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diff --git a/41570.txt b/41570.txt deleted file mode 100644 index 0b880e2..0000000 --- a/41570.txt +++ /dev/null @@ -1,2237 +0,0 @@ -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: ISO-646-US (US-ASCII) - - -***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: - - Text enclosed by underscores is in italics (_italics_). - - [pi] represents the Greek letter pi, and [AN] the symbol for - the ascending node. The degree sign has been replaced by D - (example: 246D). - - Every effort has been made to replicate this text as faithfully - as possible, including non-standard spelling and punctuation. - Some apparent typographical errors in the indices and names of - asteroids in Tables I and II have been corrected. - - - - - -THE ASTEROIDS, - -Or Minor Planets Between Mars and Jupiter. - -by - -DANIEL KIRKWOOD, LL.D., - -Professor Emeritus in the University of Indiana; Author of "Comets -and Meteors," "Meteoric Astronomy," etc. - - - - - - - -Philadelphia: -J. B. Lippincott Company. -1888. - -Copyright, 1887, by Daniel Kirkwood. - -[Illustration] - - - - -PREFACE. - - -The rapid progress of discovery in the zone of minor planets, the -anomalous forms and positions of their orbits, the small size as well as -the great number of these telescopic bodies, and their peculiar -relations to Jupiter, the massive planet next exterior,--all entitle -this part of the system to more particular consideration than it has -hitherto received. The following essay is designed, therefore, to supply -an obvious want. Its results are given in some detail up to the date of -publication. Part I. presents in a popular form the leading historical -facts as to the discovery of Ceres, Pallas, Juno, Vesta, and Astraea; a -tabular statement of the dates and places of discovery for the entire -group; a list of the names of discoverers, with the number of minor -planets detected by each; and a table of the principal elements so far -as computed. - -In Part II. this descriptive summary is followed by questions relating -to the origin of the cluster; the elimination of members from particular -parts; the eccentricities and inclinations of the orbits; and the -relation of the zone to comets of short period. The elements are those -given in the Paris _Annuaire_ for 1887, or in recent numbers of the -_Circular zum Berliner Astronomischen Jahrbuch_. - -DANIEL KIRKWOOD. - -BLOOMINGTON, INDIANA, November, 1887. - - - - -CONTENTS. - - - PART I. PAGE - - PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN 9 - - DISCOVERY OF THE FIRST ASTEROIDS 11 - - TABLE I.--ASTEROIDS IN THE ORDER OF THEIR DISCOVERY 17 - - NUMBERS FOUND BY THE RESPECTIVE DISCOVERERS 23 - - NUMBERS DISCOVERED IN THE DIFFERENT MONTHS 25 - - MODE OF DISCOVERY 25 - - NAMES AND SYMBOLS 25 - - MAGNITUDES OF THE ASTEROIDS 26 - - ORBITS OF THE ASTEROIDS 28 - - TABLE II.--ELEMENTS OF THE ASTEROIDS 29 - - - PART II. - - EXTENT OF THE ZONE 37 - - THEORY OF OLBERS 38 - - SMALL MASS OF THE ASTEROIDS 38 - - LIMITS OF PERIHELION DISTANCE 39 - - DISTRIBUTION OF THE ASTEROIDS IN SPACE 40 - - LAW OF GAP FORMATION 42 - - COMMENSURABILITY OF PERIODS WITH THAT OF JUPITER 43 - - ORDERS OF COMMENSURABILITY 44 - - ELIMINATION OF VERY ECCENTRIC ORBITS 46 - - RELATIONS BETWEEN CERTAIN ADJACENT ORBITS 47 - - THE ECCENTRICITIES 48 - - THE INCLINATIONS 49 - - LONGITUDES OF THE PERIHELIA AND OF THE ASCENDING NODES 50 - - THE PERIODS 51 - - ORIGIN OF THE ASTEROIDS 52 - - VARIABILITY OF CERTAIN ASTEROIDS 53 - - THE AVERAGE ASTEROID ORBIT 54 - - THE RELATION OF SHORT-PERIOD COMETS TO THE ZONE OF ASTEROIDS 55 - - APPENDIX 59 - - - - -PART I. - - - - -THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER. - - - - -1. Introductory. - - -PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN. - -The first observer who watched the skies with any degree of care could -not fail to notice that while the greater number of stars maintained the -same relative places, a few from night to night were ever changing their -positions. The planetary character of Mercury, Venus, Mars, Jupiter, and -Saturn was thus known before the dawn of history. The names, however, of -those who first distinguished them as "wanderers" are hopelessly lost. -Venus, the morning and evening star, was long regarded as two distinct -bodies. The discovery that the change of aspect was due to a single -planet's change of position is ascribed to Pythagoras. - -At the beginning of the seventeenth century but six primary planets and -one satellite were known as members of the solar system. Very few, even -of the learned, had then accepted the theory of Copernicus; in fact, -before the invention of the telescope the evidence in its favor was not -absolutely conclusive. On the 7th of January, 1610, Galileo first saw -the satellites of Jupiter. The bearing of this discovery on the theory -of the universe was sufficiently obvious. Such was the prejudice, -however, against the Copernican system that some of its opponents denied -even the reality of Galileo's discovery. "Those satellites," said a -Tuscan astronomer, "are invisible to the naked eye, and therefore can -exercise no influence on the earth, and therefore would be useless, and -therefore do not exist. Besides, the Jews and other ancient nations, as -well as modern Europeans, have adopted the division of the week into -_seven_ days, and have named them from the seven planets; now, if we -increase the number of planets this whole system falls to the ground." - -No other secondary planet was discovered till March 25, 1655, when -Titan, the largest satellite of Saturn, was detected by Huyghens. About -two years later (December 7, 1657) the same astronomer discovered the -true form of Saturn's ring; and before the close of the century -(1671-1684) four more satellites, Japetus, Rhea, Tethys, and Dione, were -added to the Saturnian system by the elder Cassini. Our planetary -system, therefore, as known at the close of the seventeenth century, -consisted of six primary and ten secondary planets. - -Nearly a century had elapsed from the date of Cassini's discovery of -Dione, when, on the 13th of March, 1781, Sir William Herschel -enlarged the dimensions of our system by the detection of a -planet--Uranus--exterior to Saturn. A few years later (1787-1794) the -same distinguished observer discovered the first and second satellites -of Saturn, and also the four Uranian satellites. He was the only planet -discoverer of the eighteenth century. - - -2. Discovery of the First Asteroids. - -As long ago as the commencement of the seventeenth century the -celebrated Kepler observed that the respective distances of the planets -from the sun formed nearly a regular progression. The series, however, -by which those distances were expressed required the interpolation of a -term between Mars and Jupiter,--a fact which led the illustrious German -to predict the discovery of a planet in that interval. This conjecture -attracted but little attention till after the discovery of Uranus, whose -distance was found to harmonize in a remarkable manner with Kepler's -order of progression. Such a coincidence was of course regarded with -considerable interest. Towards the close of the last century Professor -Bode, who had given the subject much attention, published the law of -distances which bears his name, but which, as he acknowledged, is due to -Professor Titius. According to this formula the distances of the planets -from Mercury's orbit form a geometrical series of which the ratio is -two. In other words, if we reckon the distances of Venus, the earth, -etc., from the orbit of Mercury, instead of from the sun, we find -that--interpolating a term between Mars and Jupiter--the distance of any -member of the system is very nearly half that of the next exterior. -Baron De Zach, an enthusiastic astronomer, was greatly interested in -Bode's empirical scheme, and undertook to determine the elements of the -hypothetical planet. In 1800 a number of astronomers met at Lilienthal, -organized an astronomical society, and assigned one twenty-fourth part -of the zodiac to each of twenty-four observers, in order to detect, if -possible, the unseen planet. When it is remembered that at this time no -primary planet had been discovered within the ancient limits of the -solar system, that the object to be looked for was comparatively near -us, and that the so-called law of distances was purely empirical, the -prospect of success, it is evident, was extremely uncertain. How long -the watch, if unsuccessful, might have been continued is doubtful. The -object of research, however, was fortunately brought to light before the -members of the astronomical association had fairly commenced their -labors.[1] - -On the 1st of January, 1801, Professor Giuseppe Piazzi, of Palermo, -noticed a star of the eighth magnitude, not indicated in Wollaston's -catalogue. Subsequent observations soon revealed its planetary -character, its mean distance corresponding very nearly with the -calculations of De Zach. The discoverer called it Ceres Ferdinandea, in -honor of his sovereign, the King of Naples. In this, however, he was not -followed by astronomers, and the planet is now known by the name of -Ceres alone. The discovery of this body was hailed by astronomers with -the liveliest gratification as completing the harmony of the system. -What, then, was their surprise when in the course of a few months this -remarkable order was again interrupted! On the 28th of March, 1802, Dr. -William Olbers, of Bremen, while examining the relative positions of the -small stars along the path of Ceres, in order to find that planet with -the greater facility, noticed a star of the seventh or eighth magnitude, -forming with two others an equilateral triangle where he was certain no -such configuration existed a few months before. In the course of a few -hours its motion was perceptible, and on the following night it had very -sensibly changed its position with respect to the neighboring stars. -Another planet was therefore detected, and Dr. Olbers immediately -communicated his discovery to Professor Bode and Baron De Zach. In his -letter to the former he suggested Pallas as the name of the new member -of the system,--a name which was at once adopted. Its orbit, which was -soon computed by Gauss, was found to present several striking anomalies. -The inclination of its plane to that of the ecliptic was nearly -thirty-five degrees,--an amount of deviation altogether extraordinary. -The eccentricity also was greater than in the case of any of the old -planets. These peculiarities, together with the fact that the mean -distances of Ceres and Pallas were nearly the same, and that their -orbits approached very near each other at the intersection of their -planes, suggested the hypothesis that they are fragments of a single -original planet, which, at a very remote epoch, was disrupted by some -mysterious convulsion. This theory will be