Electra | 3.1145 | 2007.7 | 0.2132 | 20 34 | 146 6 | 22 57 212. Medea | 3.1157 | 2008.8 | 0.1013 | 56 18 | 315 16 | 4 16 120. Lachesis | 3.1211 | 2014.0 | 0.0475 | 214 0 | 342 51 | 7 1 181. Eucharis | 3.1226 | 2015.4 | 0.2205 | 95 25 | 144 45 | 18 38 62. Erato | 3.1241 | 2016.9 | 0.1756 | 39 0 | 125 46 | 2 12 222. Lucia | 3.1263 | 2019.0 | 0.1453 | 258 2 | 80 11 | 2 11 137. Melibœa | 3.1264 | 2019.1 | 0.2074 | 307 58 | 204 22 | 13 22 165. Loreley | 3.1269 | 2019.6 | 0.0734 | 223 50 | 304 6 | 10 12 251. Sophia | 3.1315 | 2024.1 | 0.1243 | 77 7 | 157 6 | 10 20 24. Themis | 3.1357 | 2028.1 | 0.1242 | 144 8 | 35 49 | 0 49 152. Atala | 3.1362 | 2028.6 | 0.0862 | 84 23 | 41 29 | 12 12 10. Hygeia | 3.1366 | 2029.1 | 0.1156 | 237 2 | 285 38 | 3 49 259. Aletheia | 3.1369 | 2029.3 | 0.1176 | 241 45 | 88 32 | 10 40 227. Philosophia | 3.1393 | 2031.6 | 0.2131 | 226 23 | 330 52 | 9 16 147. Protogenea | 3.1393 | 2031.6 | 0.0247 | 25 38 | 251 16 | 1 54 171. Ophelia | 3.1432 | 2035.4 | 0.1168 | 143 59 | 101 10 | 2 34 209. Dido | 3.1436 | 2035.9 | 0.0637 | 257 33 | 2 0 | 7 15 31. Euphrosyne | 3.1468 | 2039.0 | 0.2228 | 93 26 | 31 31 | 26 27 90. Antiope | 3.1475 | 2039.7 | 0.1645 | 301 15 | 71 29 | 2 17 104. Clymene | 3.1507 | 2042.7 | 0.1579 | 59 32 | 43 32 | 2 54 57. Mnemosyne | 3.1510 | 2043.0 | 0.1145 | 53 25 | 200 2 | 15 12 250. Bettina | 3.1524 | 2044.3 | 0.1302 | 87 28 | 26 12 | 12 54 252. Clementina | 3.1552 | 2047.1 | 0.0837 | 355 8 | 208 19 | 10 2 94. Aurora | 3.1602 | 2052.0 | 0.0827 | 48 46 | 4 9 | 8 4 106. Dione | 3.1670 | 2058.6 | 0.1788 | 25 57 | 63 14 | 4 38 199. Byblis | 3.1777 | 2069.0 | 0.1687 | 261 20 | 89 52 | 15 22 92. Undina | 3.1851 | 2076.3 | 0.1024 | 331 27 | 102 52 | 9 57 184. Deiopea | 3.1883 | 2079.4 | 0.0725 | 169 22 | 336 18 | 1 12 176. Idunna | 3.1906 | 2081.6 | 0.1641 | 20 34 | 201 13 | 22 31 154. Bertha | 3.1976 | 2088.5 | 0.0788 | 190 47 | 37 35 | 20 59 108. Hecuba | 3.2113 | 2101.0 | 0.1005 | 173 49 | 352 17 | 4 24 122. Gerda | 3.2177 | 2108.2 | 0.0415 | 203 45 | 178 43 | 1 36 168. Sibylla | 3.3765 | 2266.2 | 0.0707 | 11 26 | 209 47 | 4 33 225. Henrietta | 3.4007 | 2277.8 | 0.2661 | 299 13 | 200 45 | 20 45 229. Adelinda | 3.4129 | 2302.9 | 0.1562 | 332 7 | 30 49 | 2 11 76. Freia | 3.4140 | 2304.1 | 0.1700 | 90 49 | 212 5 | 2 3 260. Huberta | 3.4212 | 2311.5 | 0.1113 | 313 22 | 168 48 | 6 18 65. Maximiliana | 3.4270 | 2317.2 | 0.1097 | 260 36 | 158 50 | 3 29 121. Hermione | 3.4535 | 2344.2 | 0.1255 | 357 50 | 76 46 | 7 36 87. Sylvia | 3.4833 | 2374.5 | 0.0922 | 333 48 | 75 49 | 10 55 107. Camilla | 3.4847 | 2376.0 | 0.0756 | 115 53 | 176 18 | 9 54 175. Andromache | 3.5071 | 2399.0 | 0.3476 | 293 0 | 23 35 | 3 46 190. Ismene | 3.9471 | 2864.3 | 0.1634 | 105 39 | 177 0 | 6 7 153. Hilda | 3.9523 | 2869.9 | 0.1721 | 285 47 | 228 20 | 7 55 -----------------+--------+---------+--------+----------+----------+--------

PART II.

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 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.

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 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 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 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 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 1/2, where the difference between the numerator and the denominator is one, the commensurability is of the first order; 1/3 is of the second; 2/5, 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 1/2, is the only case of the first order in the entire ring; those of the second order, answering to 1/3 and 3/5, 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:

+--------+----------------+-----------+ | Order. | Ratio. | Distance. | +--------+----------------+-----------+ | First | 1/2 | 3.277 | | | | | | Second | 1/3, 3/5 | { 2.50 | | | | { 3.70 | | | | | | | | { 2.82 | | Third | 2/5, 4/7, 5/8 | { 3.58 | | | | { 3.80 | | | | | | | | { 2.95 | | Fourth | 3/7, 5/9, 7/11 | { 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-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.

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, 2/7, 3/8, 4/9, 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?

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 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 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:

+------------+--------------+--------------+ | Asteroid. | Inclination. | Eccentricity.| +------------+--------------+--------------+ | Pallas | 34° 42´ | 0.238 | | Istria | 26 30 | 0.353 | | Euphrosyne | 26 29 | 0.228 | | Anna | 25 24 | 0.263 | | Gallia | 25 21 | 0.185 | | Æthra | 25 0 | 0.380 | | Eukrate | 24 57 | 0.236 | | Eva | 24 25 | 0.347 | | Niobe | 23 19 | 0.173 | | Eunice | 23 17 | 0.129 | | Electra | 22 55 | 0.208 | | Idunna | 22 31 | 0.164 | | Phocea | 21 35 | 0.255 | | Artemis | 21 31 | 0.175 | | Bertha | 20 59 | 0.085 | | Henrietta | 20 47 | 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.

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 "

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, 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 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:

+-----------------------------+-------------+------------+ | | Harrington. | Svedstrup. | +-----------------------------+-------------+------------+ | Longitude of perihelion | 14° 39´ | 101° 48´ | | " of ascending node | 113 56 | 133 27 | | Inclination | 1 0 | 6 6 | | 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 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 correspond 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?

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:

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.