QB IRLF rfX^'lREESE LIBRARY UNIVERSITY OF .CALIFORNIA. Received ff Accessions No.OW&o Shelf X,<. THE ASTEKOIDS, OK MINOR PLANETS BETWEEN MAES AND JUPITEB. BY DANIEL KIRKWOOD, LLD., n PROFESSOR EMERITUS IN THE UNIVERSITY OF INDIANA ; AUTHOR OF " COMETS AND METEORS," "METEORIC ASTRONOMY," ETC. PHILADELPHIA : J. B. LIPPINCOTT COMPANY. 1888. Copyright, 1887, by DAJJJEL KIRK WOOD. AJJJ 4a PEEFACE. THE rapid progress of discovery in the zone of minor planets, the anomalous forms and positions of their or- bits, the small size as well as the great number of these telescopic bodies, and their peculiar relations to Jupiter, *A'^^ *^ 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 Astrsea ; 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 de- tected 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 elimi- nation of members from particular parts; the eccen- tricities and inclinations of the orbits ; and the relation 3 4 PREFACE. 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 Oireular zum Berliner Astrono- mischen JahrbucJi. 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 KESPECTIVE 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 KELATIONS BETWEEN CERTAIN ADJACENT ORBITS . . 47 1* 5 D CONTENTS. PAGE THE ECCENTRICITIES 48 THE INCLINATIONS 49 LONGITUDES OF THE PERIHELIA AND or 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 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 dis- covery 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 mem- bers 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 evi- dence in its favor was not absolutely conclusive. On 9 10 THE ASTEROIDS. the 7th of January, 1610, Galileo first saw the satel- lites of Jupiter. The bearing of this discovery on the theory of the universe was sufficiently obvious. Such was the prejudice, however, against the Copernican sys- tem that some of its opponents denied even the reality of Galileo's discovery. " Those satellites/' said a Tus- can 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 plan- ets 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 (De- cember 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, con- sisted of six primary and ten secondary planets. Nearly a century had elapsed from the date of Cas- sini'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. THE ASTEROID^ ! I UNIVEr 2. Discovery of the First As long ago as the commencement of the seventeenth century the celebrated Kepler observed that the respec- tive 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 man- ner with Kepler's order of progression. Such a coinci- dence 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, organ- ized 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 12 THE ASTEROIDS. been discovered within the ancient limits of the solar system, that the object to be looked for was compara- tively near us, and that the so-called law of distances was purely empirical, the prospect of success, it is evi- dent, 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 associa- tion had fairly commenced their labors.* On the 1st of January, 1801, Professor Giuseppe Piazzi, of Palermo, noticed a star of the eighth magni- tude, not indicated in Wollaston's catalogue. Subse- quent 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 com- pleting 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 tri- angle where he was certain no such configuration ex- * The discoverer, Piazzi, was not, as has been so often affirmed, one of the astronomers to whom the search had been especially committed. THE ASTEROIDS. 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 de- tected, 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 alto- gether extraordinary. The eccentricity also was greater than in the case of any of the old planets. These pecu- liarities, 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 intersec- tion 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 Hard- ing, of Lilienthal, undertook the construction of charts of all the small stars near the orbits of Ceres and Pal- las. On the evening of September 1, 1804, while en- gaged 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 mem- ber 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. 2 14 THE ASTEROIDS. Before Ceres had been generally adopted by astrono- mers as the name of the first asteroid, Laplace had ex- pressed a preference for Juno. This, however, the dis- coverer was unwilling to accept. Mr. Harding, like Laplace, deeming it appropriate to place Juno near Ju- piter, 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 near- est 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 sepa- ration. In order, therefore, to detect other members of the group, Dr. Olbers undertook a systematic examina- tion 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 THE ASTEROIDS. 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 observa- tion, 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 deter- mined, and hence its real magnitude is not well ascer- tained. Professor Harrington, of Ann Arbor, has es- timated 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 ToTofi tnat f tne ear th. It i g remarkable that not- withstanding its diminutive size it may be seen under favorable circumstances by the naked eye. Encouraged by the discovery of Vesta (which he re- garded as almost a demonstration of his favorite theory), Dr. Olbers continued his systematic search for other planetary fragments. Not meeting, however, with fur- ther 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 astrono- mer employed himself in a strict examination of the 16 THE ASTEROIDS. heavens represented by the Maps of the Berlin Acad- emy. 