considered when we come to -discuss the tabulated elements of the minor planets now known. - -For the convenience of astronomers, Professor Harding, of Lilienthal, -undertook the construction of charts of all the small stars near the -orbits of Ceres and Pallas. On the evening of September 1, 1804, while -engaged in observations for this purpose, he noticed a star of the -eighth magnitude not mentioned in the great catalogue of Lalande. This -proved to be a third member of the group of asteroids. The discovery was -first announced to Dr. Olbers, who observed the planet at Bremen on the -evening of September 7. - -Before Ceres had been generally adopted by astronomers as the name of -the first asteroid, Laplace had expressed a preference for Juno. This, -however, the discoverer was unwilling to accept. Mr. Harding, like -Laplace, deeming it appropriate to place Juno near Jupiter, selected the -name for the third minor planet, which is accordingly known by this -designation. - -Juno is distinguished among the first asteroids by the great -eccentricity of its orbit, amounting to more than 0.25. Its least and -its greatest distances from the sun are therefore to each other very -nearly in the ratio of three to five. The planet consequently receives -nearly three times as much light and heat in perihelion as in aphelion. -It follows, also, that the half of the orbit nearest the sun is -described in about eighteen months, while the remainder, or more distant -half, is not passed over in much less than three years. Schroeter -noticed a variation in the light of Juno, which he supposed to be -produced by an axial rotation in about twenty-seven hours. - -The fact that Juno was discovered not far from the point at which the -orbit of Pallas approaches very near that of Ceres, was considered a -strong confirmation of the hypothesis that the asteroids were produced -by the explosion of a large planet; for in case this hypothesis be -founded in truth, it is evident that whatever may have been the forms of -the various orbits assumed by the fragments, they must all return to the -point of separation. In order, therefore, to detect other members of the -group, Dr. Olbers undertook a systematic examination of the two opposite -regions of the heavens through which they must pass. This search was -prosecuted with great industry and perseverance till ultimately crowned -with success. On the 29th of March, 1807, while sweeping over one of -those regions through which the orbits of the known asteroids passed, a -star of the sixth magnitude was observed where none had been seen at -previous examinations. Its planetary character, which was immediately -suspected, was confirmed by observation, its motion being detected on -the very evening of its discovery. This fortunate result afforded the -first instance of the discovery of two primary planets by the same -observer. - -The astronomer Gauss having been requested to name the new planet, fixed -upon Vesta, a name universally accepted. Though the brightest of the -asteroids, its apparent diameter is too small to be accurately -determined, and hence its real magnitude is not well ascertained. -Professor Harrington, of Ann Arbor, has estimated the diameter at five -hundred and twenty miles. According to others, however, it does not -exceed three hundred. If the latter be correct, the volume is about -1/20000 that of the earth. It is remarkable that notwithstanding its -diminutive size it may be seen under favorable circumstances by the -naked eye. - -Encouraged by the discovery of Vesta (which he regarded as almost a -demonstration of his favorite theory), Dr. Olbers continued his -systematic search for other planetary fragments. Not meeting, however, -with further success, he relinquished his observations in 1816. His -failure, it may here be remarked, was doubtless owing to the fact that -his examination was limited to stars of the seventh and eighth -magnitudes. - -The search for new planets was next resumed about 1831, by Herr Hencke, -of Driessen. With a zeal and perseverance worthy of all praise, this -amateur astronomer employed himself in a strict examination of the -heavens represented by the Maps of the Berlin Academy. These maps extend -fifteen degrees on each side of the equator, and contain all stars down -to the ninth magnitude and many of the tenth. Dr. Hencke rendered some -of these charts still more complete by the insertion of smaller stars; -or rather, "made for himself special charts of particular districts." On -the evening of December 8, 1845, he observed a star of the ninth -magnitude where none had been previously seen, as he knew from the fact -that it was neither found on his own chart nor given on that of the -Academy. On the next morning he wrote to Professors Encke and Schumacher -informing them of his supposed discovery. "It is very improbable," he -remarked in his letter to the latter, "that this should prove to be -merely a variable star, since in my former observations of this region, -which have been continued for many years, I have never detected the -slightest trace of it." The new star was soon seen at the principal -observatories of Europe, and its planetary character satisfactorily -established. The selection of a name was left by the discoverer to -Professor Encke, who chose that of Astraea. - -The facts in regard to the very numerous subsequent discoveries may best -be presented in a tabular form. - - -TABLE I. - -_The Asteroids in the Order of their Discovery._ - - -----------------+----------------+---------------+------------ - Asteroids. | Date of | Name of | Place of - | Discovery. | Discoverer. | Discovery. - -----------------+----------------+---------------+------------ - 1. Ceres | 1801, Jan. 1 | Piazzi | Palermo - 2. Pallas | 1802, Mar. 28 | Olbers | Bremen - 3. Juno | 1804, Sept. 1 | Harding | Lilienthal - 4. Vesta | 1807, Mar. 29 | Olbers | Bremen - 5. Astraea | 1845, Dec. 8 | Hencke | Driessen - 6. Hebe | 1847, July 1 | Hencke | Driessen - 7. Iris | 1847, Aug. 14 | Hind | London - 8. Flora | 1847, Oct. 18 | Hind | London - 9. Metis | 1848, Apr. 26 | Graham | Markree - 10. Hygeia | 1849, Apr. 12 | De Gasparis | Naples - 11. Parthenope | 1850, May 11 | De Gasparis | Naples - 12. Victoria | 1850, Sept. 13 | Hind | London - 13. Egeria | 1850, Nov. 2 | De Gasparis | Naples - 14. Irene | 1851, May 19 | Hind | London - 15. Eunomia | 1851, July 29 | De Gasparis | Naples - 16. Psyche | 1852, Mar. 17 | De Gasparis | Naples - 17. Thetis | 1852, Apr. 17 | Luther | Bilk - 18. Melpomene | 1852, June 24 | Hind | London - 19. Fortuna | 1852, Aug. 22 | Hind | London - 20. Massalia | 1852, Sept. 19 | De Gasparis | Naples - 21. Lutetia | 1852, Nov. 15 | Goldschmidt | Paris - 22. Calliope | 1852, Nov. 16 | Hind | London - 23. Thalia | 1852, Dec. 15 | Hind | London - 24. Themis | 1853, Apr. 5 | De Gasparis | Naples - 25. Phocea | 1853, Apr. 6 | Chacornac | Marseilles - 26. Proserpine | 1853, May 5 | Luther | Bilk - 27. Euterpe | 1853, Nov. 8 | Hind | London - 28. Bellona | 1854, Mar. 1 | Luther | Bilk - 29. Amphitrite | 1854, Mar. 1 | Marth | London - 30. Urania | 1854, July 22 | Hind | London - 31. Euphrosyne | 1854, Sept. 1 | Ferguson | Washington - 32. Pomona | 1854, Oct. 26 | Goldschmidt | Paris - 33. Polyhymnia | 1854, Oct. 28 | Chacornac | Paris - 34. Circe | 1855, Apr. 6 | Chacornac | Paris - 35. Leucothea | 1855, Apr. 19 | Luther | Bilk - 36. Atalanta | 1855, Oct. 5 | Goldschmidt | Paris - 37. Fides | 1855, Oct. 5 | Luther | Bilk - 38. Leda | 1856, Jan. 12 | Chacornac | Paris - 39. Laetitia | 1856, Feb. 8 | Chacornac | Paris - 40. Harmonia | 1856, Mar. 31 | Goldschmidt | Paris - 41. Daphne | 1856, May 22 | Goldschmidt | Paris - 42. Isis | 1856, May 23 | Pogson | Oxford - 43. Ariadne | 1857, Apr. 15 | Pogson | Oxford - 44. Nysa | 1857, May 27 | Goldschmidt | Paris - 45. Eugenia | 1857, June 27 | Goldschmidt | Paris - 46. Hestia | 1857, Aug. 16 | Pogson | Oxford - 47. Aglaia | 1857, Sept. 15 | Luther | Bilk - 48. Doris | 1857, Sept. 19 | Goldschmidt | Paris - 49. Pales | 1857, Sept. 19 | Goldschmidt | Paris - 50. Virginia | 1857, Oct. 4 | Ferguson | Washington - 51. Nemausa | 1858, Jan. 22 | Laurent | Nismes - 52. Europa | 1858, Feb. 4 | Goldschmidt | Paris - 53. Calypso | 1858, Apr. 4 | Luther | Bilk - 54. Alexandra | 1858, Sept. 10 | Goldschmidt | Paris - 55. Pandora | 1858, Sept. 10 | Searle | Albany - 56. Melete | 1857, Sept. 9 | Goldschmidt | Paris - 57. Mnemosyne | 1859, Sept. 22 | Luther | Bilk - 58. Concordia | 1860, Mar. 24 | Luther | Bilk - 59. Olympia | 1860, Sept. 12 | Chacornac | Paris - 60. Echo | 1860, Sept. 16 | Ferguson | Washington - 61. Danae | 1860, Sept. 9 | Goldschmidt | Paris - 62. Erato | 1860, Sept. 14 | Foerster and | Berlin - | | Lesser | - 63. Ausonia | 1861, Feb. 10 | De Gasparis | Naples - 64. Angelina | 1861, Mar. 4 | Tempel | Marseilles - 65. Maximiliana | 1861, Mar. 8 | Tempel | Marseilles - 66. Maia | 1861, Apr. 9 | Tuttle | Cambridge, U.S. - 67. Asia | 1861, Apr. 17 | Pogson | Madras - 68. Leto | 1861, Apr. 29 | Luther | Bilk - 69. Hesperia | 1861, Apr. 29 | Schiaparelli | Milan - 70. Panopea | 1861, May 5 | Goldschmidt | Paris - 71. Niobe | 1861, Aug. 13 | Luther | Bilk - 72. Feronia | 1862, May 29 | Peters and | Clinton - | | Safford | - 73. Clytie | 1862, Apr. 7 | Tuttle | Cambridge - 74. Galatea | 1862, Aug. 29 | Tempel | Marseilles - 75. Eurydice | 1862, Sept. 22 | Peters | Clinton - 76. Freia | 1862, Oct. 21 | D'Arrest | Copenhagen - 77. Frigga | 1862, Nov. 12 | Peters | Clinton - 78. Diana | 1863, Mar. 15 | Luther | Bilk - 79. Eurynome | 1863, Sept. 14 | Watson | Ann Arbor - 80. Sappho | 1864, May 2 | Pogson | Madras - 81. Terpsichore | 1864, Sept. 30 | Tempel | Marseilles - 82. Alcmene | 1864, Nov. 27 | Luther | Bilk - 83. Beatrix | 1865, Apr. 26 | De Gasparis | Naples - 84. Clio | 1865, Aug. 25 | Luther | Bilk - 85. Io | 1865, Sept. 19 | Peters | Clinton - 86. Semele | 1866, Jan. 14 | Tietjen | Berlin - 87. Sylvia | 1866, May 16 | Pogson | Madras - 88. Thisbe | 1866, June 15 | Peters | Clinton - 89. Julia | 1866, Aug. 6 | Stephan | Marseilles - 90. Antiope | 1866, Oct. 1 | Luther | Bilk - 91. Aegina | 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. Aegle | 1868, Feb. 17 | Coggia | Marseilles - 97. Clotho | 1868, Feb. 17 | Coggia | Marseilles - 98. Ianthe | 1868, Apr. 18 | Peters | Clinton - 99. Dike | 1868, May 28 | Borelly | Marseilles - 100. Hecate | 1868, July 11 | Watson | Ann Arbor - 101. Helena | 1868, Aug. 15 | Watson | Ann Arbor - 102. Miriam | 1868, Aug. 22 | Peters | Clinton - 103. Hera | 1868, Sept. 7 | Watson | Ann Arbor - 104. Clymene | 1868, Sept. 13 | Watson | Ann Arbor - 105. Artemis | 1868, Sept. 16 | Watson | Ann Arbor - 106. Dione | 1868, Oct. 10 | Watson | Ann Arbor - 107. Camilla | 1868, Nov. 17 | Pogson | Madras - 108. Hecuba | 1869, Apr. 2 | Luther | Bilk - 109. Felicitas | 1869, Oct. 9 | Peters | Clinton - 110. Lydia | 1870, Apr. 19 | Borelly | Marseilles - 111. Ate | 1870, Aug. 14 | Peters | Clinton - 112. Iphigenia | 1870, Sept. 19 | Peters | Clinton - 113. Amalthea | 1871, Mar. 12 | Luther | Bilk - 114. Cassandra | 1871, July 23 | Peters | Clinton - 115. Thyra | 1871, Aug. 6 | Watson | Ann Arbor - 116. Sirona | 1871, Sept. 8 | Peters | Clinton - 117. Lomia | 1871, Sept. 12 | Borelly | Marseilles - 118. Peitho | 1872, Mar. 15 | Luther | Bilk - 119. Althea | 1872, Apr. 3 | Watson | Ann Arbor - 120. Lachesis | 1872, Apr. 10 | Borelly | Marseilles - 121. Hermione | 1872, May 12 | Watson | Ann Arbor - 122. Gerda | 1872, July 31 | Peters | Clinton - 123. Brunhilda | 1872, July 31 | Peters | Clinton - 124. Alceste | 1872, Aug. 23 | Peters | Clinton - 125. Liberatrix | 1872, Sept. 11 | Prosper Henry | Paris - 126. Velleda | 1872, Nov. 5 | Paul Henry | Paris - 127. Johanna | 1872, Nov. 5 | Prosper Henry | Paris - 128. Nemesis | 1872, Nov. 25 | Watson | Ann Arbor - 129. Antigone | 1873, Feb. 5 | Peters | Clinton - 130. Electra | 1873, Feb. 17 | Peters | Clinton - 131. Vala | 1873, May 24 | Peters | Clinton - 132. Aethra | 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. Meliboea | 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. Aemilia | 1876, Jan. 26 | Paul Henry | Paris - 160. Una | 1876, Feb. 20 | Peters | Clinton - 161. Athor | 1876, Apr. 19 | Watson | Ann Arbor - 162. Laurentia | 1876, Apr. 21 | Prosper Henry | Paris - 163. Erigone | 1876, Apr. 26 | Perrotin | Toulouse - 164. Eva | 1876, July 12 | Paul Henry | Paris - 165. Loreley | 1876, Aug. 9 | Peters | Clinton - 166. Rhodope | 1876, Aug. 15 | Peters | Clinton - 167. Urda | 1876, Aug. 28 | Peters | Clinton - 168. Sibylla | 1876, Sept. 27 | Watson | Ann Arbor - 169. Zelia | 1876, Sept. 28 | Prosper Henry | Paris - 170. Maria | 1877, Jan. 10 | Perrotin | Toulouse - 171. Ophelia | 1877, Jan. 13 | Borelly | Marseilles - 172. Baucis | 1877, Feb. 5 | Borelly | Marseilles - 173. Ino | 1877, Aug. 1 | Borelly | Marseilles - 174. Phaedra | 1877, Sept. 2 | Watson | Ann Arbor - 175. Andromache | 1877, Oct. 1 | Watson | Ann Arbor - 176. Idunna | 1877, Oct. 14 | Peters | Clinton - 177. Irma | 1877, Nov. 5 | Paul Henry | Paris - 178. Belisana | 1877, Nov. 6 | Palisa | Pola - 179. Clytemnestra| 1877, Nov. 11 | Watson | Ann Arbor - 180. Garumna | 1878, Jan. 29 | Perrotin | Toulouse - 181. Eucharis | 1878, Feb. 2 | Cottenot | Marseilles - 182. Elsa | 1878, Feb. 7 | Palisa | Pola - 183. Istria | 1878, Feb. 8 | Palisa | Pola - 184. Deiopea | 1878, Feb. 28 | Palisa | Pola - 185. Eunice | 1878, Mar. 1 | Peters | Clinton - 186. Celuta | 1878, Apr. 6 | Prosper Henry | Paris - 187. Lamberta | 1878, Apr. 11 | Coggia | Marseilles - 188. Menippe | 1878, June 18 | Peters | Clinton - 189. Phthia | 1878, Sept. 9 | Peters | Clinton - 190. Ismene | 1878, Sept. 22 | Peters | Clinton - 191. Kolga | 1878, Sept. 30 | Peters | Clinton - 192. Nausicaa | 1879, Feb. 17 | Palisa | Pola - 193. Ambrosia | 1879, Feb. 28 | Coggia | Marseilles - 194. Procne | 1879, Mar. 21 | Peters | Clinton - 195. Euryclea | 1879, Apr. 22 | Palisa | Pola - 196. Philomela | 1879, May 14 | Peters | Clinton - 197. Arete | 1879, May 21 | Palisa | Pola - 198. Ampella | 1879, June 13 | Borelly | Marseilles - 199. Byblis | 1879, July 9 | Peters | Clinton - 200. Dynamene | 1879, July 27 | Peters | Clinton - 201. Penelope | 1879, Aug. 7 | Palisa | Pola - 202. Chryseis | 1879, Sept. 11 | Peters | Clinton - 203. Pompeia | 1879, Sept. 25 | Peters | Clinton - 204. Callisto | 1879, Oct. 8 | Palisa | Pola - 205. Martha | 1879, Oct. 13 | Palisa | Pola - 206. Hersilia | 1879, Oct. 13 | Peters | Clinton - 207. Hedda | 1879, Oct. 17 | Palisa | Pola - 208. Lachrymosa | 1879, Oct. 21 | Palisa | Pola - 209. Dido | 1879, Oct. 22 | Peters | Clinton - 210. Isabella | 1879, Nov. 12 | Palisa | Pola - 211. Isolda | 1879, Dec. 10 | Palisa | Pola - 212. Medea | 1880, Feb. 6 | Palisa | Pola - 213. Lilaea | 1880, Feb. 16 | Peters | Clinton - 214. Aschera | 1880, Feb. 26 | Palisa | Pola - 215. Oenone | 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. Coelestina | 1884, June 27 | Palisa | Vienna - 238. Hypatia | 1884, July 1 | Knorre | Berlin - 239. Adrastea | 1884, Aug. 18 | Palisa | Vienna - 240. Vanadis | 1884, Aug. 27 | Borelly | Marseilles - 241. Germania | 1884, Sept. 12 | Luther | Dusseldorf - 242. Kriemhild | 1884, Sept. 22 | Palisa | Vienna - 243. Ida | 1884, Sept. 29 | Palisa | Vienna - 244. Sita | 1884, Oct. 14 | Palisa | Vienna - 245. Vera | 1885, Feb. 6 | Pogson | Madras - 246. Asporina | 1885, Mar. 6 | Borelly | Marseilles - 247. Eukrate | 1885, Mar. 14 | Luther | Dusseldorf - 248. Lameia | 1885, June 5 | Palisa | Vienna - 249. Ilse | 1885, Aug. 17 | Peters | Clinton - 250. Bettina | 1885, Sept. 3 | Palisa | Vienna - 251. Sophia | 1885, Oct. 4 | Palisa | Vienna - 252. Clementina | 1885, Oct. 27 | Perrotin | Nice - 253. Mathilde | 1885, Nov. 12 | Palisa | Vienna - 254. Augusta | 1886, Mar. 31 | Palisa | Vienna - 255. Oppavia | 1886, Mar. 31 | Palisa | Vienna - 256. Walpurga | 1886, Apr. 3 | Palisa | Vienna - 257. Silesia | 1886, Apr. 5 | Palisa | Vienna - 258. Tyche | 1886, May 4 | Luther | Dusseldorf - 259. Aletheia | 1886, June 28 | Peters | Clinton - 260. Huberta | 1886, Oct. 3 | Palisa | Vienna - 261. Prymno | 1886, Oct. 31 | Peters | Clinton - 262. Valda | 1886, Nov. 3 | Palisa | Vienna - 263. Dresda | 1886, Nov. 3 | Palisa | Vienna - 264. Libussa | 1886, Dec. 17 | Peters | Clinton - 265. Anna | 1887, Feb. 25 | Palisa | Vienna - 266. Aline | 1887, May 17 | Palisa | Vienna - 267. Tirza | 1887, May 27 | Charlois | Nice - 268. | 1887, June 9 | Borelly | Marseilles - 269. | 1887, Sept. 21 | Palisa | Vienna - 270. | 1887, Oct. 8 | Peters | Clinton - 271. | 1887, Oct. 16 | Knorre | Berlin - -----------------+----------------+---------------+------------ - - -3. Remarks on Table I. - -The numbers discovered by the thirty-five observers are respectively as -follows: - - Palisa 60 - Peters 47 - Luther 23 - Watson 22 - Borelly 15 - Goldschmidt 14 - Hind 10 - De Gasparis 9 - Pogson 8 - Paul Henry 7 - Prosper Henry 7 - Chacornac 6 - Perrotin 6 - Coggia 5 - Knorre 4 - Tempel 4 - Ferguson 3 - Olbers 2 - Hencke 2 - Tuttle 2 - Foerster (with Lesser) 1 - Safford (with Peters) 1 - and Messrs. Charlois, - Cottenot, - D'Arrest, - De Ball, - Graham, - Harding, - Laurent, - Piazzi, - Schiaparelli, - Schulhof, - Stephan, - Searle, - and Tietjen, each 1 - -Before arrangements had been made for the telegraphic transmission -of discoveries between Europe and America, or even between the -observatories of Europe, the same planet was sometimes independently -discovered by different observers. For example, Virginia was found by -Ferguson, at Washington, on October 4, 1857, and by Luther, at Bilk, -fifteen days later. In all cases, however, credit has been given to the -first observer. - -Hersilia, the two hundred and sixth of the group, was lost before -sufficient observations were obtained for determining its elements. It -was not rediscovered till December 14, 1884. Menippe, the one hundred -and eighty-eighth, was also lost soon after its discovery in 1878. It -has not been seen for more than nine years, and considerable uncertainty -attaches to its estimated elements. - -Of the two hundred and seventy-one members now known (1887), one hundred -and ninety-one have been discovered in Europe, seventy-four in America, -and six in Asia. The years of most successful search, together with the -number discovered in each, were: - - Asteroids. - 1879 20 - 1875 17 - 1868 12 - 1878 12 - -And six has been the average yearly number since the commencement of -renewed effort in 1845. All the larger members of the group have, -doubtless, been discovered. It seems not improbable, however, that an -indefinite number of very small bodies belonging to the zone remain to -be found. The process of discovery is becoming more difficult as the -known number increases. The astronomer, for instance, who may discover -number two hundred and seventy-two must know the simultaneous positions -of the two hundred and seventy-one previously detected before he can -decide whether he has picked up a new planet or merely rediscovered an -old one. The numbers discovered in the several months are as follows: - - January 13 - February 23 - March 19 - April 35 - May 21 - June 13 - July 14 - August 28 - September 46 - October 28 - November 26 - December 5 - -This obvious disparity is readily explained. The weather is favorable -for night watching in April and September; the winter months are too -cold for continuous observations; and the small numbers in June and July -may be referred to the shortness of the nights. - - -4. Mode of Discovery. - -The astronomer who would undertake the search for new asteroids must -supply himself with star-charts extending some considerable distance on -each side of the ecliptic, and containing all telescopic stars down to -the thirteenth or fourteenth magnitude. The detection of a star not -found in the chart of a particular section will indicate its motion, and -hence its planetary character. The construction of such charts has been -a principal object in the labors of Dr. Peters, at Clinton, New York. In -fact, his discovery of minor planets has in most instances been merely -an incidental result of his larger and more important work. - - -NAMES AND SYMBOLS. - -The fact that the names of female deities in the Greek and Roman -mythologies had been given to the first asteroids suggested a similar -course in the selection of names after the new epoch of discovery in -1845. While conformity to this rule has been the general aim of -discoverers, the departures from it have been increasingly numerous. The -twelfth asteroid, discovered in London, was named Victoria, in honor of -the reigning sovereign; the twentieth and twenty-fifth, detected at -Marseilles,[2] received names indicative of the place of their -discovery; Lutetia, the first found at Paris, received its name for a -similar purpose; the fifty-fourth was named Alexandra, for Alexander von -Humboldt; the sixty-seventh, found by Pogson at Madras, was named Asia, -to commemorate the fact that it was the first discovered on that -continent. We find, also, Julia, Bertha, Xantippe, Zelia, Maria, -Isabella, Martha, Dido, Cleopatra, Barbara, Ida, Augusta, and Anna. Why -these were selected we will not stop to inquire. - -As the number of asteroids increased it was found inconvenient to -designate them individually by particular signs, as in the case of the -old planets. In 1849, Dr. B. A. Gould proposed to represent them by the -numbers expressing their order of discovery enclosed in a small circle. -This method was at once very generally adopted. - - -5. Magnitudes of the Asteroids. - -The apparent diameter of the largest is less than one-second of arc. -They are all too small, therefore, to be accurately measured by -astronomical instruments. From photometric observations, however, -Argelander,[3] Stone,[4] and Pickering[5] have formed estimates of the -diameters, the results giving