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

Author: Daniel Kirkwood

Release Date: December 6, 2012 [EBook #41570]

Language: English

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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.

PREFACE.

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

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

DANIEL KIRKWOOD.

BLOOMINGTON, INDIANA, November, 1887.

CONTENTS.

PART I.

PAGE

PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN

9

DISCOVERY OF THE FIRST ASTEROIDS

11

TABLE I.—ASTEROIDS IN THE ORDER OF THEIR DISCOVERY

17

NUMBERS FOUND BY THE RESPECTIVE DISCOVERERS

23

NUMBERS DISCOVERED IN THE DIFFERENT MONTHS

25

MODE OF DISCOVERY

25

NAMES AND SYMBOLS

25

MAGNITUDES OF THE ASTEROIDS

26

ORBITS OF THE ASTEROIDS

28

TABLE II.—ELEMENTS OF THE ASTEROIDS

29

PART II.

EXTENT OF THE ZONE

37

THEORY OF OLBERS

38

SMALL MASS OF THE ASTEROIDS

38

LIMITS OF PERIHELION DISTANCE

39

DISTRIBUTION OF THE ASTEROIDS IN SPACE

40

LAW OF GAP FORMATION

42

COMMENSURABILITY OF PERIODS WITH THAT OF JUPITER

43

ORDERS OF COMMENSURABILITY

44

ELIMINATION OF VERY ECCENTRIC ORBITS

46

RELATIONS BETWEEN CERTAIN ADJACENT ORBITS

47

THE ECCENTRICITIES

48

THE INCLINATIONS

49

LONGITUDES OF THE PERIHELIA AND OF THE ASCENDING NODES

50

THE PERIODS

51

ORIGIN OF THE ASTEROIDS

52

VARIABILITY OF CERTAIN ASTEROIDS

53

THE AVERAGE ASTEROID ORBIT

54

THE RELATION OF SHORT-PERIOD COMETS TO THE ZONE OF ASTEROIDS

55

APPENDIX

59

[Pg 7]

[Pg 8]

PART I.

THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER.

1. Introductory.

PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN.

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

At the beginning of the seventeenth century but six primary planets and one satellite were known as members of the solar system. Very few, even of the learned, had then accepted the theory of Copernicus; in fact, before the invention of the telescope the evidence in its favor was not absolutely conclusive. On the 7th of January, 1610, Galileo first saw the satellites of Jupiter. The bearing of this discovery on the theory of the universe was sufficiently obvious. Such was the prejudice, however, against the Copernican system that some of its opponents denied even the reality of Galileo's discovery. "Those satellites," said a Tuscan astronomer, "are invisible to the naked eye, and therefore can exercise no influence on the earth, and therefore would be useless, and therefore do not exist. Besides, the Jews and other ancient nations, as well as modern Europeans, have adopted the division of the week into seven days, and have named them from the seven planets; now, if we increase the number of planets this whole system falls to the ground."

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

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

2. Discovery of the First Asteroids.

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

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

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

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

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

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

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

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

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

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

TABLE I.

The Asteroids in the Order of their Discovery.

Asteroids.

Date of

Discovery.

Name of

Discoverer.

Place of

Discovery.