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 ren- dered 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 Schu- macher 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 Astr&a. The facts in regard to the very numerous subsequent discoveries may best be presented in a tabular form. THE ASTEROIDS. 17 TABLE I. The Asteroids in the Order of their Discovery. Asteroids. Date of Discovery. Name of Discoverer. Place of Discovery. 1 Ceres 1801 Jan 1 2 Pallas 1802 Mar 28 Olbers 3 Juno .. 1804 Sept 1 Harding Lilientbal 4. Vesta 1807, Mar 29 Olbers Bremen 5. Astraea 6. Hebe 7. Iris 1845, Dec. 8 18-17, July 1 1847 Auo- 14 Hencke Hencke Hind Driessen Driessen 8. Flora 1847 Oct 18 Hind 9. Metis 1848, Apr. 26 Graham Markree 10. Hygeia 1849, Apr. 12 De Gasparis Naples 11. Parthenope... 12. Victoria 13. Eo-eria 1850, May 11 1850, Sept. 13 1850, Nov. 2 De Gasparis Hind De Gasparis Naples London Naples 14. Irene 1851, May 19 Hind London 15. Eunomia 16. Psyche 1851, July 29 1852 Mar 17 De Gasparis De Gasparis Naples Naples 17. Thetis 1852 Apr 17 Luther Bilk 18. Melpomene... 19. Fortuna 20. Massalia 21. Lutetia 22. Calliope 1852, June 24 1852, Aug. 22 1852, Sept. 19 1852, Nov. 15 1852, Nov. 16 Hind Hind De Gasparis Goldschmidt Hind London London Naples Paris London 23 Thalia 1852 Dec 15 Hind 24. Themis 25. Phocea 26. Proserpine.... 27. Euterpe 1853, Apr. 5 1853, Apr. 6 1853, May 5 1853 Nov. 8 De Gasparis Chacornac Luther Hind Naples Marseilles Bilk London 28 Bellona 1854 Mar 1 Bilk 29. Amphitrite... 30. Urania 1854, Mar. 1 1854 July 22 Marth Hind London 31. Euphrosyne .. 32. Pomona 33. Polyhymnia .. 34 Circe 1854, Sept. 1 1854, Oct. 26 1854, Oct. 28 1855 Apr 6 Ferguson Goldschmidt Chacornac Washington Paris Paris Paris 35. Lcucothea 36. Atalanta 37 Fides 1855, Apr. 19 1855, Oct. 5 1855 Oct 5 Luther Goldschmidt Bilk Paris Bilk 38 Leda 1856 Jan 12 Paris 39. Lgetitia 1856 Feb 8 Paris 40. Harmonia 41. Daphne.... 1856, Mar. 31 1856 May 22 Goldschmidt Goldschmidt Paris Paris 42. Isis 1856, May 23 Pogson Oxford 43. Ariadne 1857, Apr. 15 Pogson Oxford 2* 18 THE ASTEROIDS. Table I. Continued. Asteroids. Date of Discovery. Name of Discoverer. Place of Discovery. 44. Nysa 1857 May 27 Goldschmidt Paris 45. Eugenia 46. Hestia 1857, June 27 1857, Aug. 16 Goldschmidt Pogson Paris Oxford 47. Aglaia 1857, Sept. 15 Luther Bilk 48. Doris 1857, Sept. 19 Goldschmidt Paris 49. Pales 1857, Sept. 19 Goldschmidt Paris 50. Virginia 51. Nernausa 52. Europa 53. Calypso 1857, Oct. 4 1858, Jan. 22 1858, Feb. 4 1858, Apr. 4 Ferguson Laurent Goldschmidt Luther Washington Nismes Paris Bilk 54. Alexandra 55. Pandora . . 1858, Sept. 10 1858, Sept. 10 Goldschmidt Searle Paris Albany 56. Melete 1857, Sept. 9 Goldschmidt Paris 57. Mnemosyne... 58. Concordia 59. Olyinpia 60 Echo 1859, Sept. 22 1860, Mar. 24 1860, Sept. 12 I860 Sept 16 Luther Luther Chacornac Ferguson Bilk Bilk Paris Washington 61. Danae 1860, Sept. 9 Goldschmidt Paris 62. Erato 1860, Sept. 14 Foerster and Lesser Berlin 63. Ausonia 64. Angelina 65. Maximiliana 66. Maia 1861, Feb. 10 1861, Mar. 4 1861, Mar. 8 1861, Apr. 9 De Gasparis Tempel Tern pel Tuttle Naples Marseilles Marseilles Cambridge, U. S. 67. Asia ... . 1861, Apr 17 Pogson Madras 68. Leto 1861, Apr. 29 Luther Bilk 69. Hesperia 70. Panopea 71. Niobe 1861, Apr. 29 1861, May 5 1861, Aug. 13 Schiaparelli Goldschmidt Luther Milan Paris Bilk 72 Feronia 1862 May 29 Peters and Safford Clinton 73 Clytie 1862, Apr 7 Tuttle Cambridge 74. Galatea 1862, Aug. 29 Tempel Marseilles 75. Eurydice 76 Freia 1862, Sept. 22 1862 Oct. 21 Peters D'Arrest Clinton Copenhagen 77. Frigga 78. Diana 1862, Nov. 12 1863, Mar. 15 Peters Luther Clinton Bilk 79. Eurynome.... 80. Sappho 1863, Sept. 14 1864, May 2 Watson Pogson Ann Arbor Madras 81. Terpsichore.. 82. Alcmene 83. Beatrice 84. Clio 1864, Sept. 30 1864, Nov. 27 1865, Apr. 26 1865, Aug. 25 Tempel Luther De Gasparis Luther Marseilles Bilk Naples Bilk 85 lo 1865 Sept. 19 Peters Clinton 86. Setnele 87. Sylvia 1866, Jan. 14 1866, May 16 Tietjen Pogson Berlin Madras 88. Thisbe 89 Julia 1866, June 15 1866, Au". 6 Peters Stephan Clinton Marseilles 90. Antiope 91 JSgina 1866, Oct. 1 1866, Nov. 4 Luther Borelly Bilk Marseilles 92. Undina 1867, July 7 Peters Clinton THE ASTEROIDS. 19 Table I. Continued. Asteroids. Date of Discovery. Name of Discoverer. Place of Discovery. 93 Minerva 1867, Auo-. 24 Watson Ann Arbor 94 Aurora 1867, Sept. 6 Watson Ann Arbor 95. Arethusa 96. ^Egle 97 Clotho 1867, Nov. 24 1868, Feb. 17 1868, Feb. 17 Luth'er Coggia Cosr o 'ia Bilk Marseilles Marseilles 98 lanthe 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. Clytnene 105 Arteinis . .. 1868, Sept. 13 1868, Sept. 16 Watson Watson Ann Arbor 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 110. Lydia 1869, Oct. 9 1870, Apr. 19 Peters Borelly Clinton Marseilles 111. Ate 1870, Aug. 14 Peters Clinton 112. Iphigenia . ... 113. Amalthea 114. Cassandra 115. Thyra 1870, Sept. 19 1871, Mar. 12 1871, July 23 1871, Aug. 6 Peters Luther Peters Watson Clinton Bilk Clinton 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 121. Hermione 122 Gerda 1872, Apr. 10 1872, May 12 1872 July 31 Borelly Watson Peters Marseilles Ann Arbor Clinton 123. Brunhilda.... 