probably close approximations to the true -magnitudes. According to these estimates the diameter of the largest, -Vesta, is about three hundred miles, that of Ceres about two hundred, -and those of Pallas and Juno between one and two hundred. The diameters -of about thirty are between fifty and one hundred miles, and those of -all others less than fifty; the estimates for Menippe and Eva giving -twelve and thirteen miles respectively. The diameter of the former is to -that of the earth as one to six hundred and sixty-four; and since -spheres are to each other as the cubes of their diameters, it would -require two hundred and ninety millions of such asteroids to form a -planet as large as our globe. In other words, if the earth be -represented by a sphere one foot in diameter, the magnitude of Menippe -on the same scale would be that of a sand particle whose diameter is one -fifty-fifth of an inch. Its surface contains about four hundred and -forty square miles,--an area equal to a county twenty-one miles square. -The surface attractions of two planets having the same density are to -each other as their diameters. A body, therefore, weighing two hundred -pounds at the earth's surface would on the surface of the asteroid weigh -less than five ounces. At the earth's surface a weight falls sixteen -feet the first second, at the surface of Menippe it would fall about -one-fourth of an inch. A person might leap from its surface to a height -of several hundred feet, in which case he could not return in much less -than an hour. "But of such speculations," Sir John Herschel remarks, -"there is no end." - -The number of these planetules between the orbits of Mars and Jupiter in -all probability can never be known. It was estimated by Leverrier that -the quantity of matter contained in the group could not be greater than -one-fourth of the earth's mass. But this would be equal to five thousand -planets, each as large as Vesta, to seventy-two millions as large as -Menippe, or to four thousand millions of five miles in diameter. In -short, the existence of an indefinite number too small for detection by -the most powerful glasses is by no means improbable. The more we study -this wonderful section of the solar system, the more mystery seems to -envelop its origin and constitution. - - -6. The Orbits of the Asteroids. - -The form, magnitude, and position of a planet's orbit are determined by -the following elements: - -1. The semi-axis major, or mean distance, denoted by the symbol _a_. - -2. The eccentricity, _e_. - -3. The longitude of the perihelion, [pi]. - -4. The longitude of the ascending node, [AN]. - -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_ | [pi] | [AN] | _i_ - -----------------+--------+---------+--------+----------+----------+-------- - 149. Medusa | 2.1327 | 1137.7d | 0.1194 | 246D 37' | 342D 13' | 1D 6' - 244. Sita | 2.1765 | 1172.8 | 0.1370 | 13 8 | 208 37 | 2 50 - 228. Agathe | 2.2009 | 1192.6 | 0.2405 | 329 23 | 313 18 | 2 33 - 8. Flora | 2.2014 | 1193.3 | 0.1567 | 32 54 | 110 18 | 5 53 - 43. Ariadne | 2.2033 | 1194.5 | 0.1671 | 277 58 | 264 35 | 3 28 - 254. Augusta | 2.2060 | 1196.8 | 0.1227 | 260 47 | 28 9 | 4 36 - 72. Feronia | 2.2661 | 1246.0 | 0.1198 | 307 58 | 207 49 | 5 24 - 40. Harmonia | 2.2673 | 1247.0 | 0.0466 | 0 54 | 93 35 | 4 16 - 207. Hedda | 2.2839 | 1260.7 | 0.0301 | 217 2 | 28 51 | 3 49 - 136. Austria | 2.2863 | 1262.7 | 0.0849 | 316 6 | 186 7 | 9 33 - 18. Melpomene | 2.2956 | 1270.4 | 0.2177 | 15 6 | 150 4 | 10 9 - 80. Sappho | 2.2962 | 1270.9 | 0.2001 | 355 18 | 218 44 | 8 37 - 261. Prymno | 2.3062 | 1278.4 | 0.0794 | 179 35 | 96 33 | 3 38 - 12. Victoria | 2.3342 | 1302.7 | 0.2189 | 301 39 | 235 35 | 8 23 - 27. Euterpe | 2.3472 | 1313.5 | 0.1739 | 87 59 | 93 51 | 1 36 - 219. Thusnelda | 2.3542 | 1319.4 | 0.2247 | 340 34 | 200 44 | 10 47 - 163. Erigone | 2.3560 | 1320.9 | 0.1567 | 93 46 | 159 2 | 4 42 - 169. Zelia | 2.3577 | 1322.3 | 0.1313 | 326 20 | 354 38 | 5 31 - 4. Vesta | 2.3616 | 1325.6 | 0.0884 | 250 57 | 103 29 | 7 8 - 186. Celuta | 2.3623 | 1326.2 | 0.1512 | 327 24 | 14 34 | 13 6 - 84. Clio | 2.3629 | 1326.7 | 0.2360 | 339 20 | 327 28 | 9 22 - 51. Nemausa | 2.3652 | 1328.6 | 0.0672 | 174 43 | 175 52 | 9 57 - 220. Stephania | 2.3666 | 1329.8 | 0.2653 | 332 53 | 258 24 | 7 35 - 30. Urania | 2.3667 | 1329.9 | 0.1266 | 31 46 | 308 12 | 2 6 - 105. Artemis | 2.3744 | 1336.4 | 0.1749 | 242 38 | 188 3 | 21 31 - 113. Amalthea | 2.3761 | 1337.8 | 0.0874 | 198 44 | 123 11 | 5 2 - 115. Thyra | 2.3791 | 1340.3 | 0.1939 | 43 2 | 309 5 | 11 35 - 161. Athor | 2.3792 | 1340.5 | 0.1389 | 310 40 | 18 27 | 9 3 - 172. Baucis | 2.3794 | 1340.6 | 0.1139 | 329 23 | 331 50 | 10 2 - 249. Ilse | 2.3795 | 1340.6 | 0.2195 | 14 17 | 334 49 | 9 40 - 230. Athamantis | 2.3842 | 1344.6 | 0.0615 | 17 31 | 239 33 | 9 26 - 7. Iris | 2.3862 | 1346.4 | 0.2308 | 41 23 | 259 48 | 5 28 - 9. Metis | 2.3866 | 1346.7 | 0.1233 | 71 4 | 68 32 | 5 36 - 234. Barbara | 2.3873 | 1347.3 | 0.2440 | 333 26 | 144 9 | 15 22 - 60. Echo | 2.3934 | 1352.4 | 0.1838 | 98 36 | 192 5 | 3 35 - 63. Ausonia | 2.3979 | 1356.3 | 0.1239 | 270 25 | 337 58 | 5 48 - 25. Phocea | 2.4005 | 1358.5 | 0.2553 | 302 48 | 208 27 | 21 35 - 192. Nausicaa | 2.4014 | 1359.3 | 0.2413 | 343 19 | 160 46 | 6 50 - 20. Massalia | 2.4024 | 1365.8 | 0.1429 | 99 7 | 206 36 | 0 41 - 265. Anna | 2.4096 | 1366.2 | 0.2628 | 226 18 | 335 26 | 25 24 - 182. Elsa | 2.4157 | 1371.4 | 0.1852 | 51 52 | 106 30 | 2 0 - 142. Polana | 2.4194 | 1374.5 | 0.1322 | 219 54 | 317 34 | 2 14 - 67. Asia | 2.4204 | 1375.4 | 0.1866 | 306 35 | 202 47 | 5 59 - 44. Nysa | 2.4223 | 1377.0 | 0.1507 | 111 57 | 131 11 | 3 42 - 6. Hebe | 2.4254 | 1379.3 | 0.2034 | 15 16 | 138 43 | 10 47 - 83. Beatrix | 2.4301 | 1383.6 | 0.0859 | 191 46 | 27 32 | 5 0 - 135. Hertha | 2.4303 | 1383.8 | 0.2037 | 320 11 | 344 3 | 2 19 - 131. Vala | 2.4318 | 1385.1 | 0.0683 | 222 50 | 65 15 | 4 58 - 112. Iphigenia | 2.4335 | 1386.6 | 0.1282 | 338 9 | 324 3 | 2 37 - 21. Lutetia | 2.4354 | 1388.2 | 0.1621 | 327 4 | 80 28 | 3 5 - 118. Peitho | 2.4384 | 1390.8 | 0.1608 | 77 36 | 47 30 | 7 48 - 126. Velleda | 2.4399 | 1392.1 | 0.1061 | 347 46 | 23 7 | 2 56 - 42. Isis | 2.4401 | 1392.2 | 0.2256 | 317 58 | 84 28 | 8 35 - 19. Fortuna | 2.4415 | 1394.4 | 0.1594 | 31 3 | 211 27 | 1 33 - 79. Eurynome | 2.4436 | 1395.2 | 0.1945 | 44 22 | 206 44 | 4 37 - 138. Tolosa | 2.4492 | 1400.0 | 0.1623 | 311 39 | 54 52 | 3 14 - 189. Phthia | 2.4505 | 1401.1 | 0.0356 | 6 50 | 203 22 | 5 10 - 11. Parthenope | 2.4529 | 1403.2 | 0.0994 | 318 2 | 125 11 | 4 37 - 178. Belisana | 2.4583 | 1407.8 | 0.1266 | 278 0 | 50 17 | 2 5 - 198. Ampella | 2.4595 | 1408.9 | 0.2266 | 354 46 | 268 45 | 9 20 - 248. Lameia | 2.4714 | 1419.1 | 0.0656 | 248 40 | 246 34 | 4 1 - 17. Thetis | 2.4726 | 1420.1 | 0.1293 | 261 37 | 125 24 | 5 36 - 46. Hestia | 2.5265 | 1466.8 | 0.1642 | 354 14 | 181 31 | 2 17 - 89. Julia | 2.5510 | 1488.2 | 0.1805 | 353 13 | 311 42 | 16 11 - 232. Russia | 2.5522 | 1489.3 | 0.1754 | 200 25 | 152 30 | 6 4 - 29. Amphitrite | 2.5545 | 1491.3 | 0.0742 | 56 23 | 356 41 | 6 7 - 170. Maria | 2.5549 | 1491.7 | 0.0639 | 95 47 | 301 20 | 14 23 - 262. Valda | 2.5635 | 1496.4 | 0.2172 | 61 42 | 38 40 | 7 46 - 258. Tyche | 2.5643 | 1499.8 | 0.1966 | 15 42 | 208 4 | 14 50 - 134. Sophrosyne | 2.5647 | 1500.3 | 0.1165 | 67 33 | 346 22 | 11 36 - 264. Libussa | 2.5672 | 1502.4 | 0.0925 | 0 7 | 50 23 | 10 29 - 193. Ambrosia | 2.5758 | 1510.0 | 0.2854 | 70 52 | 351 15 | 11 39 - 13. Egeria | 2.5765 | 1510.6 | 0.0871 | 120 10 | 43 12 | 16 32 - 5. Astraea | 2.5786 | 1512.4 | 0.1863 | 134 57 | 141 28 | 5 19 - 119. Althea | 2.5824 | 1515.7 | 0.0815 | 11 29 | 203 57 | 5 45 - 157. Dejanira | 2.5828 | 1516.1 | 0.2105 | 107 24 | 62 31 | 12 2 - 101. Helena | 2.5849 | 1518.0 | 0.1386 | 327 15 | 343 46 | 10 11 - 32. Pomona | 2.5873 | 1520.1 | 0.0830 | 193 22 | 220 43 | 5 29 - 91. Aegina | 2.5895 | 1522.1 | 0.1087 | 80 22 | 11 7 | 2 8 - 14. Irene | 2.5896 | 1522.1 | 0.1627 | 180 19 | 86 48 | 9 8 - 111. Ate | 2.5927 | 1524.8 | 0.1053 | 108 42 | 306 13 | 4 57 - 151. Abundantia | 2.5932 | 1525.3 | 0.0356 | 173 55 | 38 48 | 6 30 - 56. Melete | 2.6010 | 1532.2 | 0.2340 | 294 50 | 194 1 | 8 2 - 132. Aethra | 2.6025 | 1533.5 | 0.3799 | 152 24 | 260 2 | 25 0 - 214. Aschera | 2.6111 | 1541.1 | 0.0316 | 115 55 | 342 30 | 3 27 - 70. Panopea | 2.6139 | 1543.6 | 0.1826 | 299 49 | 48 18 | 11 38 - 194. Procne | 2.6159 | 1545.4 | 0.2383 | 319 33 | 159 19 | 18 24 - 53. Calypso | 2.6175 | 1546.8 | 0.2060 | 92 52 | 143 58 | 5 7 - 78. Diana | 2.6194 | 1548.5 | 0.2088 | 121 42 | 333 58 | 8 40 - 124. Alceste | 2.6297 | 1557.6 | 0.0784 | 245 42 | 188 26 | 2 56 - 23. Thalia | 2.6306 | 1558.4 | 0.2299 | 123 58 | 67 45 | 10 14 - 164. Eva | 2.6314 | 1559.1 | 0.3471 | 359 32 | 77 28 | 24 25 - 15. Eunomia | 2.6437 | 1570.0 | 0.1872 | 27 52 | 188 26 | 2 56 - 37. Fides | 2.6440 | 1570.3 | 0.1758 | 66 26 | 8 21 | 3 7 - 66. Maia | 2.6454 | 1571.6 | 0.1750 | 48 8 | 8 17 | 3 6 - 224. Oceana | 2.6465 | 1572.6 | 0.0455 | 270 51 | 353 18 | 5 52 - 253. Mathilde | 2.6469 | 1572.9 | 0.2620 | 333 39 | 180 3 | 6 37 - 50. Virginia | 2.6520 | 1577.4 | 0.2852 | 10 9 | 173 45 | 2 48 - 144. Vibilia | 2.6530 | 1578.4 | 0.2348 | 7 9 | 76 47 | 4 48 - 85. Io | 2.6539 | 1579.2 | 0.1911 | 322 35 | 203 56 | 11 53 - 26. Proserpine | 2.6561 | 1581.1 | 0.0873 | 236 25 | 45 55 | 3 36 - 233. Asterope | 2.6596 | 1584.3 | 0.1010 | 344 36 | 222 25 | 7 39 - 102. Miriam | 2.6619 | 1586.3 | 0.3035 | 354 39 | 211 58 | 5 4 - 240. Vanadis | 2.6638 | 1588.0 | 0.2056 | 51 53 | 114 54 | 2 6 - 73. Clytie | 2.6652 | 1589.3 | 0.0419 | 57 55 | 7 51 | 2 24 - 218. Bianca | 2.6653 | 1589.3 | 0.1155 | 230 14 | 170 50 | 15 13 - 141. Lumen | 2.6666 | 1590.5 | 0.2115 | 13 43 | 319 7 | 11 57 - 77. Frigga | 2.6680 | 1591.8 | 0.1318 | 58 47 | 2 0 | 2 28 - 3. Juno | 2.6683 | 1592.0 | 0.2579 | 54 50 | 170 53 | 13 1 - 97. Clotho | 2.6708 | 1594.3 | 0.2550 | 65 32 | 160 37 | 11 46 - 75. Eurydice | 2.6720 | 1595.3 | 0.3060 | 335 33 | 359 56 | 5 1 - 145. Adeona | 2.6724 | 1595.4 | 0.1406 | 117 53 | 77 41 | 12 38 - 204. Callisto | 2.6732 | 1596.4 | 0.1752 | 257 45 | 205 40 | 8 19 - 114. Cassandra | 2.6758 | 1598.8 | 0.1401 | 153 6 | 164 24 | 4 55 - 201. Penelope | 2.6764 | 1599.3 | 0.1818 | 334 21 | 157 5 | 5 44 - 64. Angelina | 2.6816 | 1603.9 | 0.1271 | 125 36 | 311 4 | 1 19 - 98. Ianthe | 2.6847 | 1606.7 | 0.1920 | 148 52 | 354 7 | 15 32 - 34. Circe | 2.6864 | 1608.3 | 0.1073 | 148 41 | 184 46 | 5 27 - 123. Brunhilda | 2.6918 | 1613.2 | 0.1150 | 72 57 | 308 28 | 6 27 - 166. Rhodope | 2.6927 | 1613.9 | 0.2140 | 30 51 | 129 33 | 12 2 - 109. Felicitas | 2.6950 | 1616.0 | 0.3002 | 56 1 | 4 56 | 8 3 - 246. Asporina | 2.6994 | 1619.9 | 0.1065 | 255 54 | 162 35 | 15 39 - 58. Concordia | 2.7004 | 1620.8 | 0.0426 | 189 10 | 161 20 | 5 2 - 103. Hera | 2.7014 | 1621.8 | 0.0803 | 321 3 | 136 18 | 5 24 - 54. Alexandra | 2.7095 | 1629.1 | 0.2000 | 295 39 | 313 45 | 11 47 - 226. Weringia | 2.7118 | 1631.2 | 0.2048 | 284 46 | 135 18 | 15 50 - 59. Olympia | 2.7124 | 1631.7 | 0.1189 | 17 33 | 170 26 | 8 37 - 146. Lucina | 2.7189 | 1637.5 | 0.0655 | 227 34 | 84 16 | 13 6 - 45. Eugenia | 2.7205 | 1639.0 | 0.0811 | 232 5 | 147 57 | 6 35 - 210. Isabella | 2.7235 | 1641.7 | 0.1220 | 44 22 | 32 58 | 5 18 - 187. Lamberta | 2.7272 | 1645.0 | 0.2391 | 214 4 | 22 13 | 10 43 - 180. Garumna | 2.7286 | 1646.3 | 0.1722 | 125 56 | 314 42 | 0 54 - 160. Una | 2.7287 | 1646.4 | 0.0624 | 55 57 | 9 22 | 3 51 - 140. Siwa | 2.7316 | 1649.0 | 0.2160 | 300 33 | 107 2 | 3 12 - 110. Lydia | 2.7327 | 1650.0 | 0.0770 | 336 49 | 57 10 | 6 0 - 185. Eunice | 2.7372 | 1654.1 | 0.1292 | 16 32 | 153 50 | 23 17 - 203. Pompeia | 2.7376 | 1654.5 | 0.0588 | 42 51 | 348 37 | 3 13 - 200. Dynamene | 2.7378 | 1654.6 | 0.1335 | 46 38 | 325 26 | 6 56 - 197. Arete | 2.7390 | 1655.8 | 0.1621 | 324 51 | 82 6 | 8 48 - 206. Hersilia | 2.7399 | 1656.5 | 0.0389 | 95 44 | 145 16 | 3 46 - 255. Oppavia | 2.7402 | 1656.6 | 0.0728 | 169 15 | 14 6 | 9 33 - 247. Eukrate | 2.7412 | 1657.7 | 0.2387 | 53 44 | 0 20 | 25 7 - 38. Leda | 2.7432 | 1659.6 | 0.1531 | 101 20 | 296 27 | 6 57 - 125. Liberatrix | 2.7437 | 1660.0 | 0.0798 | 273 29 | 169 35 | 4 38 - 173. Ino | 2.7446 | 1660.8 | 0.2047 | 13 28 | 148 34 | 14 15 - 36. Atalanta | 2.7452 | 1661.3 | 0.3023 | 42 44 | 359 14 | 18 42 - 128. Nemesis | 2.7514 | 1666.9 | 0.1257 | 16 34 | 76 31 | 6 16 - 93. Minerva | 2.7537 | 1669.0 | 0.1405 | 274 44 | 5 4 | 8 37 - 127. Johanna | 2.7550 | 1670.3 | 0.0659 | 122 37 | 31 46 | 8 17 - 71. Niobe | 2.7558 | 1671.0 | 0.1732 | 221 17 | 316 30 | 23 19 - 213. Lilaea | 2.7563 | 1671.4 | 0.1437 | 281 4 | 122 17 | 6 47 - 55. Pandora | 2.7604 | 1675.1 | 0.1429 | 10 36 | 10 56 | 7 14 - 237. Coelestina | 2.7607 | 1675.5 | 0.0738 | 282 49 | 84 33 | 9 46 - 143. Adria | 2.7619 | 1676.6 | 0.0729 | 222 27 | 333 42 | 11 30 - 82. Alcmene | 2.7620 | 1676.6 | 0.2228 | 131 45 | 26 57 | 2 51 - 116. Sirona | 2.7669 | 1681.1 | 0.1433 | 152 47 | 64 26 | 3 35 - 1. Ceres | 2.7673 | 1681.4 | 0.0763 | 149 38 | 80 47 | 10 37 - 88. Thisbe | 2.7673 | 1681.5 | 0.1632 | 308 34 | 277 54 | 16 11 - 215. Oenone | 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. Laetitia | 2.7680 | 1682.1 | 0.1142 | 3 8 | 157 15 | 10 22 - 41. Daphne | 2.7688 | 1682.8 | 0.2674 | 220 33 | 179 8 | 15 58 - 177. Irma | 2.7695 | 1683.5 | 0.2370 | 22 6 | 349 17 | 1 27 - 148. Gallia | 2.7710 | 1684.8 | 0.1855 | 36 7 | 145 13 | 25 21 - 267. Tirza | 2.7742 | 1687.6 | 0.0986 | 264 5 | 73 59 | 6 2 - 74. Galatea | 2.7770 | 1690.3 | 0.2392 | 8 18 | 197 51 | 4 0 - 205. Martha | 2.7771 | 1690.4 | 0.1752 | 21 54 | 212 12 | 10 40 - 139. Juewa | 2.7793 | 1692.4 | 0.1773 | 164 34 | 2 21 | 10 57 - 28. Bellona | 2.7797 | 1692.7 | 0.1491 | 124 1 | 144 37 | 9 22 - 68. Leto | 2.7805 | 1693.5 | 0.1883 | 345 14 | 45 1 | 7 58 - 216. Cleopatra | 2.7964 | 1708.0 | 0.2492 | 328 15 | 215 49 | 13 2 - 99. Dike | 2.7966 | 1708.3 | 0.2384 | 240 36 | 41 44 | 13 53 - 236. Honoria | 2.7993 | 1710.7 | 0.1893 | 356 59 | 186 27 | 7 37 - 183. Istria | 2.8024 | 1713.4 | 0.3530 | 45 0 | 142 46 | 26 33 - 266. Aline | 2.8078 | 1718.5 | 0.1573 | 23 52 | 236 18 | 13 20 - 188. Menippe | 2.8211 | 1730.7 | 0.2173 | 309 38 | 241 44 | 11 21 - 167. Urda | 2.8533 | 1760.4 | 0.0340 | 296 4 | 166 28 | 2 11 - 81. Terpsichore | 2.8580 | 1764.8 | 0.2080 | 49 1 | 2 25 | 7 55 - 174. Phaedra | 2.8600 | 1766.6 | 0.1492 | 253 12 | 328 49 | 12 9 - 243. Ida | 2.8610 | 1767.5 | 0.0419 | 71 22 | 326 21 | 1 10 - 242. Kriemhild | 2.8623 | 1768.7 | 0.1219 | 123 1 | 207 57 | 11 17 - 129. Antigone | 2.8678 | 1773.9 | 0.2126 | 242 4 | 137 37 | 12 10 - 217. Eudora | 2.8690 | 1774.9 | 0.3068 | 314 41 | 164 10 | 10 19 - 158. Coronis | 2.8714 | 1777.2 | 0.0545 | 56 56 | 281 30 | 1 0 - 33. Polyhymnia | 2.8751 | 1780.7 | 0.3349 | 342 59 | 9 19 | 1 56 - 195. Euryclea | 2.8790 | 1784.2 | 0.0471 | 115 48 | 7 57 | 7 1 - 235. Caroline | 2.8795 | 1784.7 | 0.0595 | 268 29 | 66 35 | 9 4 - 47. Aglaia | 2.8819 | 1786.9 | 0.1317 | 312 40 | 40 20 | 5 1 - 208. Lachrymosa | 2.8926 | 1796.9 | 0.0149 | 127 52 | 5 43 | 1 48 - 191. Kolga | 2.8967 | 1800.8 | 0.0876 | 23 21 | 159 47 | 11 29 - 22. Calliope | 2.9090 | 1801.0 | 0.0193 | 62 43 | 4 47 | 1 45 - 155. Scylla | 2.9127 | 1815.7 | 0.2559 | 82 1 | 42 52 | 14 4 - 238. Hypatia | 2.9163 | 1819.0 | 0.0946 | 32 18 | 184 26 | 12 28 - 231. Vindobona | 2.9192 | 1821.7 | 0.1537 | 253 23 | 352 49 | 5 10 - 16. Psyche | 2.9210 | 1823.4 | 0.1392 | 15 9 | 150 36 | 3 4 - 179. Clytemnestra| 2.9711 | 1870.6 | 0.1133 | 355 39 | 253 13 | 7 47 - 239. Adrastea | 2.9736 | 1873.0 | 0.2279 | 26 1 | 181 34 | 6 4 - 69. Hesperia | 2.9779 | 1877.0 | 0.1712 | 108 19 | 187 12 | 8 28 - 150. Nuwa | 2.9785 | 1877.5 | 0.1307 | 355 27 | 207 35 | 2 9 - 61. Danae | 2.9855 | 1884.2 | 0.1615 | 344 4 | 334 11 | 18 14 - 117. Lomia | 2.9907 | 1889.1 | 0.0229 | 48 46 | 349 39 | 14 58 - 35. Leucothea | 2.9923 | 1890.6 | 0.2237 | 202 25 | 355 49 | 8 12 - 263. Dresda | 3.0120 | 1909.3 | 0.3051 | 308 49 | 217 56 | 1 27 - 221. Eos | 3.0134 | 1910.7 | 0.1028 | 330 58 | 142 35 | 10 51 - 162. Laurentia | 3.0241 | 1920.8 | 0.1726 | 145 52 | 38 15 | 6 4 - 156. Xantippe | 3.0375 | 1933.7 | 0.2637 | 155 58 | 246 11 | 7 29 - 241. Germania | 3.0381 | 1934.0 | 0.1013 | 340 7 | 272 28 | 5 30 - 256. Walpurga | 3.0450 | 1940.8 | 0.1180 | 240 17 | 183 35 | 12 44 - 211. Isolda | 3.0464 | 1942.2 | 0.1541 | 74 12 | 265 29 | 3 51 - 96. Aegle | 3.0497 | 1945.3 | 0.1405 | 163 10 | 322 50 | 16 7 - 257. Silesia | 3.0572 | 1952.5 | 0.2555 | 54 16 | 34 31 | 4 41 - 133. Cyrene | 3.0578 | 1953.0 | 0.1398 | 247 13 | 321 8 | 7 14 - 95. Arethusa | 3.0712 | 1965.9 | 0.1447 | 32 58 | 244 17 | 12 54 - 202. Chryseis | 3.0777 | 1972.1 | 0.0959 | 129 46 | 137 47 | 8 48 - 268. ---- | 3.0852 | 1973.9 | 0.1285 | 184 48 | 121 53 | 2 25 - 100. Hecate | 3.0904 | 1984.3 | 0.1639 | 308 3 | 128 12 | 6 23 - 49. Pales | 3.0908 | 1984.7 | 0.2330 | 31 15 | 290 40 | 3 8 - 223. Rosa | 3.0940 | 1987.9 | 0.1186 | 102 48 | 49 0 | 1 59 - 52. Europa | 3.0955 | 1988.0 | 0.1098 | 106 57 | 129 40 | 7 27 - 245. Vera | 3.0985 | 1992.1 | 0.1950 | 25 29 | 62 37 | 5 10 - 86. Semele | 3.1015 | 1995.1 | 0.2193 | 29 10 | 87 45 | 4 47 - 159. Aemilia | 3.1089 | 2002.2 | 0.1034 | 101 22 | 135 9 | 6 4 - 48. Doris | 3.1127 | 2005.9 | 0.0649 | 70 33 | 184 55 | 6 31 - 196. Philomela | 3.1137 | 2006.8 | 0.0118 | 309 19 | 73 24 | 7 16 - 130. Electra | 3.1145 | 2007.7 | 0.2132 | 20 34 | 146 6 | 22 57 - 212. Medea | 3.1157 | 2008.8 | 0.1013 | 56 18 | 315 16 | 4 16 - 120. Lachesis | 3.1211 | 2014.0 | 0.0475 | 214 0 | 342 51 | 7 1 - 181. Eucharis | 3.1226 | 2015.4 | 0.2205 | 95 25 | 144 45 | 18 38 - 62. Erato | 3.1241 | 2016.9 | 0.1756 | 39 0 | 125 46 | 2 12 - 222. Lucia | 3.1263 | 2019.0 | 0.1453 | 258 2 | 80 11 | 2 11 - 137. Meliboea | 3.1264 | 2019.1 | 0.2074 | 307 58 | 204 22 | 13 22 - 165. Loreley | 3.1269 | 2019.6 | 0.0734 | 223 50 | 304 6 | 10 12 - 251. Sophia | 3.1315 | 2024.1 | 0.1243 | 77 7 | 157 6 | 10 20 - 24. Themis | 3.1357 | 2028.1 | 0.1242 | 144 8 | 35 49 | 0 49 - 152. Atala | 3.1362 | 2028.6 | 0.0862 | 84 23 | 41 29 | 12 12 - 10. Hygeia | 3.1366 | 2029.1 | 0.1156 | 237 2 | 285 38 | 3 49 - 259. Aletheia | 3.1369 | 2029.3 | 0.1176 | 241 45 | 88 32 | 10 40 - 227. Philosophia | 3.1393 | 2031.6 | 0.2131 | 226 23 | 330 52 | 9 16 - 147. Protogenea | 3.1393 | 2031.6 | 0.0247 | 25 38 | 251 16 | 1 54 - 171. Ophelia | 3.1432 | 2035.4 | 0.1168 | 143 59 | 101 10 | 2 34 - 209. Dido | 3.1436 | 2035.9 | 0.0637 | 257 33 | 2 0 | 7 15 - 31. Euphrosyne | 3.1468 | 2039.0 | 0.2228 | 93 26 | 31 31 | 26 27 - 90. Antiope | 3.1475 | 2039.7 | 0.1645 | 301 15 | 71 29 | 2 17 - 104. Clymene | 3.1507 | 2042.7 | 0.1579 | 59 32 | 43 32 | 2 54 - 57. Mnemosyne | 3.1510 | 2043.0 | 0.1145 | 53 25 | 200 2 | 15 12 - 250. Bettina | 3.1524 | 2044.3 | 0.1302 | 87 28 | 26 12 | 12 54 - 252. Clementina | 3.1552 | 2047.1 | 0.0837 | 355 8 | 208 19 | 10 2 - 94. Aurora | 3.1602 | 2052.0 | 0.0827 | 48 46 | 4 9 | 8 4 - 106. Dione | 3.1670 | 2058.6 | 0.1788 | 25 57 | 63 14 | 4 38 - 199. Byblis | 3.1777 | 2069.0 | 0.1687 | 261 20 | 89 52 | 15 22 - 92. Undina | 3.1851 | 2076.3 | 0.1024 | 331 27 | 102 52 | 9 57 - 184. Deiopea | 3.1883 | 2079.4 | 0.0725 | 169 22 | 336 18 | 1 12 - 176. Idunna | 3.1906 | 2081.6 | 0.1641 | 20 34 | 201 13 | 22 31 - 154. Bertha | 3.1976 | 2088.5 | 0.0788 | 190 47 | 37 35 | 20 59 - 108. Hecuba | 3.2113 | 2101.0 | 0.1005 | 173 49 | 352 17 | 4 24 - 122. Gerda | 3.2177 | 2108.2 | 0.0415 | 203 45 | 178 43 | 1 36 - 168. Sibylla | 3.3765 | 2266.2 | 0.0707 | 11 26 | 209 47 | 4 33 - 225. Henrietta | 3.4007 | 2277.8 | 0.2661 | 299 13 | 200 45 | 20 45 - 229. Adelinda | 3.4129 | 2302.9 | 0.1562 | 332 7 | 30 49 | 2 11 - 76. Freia | 3.4140 | 2304.1 | 0.1700 | 90 49 | 212 5 | 2 3 - 260. Huberta | 3.4212 | 2311.5 | 0.1113 | 313 22 | 168 48 | 6 18 - 65. Maximiliana | 3.4270 | 2317.2 | 0.1097 | 260 36 | 158 50 | 3 29 - 121. Hermione | 3.4535 | 2344.2 | 0.1255 | 357 50 | 76 46 | 7 36 - 87. Sylvia | 3.4833 | 2374.5 | 0.0922 | 333 48 | 75 49 | 10 55 - 107. Camilla | 3.4847 | 2376.0 | 0.0756 | 115 53 | 176 18 | 9 54 - 175. Andromache | 3.5071 | 2399.0 | 0.3476 | 293 0 | 23 35 | 3 46 - 190. Ismene | 3.9471 | 2864.3 | 0.1634 | 105 39 | 177 0 | 6 7 - 153. Hilda | 3.9523 | 2869.9 | 0.1721 | 285 47 | 228 20 | 7 55 - -----------------+--------+---------+--------+----------+----------+-------- - - - - -PART II. - - - - -DISCUSSION OF THE FACTS IN TABLE II. - - -1. Extent of the Zone. - -In Table II. the unit of column _a_ is the earth's mean distance from -the sun, or ninety-three million miles. On this scale the breadth of the -zone is 1.8196. Or, if we estimate the breadth from the perihelion of -Aethra (1.612) to the aphelion of Andromache (4.726), it is 3.114,--more -than three times the radius of the earth's orbit. A very remarkable -characteristic of the group is the interlacing or intertwining of -orbits. "One fact," says D'Arrest, "seems above all to confirm the idea -of an intimate relation between all the minor planets; it is, that if -their orbits are figured under the form of material rings, these rings -will be found so entangled that it would be possible, by means of one -among them taken at hazard, to lift up all the rest."