The Project Gutenberg eBook, The Asteroids, by Daniel Kirkwood This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: The Asteroids Or Minor Planets Between Mars and Jupiter. Author: Daniel Kirkwood Release Date: December 6, 2012 [eBook #41570] Language: English Character set encoding: UTF-8 ***START OF THE PROJECT GUTENBERG EBOOK THE ASTEROIDS*** E-text prepared by Paul Clark, sp1nd, and the Online Distributed Proofreading Team (http://www.pgdp.net) from page images generously made available by Internet Archive (http://archive.org) Note: Images of the original pages are available through Internet Archive. See http://archive.org/details/asteroidsorminor00kirkrich Transcriber's Note: Every effort has been made to replicate this text as faithfully as possible, including non-standard spelling and punctuation. Some apparent typographical errors in the indices and names of asteroids in Tables I and II have been corrected. THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER. [Pg 1] 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. 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 [Pg 2] [Pg 3] [Pg 4] [Pg 5] 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 [Pg 6] [Pg 7] [Pg 8] [Pg 9] [Pg 10] [Pg 11] 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. [Pg 12] [Pg 13] [Pg 14] [Pg 15] 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 Discovery. Name of Discoverer. Place of 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 [Pg 16] [Pg 17] 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 [Pg 18] 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 Lesser Berlin 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 Safford Clinton 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 [Pg 19] 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 [Pg 20] 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 [Pg 21] 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 [Pg 22] 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 [Pg 23] [Pg 24] 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." [Pg 25] [Pg 26] [Pg 27] 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 [Pg 28] [Pg 29]