124. Alceste 125. Liberatrix. ... 126 Velleda 1872, July 31 1872, Aug. 23 1872, Sept. 11 1872 Nov 5 Peters Peters Prosper Henry Paul Henry Clinton Clinton Paris Paris 127. Johanna 128. Nemesis 1872, Nov. 5 1872, Nov. 25 Prosper Henry Watson Paris Ann Arbor 129. Antigone 130 Electra 1873, Feb. 5 1873 Feb 17 Peters Peters Clinton Clinton 131 Vala 1873, May 24 Peters Clinton 132. jEthra 1873, June 13 Watson Ann Arbor 133. Gyrene... 134. Sophrosyne... 135 Hertha 1873, Aug. 16 1873, Sept. 27 1874 Feb 18 Watson Luther Peters Ann Arbor Bilk Clinton 136. Austria 1874, Mar. 18 Palisa Pol a 137. Meliboea 138. Tolosa 1.874, Apr. 21 1-874, May 19 Palisa Perrotin Pola Toulouse 139 Juewa 1874 Oct 10 Watson Pekin 140. Siwa . .. 1874, Oct. 13 Palisa Pola 141. Lumen 1875, Jan. 13 Paul Henry Paris 20 THE ASTEROIDS. Table I. Continued. Asteroids. Date of Discovery. Name of Discoverer. Place of Discovery. 142. Polana 1875, Jan. 28 Palisa Pola 143. Adria. 1875, Feb. 23 Palisa Pola 144 Vibilia 1875 June 3 Peters 145 Adeona 1875 June 3 Peters 146. Lucina 1875, June 8 Borelly Marseilles 147. Protogenea ... 148. Gallia 1875, July 10 1875 Aug 7 Schulhof Prosper Henry Vienna 149. Medusa.. .... 1875, Sept. 21 Perrotin Toulouse 150. Nuwa 151. Abundantia... 152. Atala 1875, Oct. 18 1875, Nov. 1 1875, Nov. 2 Watson Palisa Paul Henry Ann Arbor Pola Paris 153 Hilda 1875 Nov 2 Palisa Pola 154. Bertha 1875 Nov 4 Paris 155. Scylla 1875, Nov. 8 Palisa Pola 156. Xantippe 157. Dejanira 158. Coronis 1875, Nov. 22 1875, Dec. 1 1876, Jan. 4 Palisa Borelly Knorre Pola Marseilles Berlin 159 JEtnilia 1876 Jan 26 Paris 160. Una . . 1876 Feb 20 Peters Clinton 161. Athor 1876 Apr. 19 Watson Ann Arbor 162. Laurentia 163 Erigone .... 1876, Apr. 21 1876 Apr 26 Prosper Henry Perrotin Paris Toulouse 164. Eva 1876 July 12 Paul Henry Paris 165 Loreley 1876 Aug 9 Peters 166 Rhodope 1876 Auo- 15 Peters Clinton 167. Urda 1876 Aug 28 Peters Clinton 168 Sibylla 1876 Sept 27 Watson 169 Zelia 1876' Sept 28 Paris 170. Maria 171. Ophelia 1877, Jan. 10 1877, Jan. 13 Perrotin Borelly Toulouse Marseilles 172 Baucis 1877 Feb 5 Borelly Marseilles 173. Ino 1877 Auf 1 Borellv Marseilles 174. Phaedra 175. Andromache.. 176. Idunna 1877, Sept. 2 1877, Oct. 1 1877 Oct 14 Watson Watson Peters Ann Arbor Ann Arbor Clinton 177. Irma 1877, Nov. 5 Paul Henry Paris 178. Belisana 179. Clytemnestra. 180. Garumna 181. Eucharis 182. Elsa 1877, Nov. 6 1877, Nov. 11 1878, Jan. 29 1878, Feb. 2 1878 Feb 7 Palisa Watson Perrotin Cottenot Palisa Pola Ann Arbor Toulouse Marseilles Pola 183. Istria 1878, Feb. 8 Palisa Pola 184. Deiopea 185. Eunice 1878, Feb. 28 1878, Mar. 1 Palisa Peters Pola Clinton 186 Celuta 1878 Apr 6 Prosper Henry Paris 187. Lamberta 188. Menippe 189. Phthia 1878, Apr. 11 1878, June 18 1878, Sept. 9 Coggia Peters Peters Marseilles Clinton Clinton 190 Ismene 1878 Sept 22 Peters Clinton THE ASTEROIDS. Table I. Continued. 21 Asteroids. Date of Discovery. Name of Discoverer. Place of Discovery. 191 Kolga 1878 Sept 30 Peters Clinton 192. Nausicaa 193. Ambrosia 194 Procne 1879, Feb. 17 1879, Feb. 28 1879 Mar 21 Palisa Coggia Peters Pola Marseilles 195. Euryclea 196. Philomela 197. Arete 1879, Apr. 22 1879, May 14 1879, May 21 Palisa Peters Palisa Pola Clinton Pola 198 Ampella 1879 June 13 Borelly Marseilles 199. Byblis. . . 1879 July 9 Peters Clinton 200. Dynamene 201. Penelope 202. Chryseis 203. Pompeia 204 Calli^to 1879, July 27 1879, Aug. 7 1879, Sept. 11 1879, Sept. 25 1879 Oct 8 Peters Palisa Peters Peters Palisa, Clinton Pola Clinton Clinton Pola 205. Martha 206 Hersilia . . 1879, Oct. .13 1879 Oct 13 Palisa Peters Pola 207. Hedda 1879 Oct. 17 Palisa Pola 208. Isabella 1879, Oct. 21 Palisa Pola 209 Dido 1879 Oct 22 Peters 210. Lachrymosn .. 211. Isolda 1879, Nov. 12 1879 Dec 10 Palisa Palisa Pola Pola 212. Medea 1880, Feb 6 Palisa Pola 213. Liljea 1880, Feb. 16 Peters Clinton 214 Aschera . 1880 Feb 26 Palia Pola 215. (Enone 216. Cleopatra 217. Eudora 1880, Apr. 7 1880, Apr. 10 1880, Au<*. 30 Knorre Palisa Co^gia Berlin Pola Marseilles 218 Bianca 1880 Sept 4 Pola 219. Thusnelda 220. Stephania 221. Eos 1880, Sept. 20 1881, May 19 1882, Jan. 18 Palisa Palisa Palisa Pola Vienna Vienna 222. Lucia 1882 Feb 9 223. Rosa 1882 Mar 9 Palisa Vienna 224. Oceana 225. Henrietta 226. Weringia 227. Philosophia... 228. Agathe 1882, Mar. 30 1882, Apr. 19 1882, July 19 1882, Aug. 12 1882, Aug. 19 Palisa Palisa Palisa Paul Henry Palisa Vienna Vienna Vienna Paris Vienna 229. Adelinda 230. Athatnantis... 231. Vindobona.... 232. Russia 1882, Aug. 22 1882, Sept. 3 1882, Sept. 10 1883, Jan. 31 Palisa De Ball Palisa Palisa Vienna Bothcamp Vienna Vienna 233. Asterope 234. Barbara 235. Caroline 236. Honoria... 237. Coelestina 238. Hypatia 239. Adrastea 1883, May 11 1883, Aug. 13 1883, Nov. 29 1884, Apr. 26 1884, June 27 1884, July 1 1884, Aug. 18 Borelly Peters Palisa Palisa Palisa Knorre Palisa Marseilles Clinton Vienna Vienna Vienna Berlin Vienna TiiE ASTEROIDS. Table I. Continued. Asteroids. Date of Discovery. Name of Discoverer. Place of Discovery. 