[6] Our present -knowledge of this wide and complicated cluster is the result of a vast -amount, not only of observations, but also of mathematical labor. In -view, however, of the perturbations of these bodies by the larger -planets, and especially by Jupiter, it is easy to see that the -discussion of their motions must present a field of investigation -practically boundless. - -While the known minor planets were but few in number the theory of -Olbers in regard to their origin seemed highly probable; it has, -however, been completely disproved by more recent discoveries. The -breadth of the zone being now greater than the distance of Mars from the -sun, it is no more probable that the asteroids were produced by the -disruption of a single planet than that Mercury, Venus, the earth, and -Mars originated in a similar manner. - - -2. The Small Mass of the Asteroids. - -In taking a general view of the solar system we cannot fail to be struck -by the remarkable fact that Jupiter, whose mass is much greater than -that of all other planets united, should be immediately succeeded by a -region so nearly destitute of matter as the zone of asteroids. Leverrier -inferred from the motion of Mars's perihelion that the mass of Jupiter -is at least twelve hundred times greater than that of all the planets in -the asteroid ring. The fact is suggestive of Jupiter's dominating energy -in the evolution of the asteroid system. We find also something -analogous among the satellites of Jupiter, Saturn, and Uranus. Jupiter's -third satellite, the largest of the number, is nearly four times greater -than the second. Immediately within the orbit of Titan, the largest -satellite of Saturn, occurs a wide hiatus, and the volume of the next -interior satellite is to that of Titan in the ratio of one to -twenty-one. In the Uranian system the widest interval between adjacent -orbits is just within the orbit of the bright satellite, Titania. - -The foregoing facts suggest the inquiry, What effect would be produced -by a large planet on interior masses abandoned by a central spheroid? As -the phenomena in all instances would be of the same nature, we will -consider a single case,--that of Jupiter and the asteroids. - -The powerful mass of the exterior body would produce great perturbations -of the neighboring small planets abandoned at the solar equator. The -disturbed orbits, in some cases, would thus attain considerable -eccentricity, so that the matter moving in them would, in perihelion, be -brought in contact with the equatorial parts of the central body, and -thus become reunited with it.[7] The extreme rarity of the zone between -Mars and Jupiter, regarded as a single ring, is thus accounted for in -accordance with known dynamical laws. - - -3. The Limits of Perihelion Distance. - -It is sufficiently obvious that whenever the perihelion distance of a -planet or comet is less than the sun's radius, a collision must occur as -the moving body approaches the focus of its path. The great comet of -1843 passed so near the sun as almost to graze its surface. With a -perihelion distance but very slightly less, it would have been -precipitated into the sun and incorporated with its mass. In former -epochs, when the dimensions of the sun were much greater than at -present, this falling of comets into the central orb of the system must -have been a comparatively frequent occurrence. Again, if Mercury's orbit -had its present eccentricity when the radius of the solar spheroid was -twenty-nine million miles, the planet at its nearest approach to the -centre of its motion must have passed through the outer strata of the -central body. In such case a lessening of the planet's mean distance -would be a necessary consequence. We thus see that in the formation of -the solar system the eccentricity of an asteroidal orbit could not -increase beyond a moderate limit without the planet's return to the -solar mass. The bearing of these views on the arrangement of the minor -planets will appear in what follows. - - -4. Was the Asteroid Zone originally Stable?--Distribution of the Members -in Space. - -One of the most interesting discoveries of the eighteenth century was -Lagrange's law securing the stability of the solar system. This -celebrated theorem, however, is not to be understood in an absolute or -unlimited sense. It makes no provision against the effect of a resisting -medium, or against the entrance of cosmic matter from without. It does -not secure the stability of all periodic comets nor of the meteor -streams revolving about the sun. In the early stages of the system's -development the matter moving in unstable orbits may have been, and -probably was, much more abundant than at present. But even now, are we -justified in concluding that all known asteroids have stable orbits? For -the major planets the secular variations of eccentricity have been -calculated, but for the orbits between Mars and Jupiter these limits are -unknown. With an eccentricity of 0.252 (less than that of many -asteroids), the distance of Hilda's aphelion would be greater than that -of Jupiter's perihelion. It seems possible, therefore, that certain -minor planets may have their orbits much changed by Jupiter's disturbing -influence.[8] - -Whoever looks at a table of asteroids arranged in their order of -discovery will find only a perplexing mass of figures. Whether we regard -their distances, their inclinations, or the forms of their orbits, the -elements of the members are without any obvious connection. Nor is the -confusion lessened when the orbits are drawn and presented to the eye. -In fact, the crossing and recrossing of so many ellipses of various -forms merely increase the entanglement. But can no order be traced in -all this complexity? Are there no breaks or vacant spaces within the -zone's extreme limits? Has Jupiter's influence been effective in fixing -the position and arrangement of the cluster? Such are some of the -questions demanding our attention. If "the universe is a book written -for man's reading," patient study may resolve the problem contained in -these mysterious leaves. - -Simultaneously with the discovery of new members in the cluster of minor -planets, near the middle of the century, occurred the resolution of the -great nebula in Orion. This startling achievement by Lord Rosse's -telescope was the signal for the abandonment of the nebular hypothesis -by many of its former advocates. To the present writer, however, the -partial resolution of a single nebula seemed hardly a sufficient reason -for its summary rejection. The question then arose whether any probable -test of Laplace's theory could be found in the solar system itself. The -train of thought was somewhat as follows: Several new members have been -found in the zone of asteroids; its dimensions have been greatly -extended, so that we can now assign no definite limits either to the -ring itself or to the number of its planets; if the nebular hypothesis -be true, the sun, after Jupiter's separation, extended successively to -the various decreasing distances of the several asteroids; the -eccentricities of these bodies are generally greater than those of the -old planets; this difference is probably due to the disturbing force of -Jupiter; the zone includes several distances at which the periods of -asteroids would be commensurable with that of Jupiter; in such case the -conjunctions of the minor with the major planet would occur in the same -parts of its path, the disturbing effects would accumulate, and the -eccentricity would become very marked; such bodies in perihelion would -return to the sun, and hence blanks or chasms would be formed in -particular parts of the zone. On the other hand, if the nebular -hypothesis was not true, the occurrence of these gaps was not to be -expected. Having thus pointed out a prospective test of the theory, it -was announced with some hesitation that _those parts of the asteroid -zone in which a simple relation of commensurability would obtain between -the period of a minor planet and that of Jupiter are distinguished as -gaps or chasms similar to the interval in Saturn's ring_. - -The existence of these blanks was thus predicted in theory before it was -established as a fact of observation. When the law was first publicly -stated in 1866, but ten asteroids had been found with distances greater -than three times that of the earth. The number of such now known is -sixty-five. For more than a score of years the progress of discovery -has been watched with lively interest, and the one hundred and eighty -new members of the group have been found moving in harmony with this law -of distribution.[9] - - -COMMENSURABILITY OF PERIODS. - -When we say that an asteroid's period is commensurable with that of -Jupiter, we mean that a certain whole number of the former is equal to -another whole number of the latter. For instance, if a minor planet -completes two revolutions to Jupiter's one, or five to Jupiter's two, -the periods are commensurable. It must be remarked, however, that -Jupiter's effectiveness in disturbing the motion of a minor planet -depends on the _order_ of commensurability. Thus, if the ratio of the -less to the greater period is expressed by the fraction 1/2, where the -difference between the numerator and the denominator is one, the -commensurability is of the first order; 1/3 is of the second; 2/5, of -the third, etc. The difference between the terms of the ratio indicates -the frequency of conjunctions while Jupiter is completing the number -of revolutions expressed by the numerator. The distance 3.277, -corresponding to the ratio 1/2, is the only case of the first order in -the entire ring; those of the second order, answering to 1/3 and 3/5, -are 2.50 and 3.70. These orders of commensurability may be thus arranged -in a tabular form, the radius of the earth's orbit being the unit of -distance: - - +--------+----------------+-----------+ - | Order. | Ratio. | Distance. | - +--------+----------------+-----------+ - | First | 1/2 | 3.277 | - | | | | - | Second | 1/3, 3/5 | { 2.50 | - | | | { 3.70 | - | | | | - | | | { 2.82 | - | Third | 2/5, 4/7, 5/8 | { 3.58 | - | | | { 3.80 | - | | | | - | | | { 2.95 | - | Fourth | 3/7, 5/9, 7/11 | { 3.51 | - | | | { 3.85 | - +--------+----------------+-----------+ - -Do these parts of the ring present discontinuities? and, if so, can they -be ascribed to a chance distribution? Let us consider them in order. - - -I.--The Distance 3.277. - -At this distance an asteroid's conjunctions with Jupiter would all occur -at the same place, and its perturbations would be there repeated at -intervals equal to Jupiter's period (11.86 y.). Now, when the asteroids -are arranged in the order of their mean distances (as in Table II.) this -part of the zone presents a wide chasm. The space between 3.218 and -3.376 remains, hitherto a perfect blank, while the adjacent portions of -equal breadth, interior and exterior, contain fifty-four minor planets. -The probability that this distribution is not the result of chance is -more than three hundred billions to one. - -The breadth of this chasm is one-twentieth part of its distance from the -sun, or one-eleventh part of the breadth of the entire zone. - - -II.--The Second Order of Commensurability.--The Distances 2.50 and 3.70. - -At the former of these distances an asteroid's period would be one-third -of Jupiter's, and at the latter, three-fifths. That part of the zone -included between the distances 2.30 and 2.70 contains one hundred and -ten intervals, exclusive of the maximum at the critical distance 2.50. -This gap--between Thetis and Hestia--is not only much greater than any -other of this number, but is more than sixteen times greater than their -average. The distance 3.70 falls in the wide hiatus interior to the -orbit of Ismene. - - -III.--Chasms corresponding to the Third Order.