240 Vanadis 1884 Aug 27 Borelly 241. Germania 242. Kriemhild 243 Ida 1884, Sept. 12 1884, Sept. 22 1884 Sept 29 Luther Palisa Pajisa Dusseldorf Vienna 244. Sita 1884 Oct 14 Palisa 245. Vera 1885, Feb 6 Pogson Madras 1885 Mar 6 Borelly 247. Eukrate 248. Lameia 1885, Mar. 1 4 1885 June 5 Luther Palisa Dusseldorf Vienna 249 Use 1885 Au- 17 Peters 250 Bettina 1885 Sept 3 Palisa Vienna 251. Sophia 1885 Oct 4 Palisa Vienna 252. Clementina.... 253 Mathilda 1885, Oct. 27. 1885 Nov 12 Perrotin Palisa Nice Vienna 254. Augusta 1886, Mar. 31 1886 Mar 31 Palisa Palisa Vienna 256. Walpurga 257. Silesia 1886, Apr. 3 1886 Apr. 5 Palisa Palisa Vienna Vienna 258 Tyche 1886 May 4 259. Altheia 260. Huberta 261. Prymno 1 886, June 28 1886, Oct. 3 1886, Oct. 31 Peters Palisa Peters Clinton Vienna 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 THE ASTEROIDS. /yv^ v 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 Gibers 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 tele- graphic 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, 24 THE ASTEROIDS. 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 dis- covered. 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 : THE ASTEROIDS. 25 January 13 February 23 March 19 April 35 May i 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 continu- ous 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 ex- tending 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 26 THE ASTEROIDS. of discoverers, the departures from it have been increas- ingly numerous. The twelfth asteroid, discovered in London, was named Victoria, in honor of the reigning sovereign ; the twentieth and twenty-fifth, detected at Marseilles,* received names indicative of the place of their discovery ; Lutetia, the first found at Paris, re- ceived 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 in- convenient 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,f Stone,J and Pickering have formed estimates of the diameters, * Massalia was discovered by De Gasparis, at Naples, Sept. 19, 1852, and independently, the next night, by Chacornac, at Mar- seilles. The name was given by the latter. f Astr. Nach., No. 932. J Monthly Notices, vol. xxvii. a Annals of the Obs. of Harv. Coll., 1879. THE ASTEROIDS. 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 hun- dred miles, and those of all others less than fifty ; the estimates for Menippe and Eva giving twelve and thir- teen 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 par- ticle 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 sur- face 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 re- turn in much less than an hour. " But of such specula- tions/' 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- 28 THE ASTEROIDS. 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 exist- ence 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, n. 4. The longitude of the ascending node, Q,. 5. The inclination, or the angle contained between the plane of the orbit and that of the ecliptic, i. 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, /, 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. THE ASTEROIDS. 29 TABLE II. Elements of the Asteroids. Name a P e ir a i 149. Medusa 2 1327 1137 7d 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 2405 329 23 313 18 2 33 8. Flora 43. Ariadne 254. Augusta 2.2014 2.2033 2 2060 1193.3 1194.5 1196 8 0.1567 0.1671 1227 32 54 277 58 260 47 110 18 264 35 28 9 5 53 3 28 4 36 72. Feronia 2 2661 1246.0 0.1198 307 58 207 49 5 24 40. Harinonia 2 2673 1247 0466 54 93 35 4 16 207. Iledda . 2 2839 1260 7 0301 217 2 28 51 3 49 136. Austria 2 2863 1262 7 0849 316 6 186 7 9 33 18. Melpomene 80 Sappho 2.2956 2 2962 1270.4 1270 9 0.2177 2001 15 6 355 18 150 4 218 44 10 9 8 37 261. Prymno 12. Victoria 27. Euterpe 2.3062 2.3342 2 3472 1278.4 1302.7 1313.5 0.0794 0.2189 1739 179 35 301 39 87 59 96 33 235 35 93 51 3 38 8 23 1 36 219. Thusnelda 163 Erigone 2.3542 2 3560 1319.4 1320 9 0.2247 1567 340 34 93 46 200 44 159 2 10 47 4 42 169. Zelia . 2 3577 1322 3 1313 326 20 354 38 5 31 4. Vesta 2 3616 1325 6 0884 250 57 103 29 7 8 186. Celuta 2 3623 1326 2 1512 327 24 14 34 13 6 84 Clio 23629 1326 7 2360 339 20 327 28 9 22 51. Nemausa 220. Stephania 30. Urania 105. Artemis 113. Amalthea 2.3652 2.3666 2.3667 2.3744 2 3761 1328.6 1329.8 1329.9 1336.4 1337 8 0.0672 0.2653 0.1266 0.1749 0874 174 43 332 53 31 46 242 38 198 44 175 52 258 24 308 12 188 3 123 11 9 57 7 35 2 6 21 31 5 2 115. Thyra. 2 3791 1340 3 1939 43 2 309 5 11 35 161. Athor 172. Baucis.., 249 Use 2.3792 2.3794 2 3795 1340.5 1340.6 1340 6 0.1389 0.1139 2195 310 40 329 23 14 17 18 27 331 50 334 49 9 3 10 2 9 40 230. Athamantis.... 7. Iris 2.3842 2 3862 1344.6 1346 4 0.0615 2308 17 31 41 23 239 33 259 48 9 26 5 28 9. Metis 234 Barbara 2.3866 2 3873 1346.7 1347 3 0.1233 2440 71 4 333 26 68 32 144 9 5 36 15 22 60. Echo . . 2 3934 1352 4 1838 98 36 192 5 3 35 63. Ausonia,. 2 3979 1356 3 12*9 270 25 337 58 5 48 25. Phocea 192. Nausicaa 2.4005 2 4014 1358.5 1359 3 0.2553 2413 302 48 343 19 208 27 160 46 21 35 6 50 20. Massalia 265. Anna 2.4024 2 4096 1365.8 1366 2 0.1429 9 628 99 7 226 18 206 36 335 26 41 25 24 182. Elsa 2 4157 1371 4 1852 51 52 106 30 2 142. Polana 2 4194 1374 5 1322 219 54 317 34 2 14 67. Asia.. 2 4204 1375 4 1866 306 35 202 47 5 59 44. Nysa 2 4223 1377 1507 111 57 131 11 3 42 30 THE ASTEROIDS. Table II. Continued. Name a P e 7T n i 6 Hebe 2.4254 1379 3d 0.2034 15 16' 138 43' 10 47' 83. Beatrix 2.4301 1383 6 0.0859 191 46 27 32 5 135. Hertha 131 Vala 2.4303 2.4318 1383.8 1385 1 0.2037 0683 320 11 222 50 344 3 65 15 2 19 4 58 112 Iphi< r enia 2.4335 1386 6 0.1282 338 9 324 3 2 37 21 Lutetia 2 4354 1388 2 1621 327 4 80 28 3 5 118 Peitho . 2.4384 1390 8 1608 77 36 47 30 7 48 126 Velledo 2.4399 1392.1 0.1061 347 46 23 7 2 56 42 Isis 2 4401 1392 2 2256 317 58 84 28 8 35 19. Fortuna 79. Eurynome 138 Tolosa 2.4415 2.4436 2 4492 1394.4 1395.2 1400 0.1594 0.1945 1623 31 3 44 22 311 39 211 27 206 44 54 52 1 33 4 37 3 14 189 Phthia 2 4505 1401 1 0356 6 50 203 22 5 10 11. Parthenope 178 Belisana 2.4529 2.4583 1403.2 1407.8 0.0994 0.1266 318 2 278 125 11 50 17 4 37 2 5 198. Ampella 248 Lameia 2.4595 2.4714 1408.9 1419.1 0.2266 0.0656 354 46 248 40 268 45 246 34 9 20 4 1 17 Thetis 2 4726 1420 1 1293 261 37 125 24 5 36 46. Hestia 89 Julia 2.5265 2 5510 1466.8 1488 2 0.1642 1805 354 14 353 13 181 31 31] 42 2 17 16 11 232. Russia 2.5522 1489.3 0.1754 200 25 152 30 6 4 29. Amphitrite .... 170 Maria 2.5545 2 5549 1491.3 1491 7 0.0742 0.0639 56 23 95 47 356 41 301 20 6 7 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 264 Libussa 2.5647 2.5672 1500.3 1502.4 0.1165 0.0925 67 33 7 346 22 50 23 11 36 10 29 193 Ambrosia 2.5758 1510.0 0.2854 70 52 351 15 11 39 13 Egeria 2 5765 1510 6 0871 120 10 43 12 16 32 5. Astraea 119 Althea 2.5786 2.5824 1512.4 1515.7 0.1863 0.0815 134 57 11 29 141 28 203 57 5 19 5 45 1 157. Dejanira 101 Helena 2.5828 2.5849 1516.1 1518.0 0.2105 0.1386 107 24 327 15 62 31 343 46 12 2 10 11 32 Pomona 25873 1520.1 0.0830 193 22 220 43 5 29 91 j33ina 2 5895 1522 I 1087 80 22 11 7 2 8 14 Irene 2 5896 1522.1 1627 180 19 86 48 9 8 111 Ate 2.5927 1524.8 0.1053 108 42 306 13 4 57 151. Abundantia.... 56 Melete 2.5932 2 6010 1525.3 1532.2 0.0356 2340 173 55 294 50 38 48 194 1 6 30 8 2 132. JEthra 2 6025 1533.5 0.3799 152 24 260 2 25 214 Aschera 2 6111 1541 1 0316 115 55 342 30 3 27 2 6139 1*43.6 0.1826 299 49 48 18 11 38 194. Procue 2.6159 1545.4 0.2383 319 33 159 19 18 24 53. Calypso 78 Diana ... 2.6175 2 6194 1546.8 1548 5 0.2060 0.2088 92 52 121 42 143 58 333 58 5 7 8 40 124. Alceste 23. Thalia 2.6297 2.6306 1557.6 1558.4 0.0784 0.2299 245 42 123 58 188 26 67 45 2 56 10 14 164 Eva 2 6314 1559.1 0.3471 359 32 77 28 24 1'> 15. Eunomia 37. Fides 2.6437 2.6440 1570.0 1570.3 0.1872 0.1758 27 52 66 26 188 26 8 21 2 56 3 7 THE ASTEROIDS. 31 Table II. Continued. Name a P 7T a 66 Maia 2 6454 1571 6d 0.1750 48 8' 8 17' 3 6' 224 Oceana 2.6465 1572.6 0.0455 270 51 353 18 5 52 253. Mathilde 50. Virginia 144 Vibilia 2.6469 2.6520 2 6530 1572.9 1577.4 1578.4 0.2620 0.2852 0.2348 333 39 10 9 7 9 180 3 173 45 76 47 6 37 2 48 4 48 85 Io 2.6539 1579.2 0.1911 322 35 203 56 11 53 26. Proserpine 233 Asterope . .. 2.6561 2 6596 1581.1 1584 3 0.0873 0.1010 236 25 344 36 45 55 222 25 3 36 7 39 102 Miriam 2 6619 1586 3 0.3035 354 39 211 58 5 4 240. Venadis 73 Clytie 2.6638 2 6652 1588.0 1589 3 0.2056 0419 51 53 57 55 114 54 7 51 2 6 2 24 218 Bianca 2 6653 1589 3 1155 230 14 170 50 15 13 141 Lumen 2 6666 1590.5 0.2115 13 43 319 7 11 57 2 6680 1591 8 1318 58 47 2 2 28 2 6683 1592 2579 54 50 170 53 13 1 97 Clotho 2 6708 159-1.3 2550 65 32 160 37 11 46 75 Eurydice 2 6720 1595.3 0.3060 335 33 359 56 5 1 145. Adeona 204. Callisto 114. Cassandra 201 Penelope 2.6724 2.6732 2.6758 2 6764 1595.4 1596.4 1598.8 1599 3 0.1406 0.1752 0.1401 1818 117 53 257 45 153 6 334 21 77 41 205 40 164 24 157 5 12 38 8 19 4 55 5 44 64. Angelina 98 lanthe 2.6816 2 6847 1603.9 1606 7 0.1271 1920 125 36 148 52 311 4 354 7 1 19 15 32 34. Circe 2 6864 1608 3 1073 148 41 184 46 5 27 123. Brunhilda 166. Rhodope 109. Felicitas 2.6918 2.6927 2.6950 1613.2 1613.9 1616.0 0.1150 0.2140 0.3002 72 57 30 51 56 1 308 28 129 33 4 56 6 27 12 2 8 3 246. Asporina 58. Concordia 2.6994 2 7004 1619.9 1620 8 0.1065 0426 255 54 189 10 162 35 161 20 15 39 5 2 103. Hera 2 7014 1621.8 0803 321 3 136 18 5 24 54. Alexandra 226. Weringia 59. Olympia 2.7095 2.7118 2 7124 1629.1 1631.2 1631 7 0.2000 0.2048 1189 295 39 284 46 17 33 313 45 135 18 170 26 11 47 15 50 8 37 '146. Lucina 2 7189 1637.5 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 1220 44 22 32 58 5 ig 187. Lamberta 180. Garumna 2.7272 2.7286 1645.0 1646.3 0.2391 1722 214 4 125 56 22 13 314 42 10 43 54 160 Una 2 7287 1646 4 0624 55 57 9 22 3 51 140 Siwa 2 7316 1649 2160 300 33 107 2 3 12 110. Lydia 2 7327 1650 0770 336 49 57 10 6 185. Eunice.. 2.7372 1654.1 0.1292 16 32 153 50 23 17 203. Potnpeia 200. Dynamene 197. Arete .. .. 2.7376 2.7378 2 7390 1654.5 1654.6 1655 8 0.0588 0.1335 1621 42 51 46 38 324 51 348 37 325 26 82 6 3 13 6 56 8 48 206. Hersilia 2.7399 1656.5 0.0389 95 44 145 16 3 46 255. Oppavia 247. Eukrate 2.7402 2 7412 1656.6 1657 7 0.0728 23S7 169 15 53 44 14 6 20 9 33 95 7 38. Leda .. 2 7432 1659 6 1531 101 20 296 27 6 57 125. Liberatrix 2.7437 1660.0 0.0798 273 29 169 35 4 38 32 THE ASTEROIDS. Table II. Continued. Name a P e IT Q i 173 Ino 2 7446 1660.8 d 2047 13 28' 148 34' 14 15' 36. Atalanta 2.7452 2.7514 1661.3 1666.9 0.3023 0.1257 42 44 16 34 359 14 76 31 18 42 6 16 93 Minsrva 2 7537 1669 1405 274 44 5 4 8 37 177 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 r^3. Lilsea 2.7563 1671.4 0.1437 281 4 122 17 6 47 <>5 Pandora 2.7604 1675.1 0.1429 10 36 10 56 7 14 237. Celestina 143. Adria 2.7607 2.7619 1675.5 1676.6 0.0738 0.0729 282 49 222 27 84 33 333 42 9 46 11 30 82. Alctnene 116. Sirona 2.7620 2.7669 1676.6 1681.1 0.2228 0.1433 131 45 152 47 26 57 64 26 2 51 3 35 1 Ceres 2 7673 1681 4 0763 149 38 80 47 10 37 88 Thisbe 2.7673 1681.5 0.1632 308 34 277 54 16 11 215. (Enone 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 Lsetitia 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. Irina 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 4 205 Martha 2 7771 1690.4 1752 21 54 212 12 10 40 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 99 Dike ....