--The Distances 2.82, -3.58, and 3.80. - -As the order of commensurability becomes less simple, the corresponding -breaks in the zone are less distinctly marked. In the present case -conjunctions with Jupiter would occur at angular intervals of 120D. The -gaps, however, are still easily perceptible. Between the distances 2.765 -and 2.808 we find twenty minor planets. In the next exterior space of -equal breadth, containing the distance 2.82, there is but one. This is -No. 188, Menippe, whose elements are still somewhat uncertain. The space -between 2.851 and 2.894--that is, the part of equal extent immediately -beyond the gap--contains thirteen asteroids. The distances 3.58 and 3.80 -are in the chasm between Andromache and Ismene. - - -IV.--The Distances 2.95, 3.51,[10] and 3.85, corresponding to the Fourth -Order of Commensurability. - -The first of these distances is in the interval between Psyche and -Clytemnestra; the second and third, in that exterior to Andromache. - -The nine cases considered are the only ones in which the conjunctions -with Jupiter would occur at less than five points of an asteroid's -orbit. Higher orders of commensurability may perhaps be neglected. It -will be seen, however, that the distances 2.25, 2.70, 3.03, and 3.23, -corresponding to the ratios of the fifth order, 2/7, 3/8, 4/9, and 6/11, -still afford traces of Jupiter's influence. The first is in the interval -between Augusta and Feronia; the last falls in the same gap with 3.277; -and the second and third are in breaks less distinctly marked. It may -also be worthy of notice that the rather wide interval between Prymno -and Victoria is where ten periods of a minor planet would be equal to -three of Jupiter. The distance of Medusa is somewhat uncertain. - -The FACT of the existence of well-defined gaps in the designated parts -of the ring has been clearly established. But the theory of probability -applied in a single instance gives, as we have seen, but one chance in -300,000,000,000 that the distribution is accidental. This improbability -is increased many millions of times when we include all the gaps -corresponding to simple cases of commensurability. We conclude, -therefore, that those discontinuities cannot be referred to a chance -arrangement. What, then, was their physical cause? and what has become -of the eliminated asteroids? - -What was said in regard to the limits of perihelion distance may suggest -a possible answer to these interesting questions. The doctrine of the -sun's gradual contraction is now accepted by a majority of astronomers. -According to this theory the solar radius at an epoch not relatively -remote was twice what it is at present. At anterior stages it was 0.4, -1.0, 2.0,[11] etc. At the first mentioned the comets of 1843 and 1668, -as well as several others, could not have been moving in their present -orbits, since in perihelion they must have plunged into the sun. At the -second, Encke's comet and all others with perihelia within Mercury's -orbit would have shared a similar fate. At the last named all asteroids -with perihelion distances less than two would have been re-incorporated -with the central mass. As the least distance of Aethra is but 1.587, its -orbit could not have had its present form and dimensions when the radius -of the solar nebula was equal to the aphelion distance of Mars (1.665). - -It is easy to see, therefore, that in those parts of the ring where -Jupiter would produce extraordinary disturbance the formation of chasms -would be very highly probable. - - -5. Relations between certain Adjacent Orbits. - -The distances, periods, inclinations, and eccentricities of Hilda and -Ismene, the outermost pair of the group, are very nearly identical. It -is a remarkable fact, however, that the longitudes of their perihelia -differ by almost exactly 180D. Did they separate at nearly the same -time from opposite sides of the solar nebula? Other adjacent pairs -having a striking similarity between their orbital elements are Sirona -and Ceres, Fides and Maia, Fortuna and Eurynome, and perhaps a few -others. Such coincidences can hardly be accidental. Original asteroids, -soon after their detachment from the central body, may have been -separated by the sun's unequal attraction on their parts. Such divisions -have occurred in the world of comets, why not also in the cluster of -minor planets? - - -6. The Eccentricities. - -The least eccentric orbit in the group is that of Philomela (196); the -most eccentric that of Aethra (132). Comparing these with the orbit of -the second comet of 1867 we have - - The eccentricity of Philomela = 0.01 - " " " Aethra = 0.38 - " " " Comet II. 1867 (ret. in 1885) = 0.41 - -The orbit of Aethra, it is seen, more nearly resembles the last than the -first. It might perhaps be called the connecting-link between planetary -and cometary orbits. - -The average eccentricity of the two hundred and sixty-eight asteroids -whose orbits have been calculated is 0.1569. As with the orbits of the -old planets, the eccentricities vary within moderate limits, some -increasing, others diminishing. The average, however, will probably -remain very nearly the same. An inspection of the table shows that while -but one orbit is less eccentric than the earth's, sixty-nine depart more -from the circular form than the orbit of Mercury. These eccentricities -seem to indicate that the forms of the asteroidal orbits were influenced -by special causes. It may be worthy of remark that the eccentricity does -not appear to vary with the distance from the sun, being nearly the same -for the interior members of the zone as for the exterior. - - -7. The Inclinations. - -The inclinations in Table II. are thus distributed: - - From 0D to 4D 70 - " 4D to 8D 83 - " 8D to 12D 59 - " 12D to 16D 32 - " 16D to 20D 8 - " 20D to 24D 8 - " 24D to 28D 7 - " 28D to 32D 0 - above 32D 1 - -One hundred and fifty-four, considerably more than half, have -inclinations between 3D and 11D, and the mean of the whole number is -about 8D,--slightly greater than the inclination of Mercury, or that of -the plane of the sun's equator. The smallest inclination, that of -Massalia, is 0D 41', and the largest, that of Pallas, is about 35D. -Sixteen minor planets, or six per cent. of the whole number, have -inclinations exceeding 20D. Does any relation obtain between high -inclinations and great eccentricities? These elements in the cases named -above are as follows: - - +------------+--------------+--------------+ - | Asteroid. | Inclination. | Eccentricity.| - +------------+--------------+--------------+ - | Pallas | 34D 42' | 0.238 | - | Istria | 26 30 | 0.353 | - | Euphrosyne | 26 29 | 0.228 | - | Anna | 25 24 | 0.263 | - | Gallia | 25 21 | 0.185 | - | Aethra | 25 0 | 0.380 | - | Eukrate | 24 57 | 0.236 | - | Eva | 24 25 | 0.347 | - | Niobe | 23 19 | 0.173 | - | Eunice | 23 17 | 0.129 | - | Electra | 22 55 | 0.208 | - | Idunna | 22 31 | 0.164 | - | Phocea | 21 35 | 0.255 | - | Artemis | 21 31 | 0.175 | - | Bertha | 20 59 | 0.085 | - | Henrietta | 20 47 | 0.260 | - +------------+--------------+--------------+ - -This comparison shows the most inclined orbits to be also very -eccentric; Bertha and Eunice being the only exceptions in the foregoing -list. On the other hand, however, we find over fifty asteroids with -eccentricities exceeding 0.20 whose inclinations are not extraordinary. -The dependence of the phenomena on a common cause can, therefore, hardly -be admitted. At least, the forces which produced the great eccentricity -failed in a majority of cases to cause high inclinations. - - -8. Longitudes of the Perihelia. - -The perihelia of the asteroidal orbits are very unequally distributed; -one hundred and thirty-six--a majority of the whole number -determined--being within the 120D from longitude 290D 50' to 59D 50'. -The maximum occurs between 30D and 60D, where thirty-five perihelia are -found in 30D of longitude. - - -9. Distribution of the Ascending Nodes. - -An inspection of the column containing the longitudes of the ascending -nodes, in Table II., indicates two well-marked maxima, each extending -about sixty degrees, in opposite parts of the heavens. - - I. From 310D to 10D, containing 61 ascending nodes. - II. " 120D to 180D, " 59 " " - --- - Making in 120D 120 " " - -A uniform distribution would give 89. An arc of 84D--from 46D to -130D--contains the ascending nodes of all the old planets. This arc, it -will be noticed, is not coincident with either of the maxima found for -the asteroids. - - -10. The Periods. - -Since, according to Kepler's third law, the periods of planets depend -upon their mean distances, the clustering tendency found in the latter -must obtain also in the former. This marked irregularity in the order of -periods is seen below. - - Between 1100 and 1200 days 6 periods. - " 1200 " 1300 " 7 " - " 1300 " 1400 " 43 " - " 1400 " 1500 " 13 " - " 1500 " 1600 " 46 " - " 1600 " 1700 " 54 " - " 1700 " 1800 " 20 " - " 1800 " 1900 " 13 " - " 1900 " 2000 " 19 " - " 2000 " 2100 " 33 " - " 2100 " 2200 " 2 " - " 2200 " 2300 " 2 " - " 2300 " 2400 " 8 " - " 2400 " 2800 " 0 " - " 2800 " 2900 " 2 " - -The period of Hilda (153) is more than two and a half times that of -Medusa (149). This is greater than the ratio of Saturn's period to that -of Jupiter. The maximum observed between 2000 and 2100 days corresponds -to the space immediately interior to chasm I. on a previous page, that -between 1300 and 1400 to the space interior to the second, and that -between 1500 and 1700 to the part of the zone within the fourth gap. The -table presents quite numerous instances of approximate equality; in -forty-three cases the periods differing less than twenty-four hours. It -is impossible to say, however, whether any two of these periods are -_exactly_ equal. In cases of a very close approach two asteroids, -notwithstanding their small mass, may exert upon each other quite -sensible perturbations. - - -11. Origin of the Asteroids. - -But four minor planets had been discovered when Laplace issued his last -edition of the "Systeme du Monde." The author, in his celebrated seventh -note in the second volume of that work, explained the origin of these -bodies by assuming that the primitive ring from which they were formed, -instead of collecting into a single sphere, as in the case of the major -planets, broke up into four distinct masses. But the form and extent of -the cluster as now known, as well as the observed facts bearing on the -constitution of Saturn's ring, seem to require a modification of -Laplace's theory. Throughout the greater part of the interval between -Mars and Jupiter an almost continuous succession of small planetary -masses--not nebulous rings--appears to have been abandoned at the solar -equator. The entire cluster, distributed throughout a space whose outer -radius exceeds the inner by more than two hundred millions of miles, -could not have originated, as supposed by Laplace, in a single