*... 2.7964 2.7966 1708.0 1708.3 0.2492 0.2384 328 15 240 36 215 49 41 44 13 2 13 53 236 Honoria 2.7993 1710.7 0.1893 356 59 186 27 7 37 183 Istria 2.8024 1713.4 0.3530 45 142 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 0340 296 4 166 28 2 11 81. Terpsichore 174. Phedra 243 Ida 2.8580 2.8600 2.8610 1764.8 1766.6 1767.5 0.2080 0.1492 0.0419 49 1 253 12 71 22 2 25 328 49 326 21 7 55 12 9 1 10 242. Kriemhild 129. Antigone 2.8623 2.8678 2.8690 1768.7 1773.9 1774.9 0.1219 0.2126 0.3068 123 1 242 4 314 41 207 57 137 37 164 10 11 17 12 10 10 19 158 Coronis ... 2.8714 1777.2 0.0545 56 56 281 30 1 33. Polyhymnia.... 195. Euryclea 235. Caroline 47. Aglaia 208. Lachrymosa.... 191 Kolga 2.8751 2.8790 2.8795 2.8819 2.8926 2 8967 1780.7 1784.2 1784.7 1786.9 1796.9 1800.8 0.3349 0.0471 0.0595 0.1317 0.0149 0.0876 342 59 115 48 268 29 312 40 127 52 23 21 9 19 7 57 66 35 40 20 5 43 159 47 1 56 7 1 9 4 5 1 1 48 11 29 22 Calliope 2.9090 1801.0 0.0193 62 43 4 47 1 45 155 Soylla 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 THE ASTEROIDS. Table II. Continued. 33 Name a P e 77 Q, i 16. Psyche 2 9210 1 823.4 d 0.1392 15 9' 150 36' 3 4' 179. Clytemnestra... 239 Adrastea .. 2.9711 2 9736 1870.6 1873 0.1133 2279 355 39 26 1 253 13 181 34 7 47 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 Danae 2 9855 1884 2 1615 344 4 334 11 18 14 2 9907 1889 1 0229 48 46 349 39 14 58 35. Leucothea 263. Dresda 2.9923 3 0120 1890.6 1909 3 0.2237 3051 202 25 308 49 355 49 217 56 8 12 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. Xautippe 211. Germania 3.0375 3.0381 1933.7 1934.0 0.2637 0.1013 155 58 340 7 246 11 272 28 7 29 5 30 256. Walpurga 211. Isolda .. 3.0450 3 0464 1940.8 1942.2 0.1180 0.1541 240 17 74 12 183 35 265 29 12 44 51 96. M\Q 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. Gyrene 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 49. Pales... 3.0904 3 0908 1984.3 1984.7 0.1639 0.2330 308 3 31 15 128 12 290 40 6 23 3 8 223. Rosa 3 0940 1987.9 0.1186 102 48 49 1 59 52. Europa 3.0955 1988.0 0.1098 106 57 129 40 7 27 245. Vera . 3 0985 1992 1 1950 25 29 62 37 5 10 86. Sernele 159. JEmilia .. 3.1015 3 1089 1995.1 2002.2 0.2193 0.1034 29 10 101 22 87 45 135 9 4 47 6 4 48. Doris 3 1127 2005.9 0.0649 70 33 184 55 6 31 196. Philomela 130. Electra 212. Medea 3.1137 3.1145 3 1157 2006.8 2007.7 2008 8 0.0118 0.2132 0-1013 309 19 20 34 56 18 73 24 146 6 315 16 7 16 22 57 4 16 120. Lachesis 181. Eucharis 3.1211 3.1226 2014.0 2015.4 0.0475 2205 214 95 25 342 51 144 45 7 1 18 38 62. Erato 3 1241 2016 9 1756 39 125 46 2 12 222. Lucia . . 3 1263 2019 1453 258 2 80 11 2 11 137. Meliboea 3.1264 2019 1 2074 307 58 204 22 13 22 165. Loreley 251. Sophia 24. Themis 152. Atala 3.1269 3.1315 3.1357 3 1362 2019.6 2024.1 2028.1 2028 6 0.0734 0.1243 0.1242 0862 223 50 77 7 144 8 84 23 304 6 157 6 35 49 41 29 10 12 10 20 49 12 12 10. Hygeia 3.1366 2029.1 1156 237 2 285 38 3 49 259 Aletheia 3 1369 2029 3 1176 241 45 88 32 10 40 227. Philosophia.... 147. Protogenea 171. Ophelia 3.1393 3.1393 3.1432 2031.6 2031.6 2035 4 0.2131 0.0247 1168 226 23 25 38 143 59 330 52 251 16 101 10 9 16 1 54 2 34 209 Dido 3 1436 2035 9 0637 257 33 2 7 15 31. Euphrosyne .... 90. Antiope 3.1468 3 1475 2039.0 2039 7 0.2228 1645 93 26 301 15 31 31 71 29 26 27 2 17 104. Clyinene 3.1507 2042.7 1579 59 32 43 32 2 54 34 THE ASTEROIDS. Table II. Continued. Name a P e 7T Q, i 57. Mnemosyne ... 250. Bettina 3.1510 3 1524 2043.0 d 2044.3 0.1145 0.1302 53 25' 87 28 200 2' 26 12 15 12' 12 54 252. Clementina 94. Aurora 3.1552 3.1602 2047.1 2052.0 0.0837 0827 355 8 48 46 208 19 4 9 10 2 8 4 106 Dione 3 1670 2058 6 1788 25 57 63 14 4 38 199. Byblis . 3 1777 2069 1687 261 20 89 52 15 22 99. 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 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 0.1005 173 49 352 17 4 24 122 Gerda 3 2177 2108 2 0415 203 45 178 43 1 36 168. Sibylla 225. Henrietta 229 Adelinde 3.3765 3.4007 3 4129 2266.2 2277.8 2302 9 0.0707 0.2661 1562 11 26 299 13 332 7 209 47 200 45 30 49 4 33 20 45 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... 121. Hermione 87. Sylvia. 3.4270 3.4535 3.4833 2317.2 2344.2 2374.5 0.1097 0.1255 0.0922 260 36 357 50 333 48 158 50 76 46 75 49 3 29 7 36 10 55 107. Camilla 34847 2376.0 0.0756 115 53 176 18 9 54 175. Andromache... 190 Ismene 3.5071 3 9471 2399.0 2864.3 0.3476 0.1634 293 105 39 23 35 177 3 46 6 7 153. Hilda 3.9523 2869.9 0.1721 285 47 228 20 7 55 PART II. DISCUSSION OF THE FACTS IN TABLE IT. 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 JEthra (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."* 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 * This ingenious idea may be readily extended. The least dis- tance of ^Ethra 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. 4 37 38 THE ASTEROIDS. 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 com- pletely 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 can- not 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 Ura- nian system the widest interval between adjacent orbits is just within the orbit of the bright satellite, Titania. THE ASTEROIDS. 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 pro- duce 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.* The extreme rarity of the zone between Mars and Jupiter, regarded as a single ring, is thus accounted for in ac- cordance 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 Mer- cury's orbit had its present eccentricity when the radius * The effects of Jupiter's disturbing influence will again be resumed. 40 THE ASTEROIDS. of the solar spheriocl 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 iu the formation of the solar system the eccen- tricity 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 ? Distribu- tion of the Members in Space. One of the most interesting discoveries of the eigh- teenth 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 THE ASTEROIDS. 41 minor planets may have their orbits much changed by Jupiter's disturbing influence.* 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 con- nection. Nor is the confusion lessened when the orbits are drawn and presented to the eye. In fact, the cross- ing 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 * Not only nebulae are probably unstable, but also many of the sidereal systems. The Milky Way itself was so regarded by Sir William Herschel. 4* 42 THE ASTEROIDS. the solar system itself. The train of thought was some- what 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 eccen- tricities 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 an- nounced with some hesitation that those parts of the as- teroid 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 simi- lar 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 THE ASTEROIDS. 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 har- mony with this law of distribution.* COMM-ENSURABILITY OF PERIODS. When we say that an asteroid's period is commensur- able 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 com- mensurability. Thus, if the ratio of the less to the greater period is expressed by the fraction J, where the difference between the numerator and the denominator is one, the commensurability is of the first order; J is of the second ; f , of the third, etc. The difference between the terms of the ratio indicates the frequency of conjunc- tions while Jupiter is completing the number of revolu- tions expressed by the numerator. The distance 3.277, corresponding to the ratio J, is the only case of the first order in the entire ring; those of the second order, an- swering to J and f, 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 : * Menippc, No. 188, is placed in one of the gaps by its calcu- lated elements ; but the fact that it has not been seen since the year of its discovery, 1878, indicates a probable error in its ele- ments. 44 THE ASTEROIDS. Order. Ratio. Distance. First ... .... 1 3 277 Second 2 1 3 /2.50 Third * i 4 t3.70 (282 J 3 58 Fourth 7>> 7> 7F 4 4 T V (3.80 (2.95 | 3 51 7' 9> TT I 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 ar- ranged 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 per- fect 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 Dis- tances 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- THE ASTEROIDS. 45 fifths. That part of the zone included between the dis- tances 2.30 and 2.70 contains one hundred and ten inter- vals, 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 dis- tances 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,* 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 minor planet Andromache, immediately interior to the critical distance 3.51, has elements somewhat remarkable. With 46 THE ASTEROIDS. 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 com- mensurability 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, ^, -| , -J-, and -^ T , 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 improba- bility 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 arrange- ment. What, then, was their physical cause ? and what has become of the eliminated asteroids ? two exceptions, ^Ethra (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. tl V,. THE ASTEROIDS. 47 . What was said in regard to the limits of perihelion distance may suggest a possible answer to these inter- esting questions. The doctrine of the sun's gradual contraction is now accepted by a majority of astrono- mers. According to this theory the solar radius at an epoch not relatively remote was twice what it is at pres- ent. At anterior stages it was 0.4, 1.0, 2.0,* 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 dis- tance of jEthra 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 dis- turbance 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, how- ever, that the longitudes of their perihelia differ by almost exactly 180. Did they separate at nearly the The unit being the sun's distance from the earth. 48 THE ASTEROIDS. same time from opposite sides of the solar nebula? Other adjacent pairs having a striking similarity be- tween 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 un- equal 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 Philo- mela (196); the most eccentric that of JEthra (132). Comparing these with the orbit of the second comet of 1867 we have The eccentricity of Philomela = 0.01 " J3thra = 0.38 Comet II. 1867 (ret. in 1885) = 0.41 " " The orbit of .ZEthra, 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 increas- ing, 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 ASTEEOIDS. 