nebulous -zone the different parts of which revolved with the same angular -velocity. The following considerations may furnish a suggestion in -regard to the mode in which these bodies were separated from the equator -of the solar nebula. - -(_a_) The perihelion distance of Jupiter is 4.950, while the aphelion -distance of Hilda is 4.623. If, therefore, the sun once extended to the -latter, the central attraction of its mass on an equatorial particle was -but five times greater than Jupiter's perihelion influence on the same. -It is easy to see, then, that this "giant planet" would produce enormous -tidal elevations in the solar mass. - -(_b_) The centrifugal force would be greatest at the crest of this tidal -wave. - -(_c_) Three periods of solar revolution were then about equal to two -periods of Jupiter. The disturbing influence of the planet would -therefore be increased at each conjunction with this protuberance. The -ultimate separation (not of a ring but) of a planetary mass would be the -probable result of these combined and accumulating forces. - - -12. Variability of Certain Asteroids. - -Observations of some minor planets have indicated a variation of their -apparent magnitudes. Frigga, discovered by Dr. Peters in 1862, was -observed at the next opposition in 1864; but after this it could not be -found till 1868, when it was picked up by Professor Tietjen. From the -latter date its light seems again to have diminished, as all efforts to -re-observe it were unsuccessful till 1879. According to Dr. Peters, the -change in brightness during the period of observation in that year was -greater than that due to its varying distance. No explanation of such -changes has yet been offered. It has been justly remarked, however, that -"the length of the period of the fluctuation does not allow of our -connecting it with the rotation of the planet." - - -13. The Average Asteroid Orbit. - -At the meeting of the American Association for the Advancement of -Science in 1884, Professor Mark W. Harrington, of Ann Arbor, Michigan, -presented a paper in which the elements of the asteroid system were -considered on the principle of averages. Two hundred and thirty orbits, -all that had then been determined, were employed in the discussion. -Professor Harrington supposes two planes to intersect the ecliptic at -right angles; one passing through the equinoxes and the other through -the solstices. These planes will intersect the asteroidal orbits, each -in four points, and "the mean intersection at each solstice and equinox -may be considered a point in the average orbit." - -In 1883 the Royal Academy of Denmark offered its gold medal for a -statistical examination of the orbits of the small planets considered as -parts of a ring around the sun. The prize was awarded in 1885 to M. -Svedstrup, of Copenhagen. The results obtained by these astronomers -severally are as follows: - - +-----------------------------+-------------+------------+ - | | Harrington. | Svedstrup. | - +-----------------------------+-------------+------------+ - | Longitude of perihelion | 14D 39' | 101D 48' | - | " of ascending node | 113 56 | 133 27 | - | Inclination | 1 0 | 6 6 | - | Eccentricity | 0.0448 | 0.0281 | - | Mean distance | 2.7010 | 2.6435 | - +-----------------------------+-------------+------------+ - -These elements, with the exception of the first, are in reasonable -harmony. - - -14. The Relation of Short-Period Comets to the Zone of Asteroids. - -Did comets originate within the solar system, or do they enter it from -without? Laplace assigned them an extraneous origin, and his view is -adopted by many eminent astronomers. With all due respect to the -authority of great names, the present writer has not wholly abandoned -the theory that some comets of short period are specially related to the -minor planets. According to M. Lehmann-Filhes, the eccentricity of the -third comet of 1884, before its last close approach to Jupiter, was only -0.2787.[12] This is exceeded by that of twelve known minor planets. Its -mean distance before this great perturbation was about 4.61, and six of -its periods were nearly equal to five of Jupiter's,--a commensurability -of the first order. According to Hind and Krueger, the great -transformation of its orbit by Jupiter's influence occurred in May, -1875. It had previously been an asteroid too remote to be seen even in -perihelion. This body was discovered by M. Wolf, at Heidelberg, -September 17, 1884. Its present period is about six and one-half years. - -The perihelion distance of the comet 1867 II. at its return in 1885 was -2.073; its aphelion is 4.897; so that its entire path, like those of the -asteroids, is included between the orbits of Mars and Jupiter. Its -eccentricity, as we have seen, is little greater than that of Aethra, and -its period, inclination, and longitude of the ascending node are -approximately the same with those of Sylvia, the eighty-seventh minor -planet. In short, this comet may be regarded as an asteroid whose -elements have been considerably modified by perturbation. - -It has been stated that the gap at the distance 3.277 is the only one -corresponding to the first order of commensurability. The distance -3.9683, where an asteroid's period would be two-thirds of Jupiter's, is -immediately beyond the outer limit of the cluster as at present known; -the mean distance of Hilda being 3.9523. The discovery of new members -beyond this limit is by no means improbable. Should a minor planet at -the mean distance 3.9683 attain an eccentricity of 0.3--and this is less -than that of eleven now known--its aphelion would be more remote than -the perihelion of Jupiter. Such an orbit might not be stable. Its form -and extent might be greatly changed after the manner of Lexell's comet. -Two well-known comets, Faye's and Denning's, have periods approximately -equal to two-thirds of Jupiter's. In like manner the periods of -D'Arrest's and Biela's comets correspond to the hiatus at 3.51, and that -of 1867 II. to that at 3.277. - -Of the thirteen telescopic comets whose periods correspond to mean -distances within the asteroid zone, all have direct motion; all have -inclinations similar to those of the minor planets; and their -eccentricities are generally less than those of other known comets. Have -these facts any significance in regard to their origin? - - - - -APPENDIX. - - -NOTE A. - -THE POSSIBLE EXISTENCE OF ASTEROIDS IN UNDISCOVERED RINGS. - -If Jupiter's influence was a factor in the separation of planetules at -the sun's equator, may not similar clusters exist in other parts of our -system? The hypothesis is certainly by no means improbable. For anything -we know to the contrary a group may circulate between Jupiter and -Saturn; such bodies, however, could not be discovered--at least not by -ordinary telescopes--on account of their distance. The Zodiacal Light, -it has been suggested, may be produced by a cloud of indefinitely small -particles related to the planets between the sun and Mars. The rings of -Saturn are merely a dense asteroidal cluster; and, finally, the -phenomena of luminous meteors indicate the existence of small masses of -matter moving with different velocities in interstellar space. - - -NOTE B. - -THE ORIGIN AND STRUCTURE OF COSMICAL RINGS. - -The general theory of cosmical rings and of their arrangement in -sections or clusters with intervening chasms may be briefly stated in -the following propositions: - - -I. - -Whenever the separating force of a primary body on a secondary or -satellite is greater than the central attraction of the latter on its -superficial stratum, the satellite, if either gaseous or liquid, will be -transformed into a ring. - -EXAMPLES.--Saturn's ring, and the meteoric rings of April 20, August 10, -November 14, and November 27. - -See Payne's _Sidereal Messenger_, April, 1885. - - -II. - -When a cosmical body is surrounded by a ring of considerable breadth, -and has also exterior satellites at such distances that a simple -relation of commensurability would obtain between the periods of these -satellites and those of certain particles of the ring, the disturbing -influence of the former will produce gaps or intervals in the ring so -disturbed. - -See "Meteoric Astronomy," Chapter XII.; also the _Proceedings of the -American Philosophical Society_, October 6, 1871; and the _Sidereal -Messenger_ for February, 1884; where the papers referred to assign a -physical cause for the gaps in Saturn's ring. - - -THE END. - - -FOOTNOTES: - -[1] The discoverer, Piazzi, was not, as has been so often affirmed, one -of the astronomers to whom the search had been especially committed. - -[2] Massalia was discovered by De Gasparis, at Naples, Sept. 19, 1852, -and independently, the next night, by Chacornac, at Marseilles. The name -was given by the latter. - -[3] Astr. Nach., No. 932. - -[4] Monthly Notices, vol. xxvii. - -[5] Annals of the Obs. of Harv. Coll., 1879. - -[6] This ingenious idea may be readily extended. The least distance of -Aethra is less than the present aphelion distance of Mars; and the -maximum aphelion distance of the latter exceeds the perihelion distance -of several known asteroids. Moreover, if we represent the orbits of the -major planets, and also those of the comets of known periods, by -material rings, it is easy to see that the major as well as the minor -planets are all linked together in the manner suggested by D'Arrest. - -[7] The effects of Jupiter's disturbing influence will again be resumed. - -[8] Not only nebulae are probably unstable, but also many of the sidereal -systems. The Milky Way itself was so regarded by Sir William Herschel. - -[9] Menippe, No. 188, is placed in one of the gaps by its calculated -elements; but the fact that it has not been seen since the year of its -discovery, 1878, indicates a probable error in its elements. - -[10] The minor planet Andromache, immediately interior to the critical -distance 3.51, has elements somewhat remarkable. With two exceptions, -Aethra (132) and Istria (183), it has the greatest eccentricity -(0.3571),--nearly equal to that of the comet 1867 II. at its last -return. Its perihelion distance is 2.2880, its aphelion 4.7262; hence -the distance from the perihelion to the aphelion of its orbit is greater -than its least distance from the sun, and it crosses the orbits of all -members of the group so far as known; its least distance from the sun -being considerably less than the aphelion of Medusa, and its greatest -exceeding the aphelion of Hilda. - -[11] The unit being the sun's distance from the earth. - -[12] Annuaire, 1886. - - - -***END OF THE PROJECT GUTENBERG EBOOK THE ASTEROIDS*** - - -******* This file should be named 41570.txt or 41570.zip ******* - - -This and all associated files of various formats will be found in: -http://www.gutenberg.org/dirs/4/1/5/7/41570 - - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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