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 to 4 70 " 4 to 8 83 " 8 to 12 '.. 59 " 12 to 16 , 32 " 10 to 20 8 " 20 to 24 8 24 to 28 7 " 28 to 32 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 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 : 50 THE ASTEKOIDS. Asteroid. Inclination. Eccentricity. Pallas 34 42' 238 Istria 26 30 353 Euphrosync 26 29 0228 Anna 25 24 263 Gallia 25 21 185 ^Ethra 25 380 Eukrate 24 57 0.236 Eva 24 25 347 Niot)p 23 19 173 Eunice 23 17 129 Electra 22 55 208 Idunna 22 31 164 Phocea 21 35 0255 Artemis 21 31 0.175 Bertha 20 59 0085 Henrietta .. 20 47 0260 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 un- equally distributed ; one hundred and thirty-six a ma- jority 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. THE ASTEKOIDS. 51 9. Distribution of the Ascending Nodes. An inspection of the column containing the longi- tudes of the ascending nodes, in Table II., indicates two well-marked maxima, each extending about sixty de- grees, 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 for- mer. This marked irregularity in the order of periods is seen below. Between 1100 and 1200 days 6 periods. 1200 ' 1300 7 1300 1 1400 43 1400 ' 1500 13 1500 ' 1600 46 1600 ' 1700 54 1700 ' 1800 20 1800 ' 1900 13 1900 ' 2000 19 2000 ' 2100 33 2100 1 2200 2 2200 ' 2300 2 2300 ' 2400 ... 8 2400 1 2800 2800 ' 2900 . 2 52 THE ASTEROIDS. 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 maxi- mum observed between 2000 and 2100 days corresponds to the space immediately interior to chasm I. on a pre- vious 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, how- ever, whether any two of these periods are exactly equal. In cases of a very close approach two asteroids, notwith- standing 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 "Syste~me 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 re- quire a modification of Laplace's theory. Throughout the greater part of the interval between Mars and Ju- piter an almost continuous succession of small planet- ary masses not nebulous rings appears to have been abandoned at the solar equator. The entire cluster, THE ASTEROIDS. 53 distributed throughout a space whose outer radius ex- ceeds the inner by more than two hundred millions of miles, could not have originated, as supposed by La- place, 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 attrac- tion 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. (6) 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 influ- ence of the planet would therefore be increased at each conjunction with this protuberance. The ultimate sep- aration (not of a ring but) of a planetary mass would be the probable result of these combined and accumu- lating forces. 12. Variability of Certain Asteroids. Observations of some minor planets have indicated a variation of their apparent magnitudes. Frigga, dis- covered by Dr. Peters in 1862, was observed at the next opposition in 1864 ; but after this it could not be 5* 54 THE ASTEROIDS. 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 pa- per 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 con- sidered 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. Sved- strup, of Copenhagen. The results obtained by these astronomers severally are as follows : THE ASTEROIDS. 55 Harrington. Svedstrup. 14 39' 101 48' " of ascGndin " node 113 56 133 27 1 6 6 0448 00281 Aea.n 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 au- thority 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-Filhes, the eccentricity of the third comet of 1884, before its last close approach to Jupiter, was only 0.2787.* 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 commensura- bility of the first order. According to Hind and Krue- ger, the great transformation of its orbit by Jupiter's influence occurred in May, 1875. It had previously Annuaire, 1886. 56 THE ASTEROIDS. 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 be- tween the orbits of Mars and Jupiter. Its eccentricity, as we have seen, is little greater than that of JEthra, 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 com- mensurability. 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 LexelPs comet. Two well-known comets, Faye's and Denning's, have periods approximately equal to two-thirds of Ju- piter'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- THE ASTEROIDS. 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 gen- erally 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 UNDIS- COVERED 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 indefi- nitely 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 lumi- nous 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 propo- sitions : 69 60 APPENDIX. 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 con- siderable 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, Oc- tober 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. FOURTEEN DAY USE RETURN TO DESK FROM WHICH BORROWED This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. 1 9 1357 iqcq 1393 RECTD LD MAY 3 5 1969 6 9 LD 21-100m-2,'55 (B139s22)476 General Library University of California Berkeley