1.   Ceres

1801, Jan. 1

Piazzi

Palermo

2.   Pallas

1802, Mar. 28

Olbers

Bremen

3.   Juno

1804, Sept. 1

Harding

Lilienthal

4.   Vesta

1807, Mar. 29

Olbers

Bremen

5.   Astræa

1845, Dec. 8

Hencke

Driessen

6.   Hebe

1847, July 1

Hencke

Driessen

7.   Iris

1847, Aug. 14

Hind

London

8.   Flora

1847, Oct. 18

Hind

London

9.   Metis

1848, Apr. 26

Graham

Markree

10.   Hygeia

1849, Apr. 12

De Gasparis

Naples

11.   Parthenope

1850, May 11

De Gasparis

Naples

12.   Victoria

1850, Sept. 13

Hind

London

13.   Egeria

1850, Nov. 2

De Gasparis

Naples

14.   Irene

1851, May 19

Hind

London

15.   Eunomia

1851, July 29

De Gasparis

Naples

16.   Psyche

1852, Mar. 17

De Gasparis

Naples

17.   Thetis

1852, Apr. 17

Luther

Bilk

18.   Melpomene

1852, June 24

Hind

London

19.   Fortuna

1852, Aug. 22

Hind

London

20.   Massalia

1852, Sept. 19

De Gasparis

Naples

21.   Lutetia

1852, Nov. 15

Goldschmidt

Paris

22.   Calliope

1852, Nov. 16

Hind

London

23.   Thalia

1852, Dec. 15

Hind

London

24.   Themis

1853, Apr. 5

De Gasparis

Naples

25.   Phocea

1853, Apr. 6

Chacornac

Marseilles

26.   Proserpine

1853, May 5

Luther

Bilk

27.   Euterpe

1853, Nov. 8

Hind

London

28.   Bellona

1854, Mar. 1

Luther

Bilk

29.   Amphitrite

1854, Mar. 1

Marth

London

30.   Urania

1854, July 22

Hind

London

31.   Euphrosyne

1854, Sept. 1

Ferguson

Washington

32.   Pomona

1854, Oct. 26

Goldschmidt

Paris

33.   Polyhymnia

1854, Oct. 28

Chacornac

Paris

34.   Circe

1855, Apr. 6

Chacornac

Paris

35.   Leucothea

1855, Apr. 19

Luther

Bilk

36.   Atalanta

1855, Oct. 5

Goldschmidt

Paris

37.   Fides

1855, Oct. 5

Luther

Bilk

38.   Leda

1856, Jan. 12

Chacornac

Paris

39.   Lætitia

1856, Feb. 8

Chacornac

Paris

40.   Harmonia

1856, Mar. 31

Goldschmidt

Paris

41.   Daphne

1856, May 22

Goldschmidt

Paris

42.   Isis

1856, May 23

Pogson

Oxford

43.   Ariadne

1857, Apr. 15

Pogson

Oxford

44.   Nysa

1857, May 27

Goldschmidt

Paris

45.   Eugenia

1857, June 27

Goldschmidt

Paris

46.   Hestia

1857, Aug. 16

Pogson

Oxford

47.   Aglaia

1857, Sept. 15

Luther

Bilk

48.   Doris

1857, Sept. 19

Goldschmidt

Paris

49.   Pales

1857, Sept. 19

Goldschmidt

Paris

50.   Virginia

1857, Oct. 4

Ferguson

Washington

51.   Nemausa

1858, Jan. 22

Laurent

Nismes

52.   Europa

1858, Feb. 4

Goldschmidt

Paris

53.   Calypso

1858, Apr. 4

Luther

Bilk

54.   Alexandra

1858, Sept. 10

Goldschmidt

Paris

55.   Pandora

1858, Sept. 10

Searle

Albany

56.   Melete

1857, Sept. 9

Goldschmidt

Paris

57.   Mnemosyne

1859, Sept. 22

Luther

Bilk

58.   Concordia

1860, Mar. 24

Luther

Bilk

59.   Olympia

1860, Sept. 12

Chacornac

Paris

60.   Echo

1860, Sept. 16

Ferguson

Washington

61.   Danaë

1860, Sept. 9

Goldschmidt

Paris

62.   Erato

1860, Sept. 14

Foerster and Lesser

Berlin

63.   Ausonia

1861, Feb. 10

De Gasparis

Naples

64.   Angelina

1861, Mar. 4

Tempel

Marseilles

65.   Maximiliana

1861, Mar. 8

Tempel

Marseilles

66.   Maia

1861, Apr. 9

Tuttle

Cambridge, U.S.

67.   Asia

1861, Apr. 17

Pogson

Madras

68.   Leto

1861, Apr. 29

Luther

Bilk

69.   Hesperia

1861, Apr. 29

Schiaparelli

Milan

70.   Panopea

1861, May 5

Goldschmidt

Paris

71.   Niobe

1861, Aug. 13

Luther

Bilk

72.   Feronia

1862, May 29

Peters and Safford

Clinton

73.   Clytie

1862, Apr. 7

Tuttle

Cambridge

74.   Galatea

1862, Aug. 29

Tempel

Marseilles

75.   Eurydice

1862, Sept. 22

Peters

Clinton

76.   Freia

1862, Oct. 21

D'Arrest

Copenhagen

77.   Frigga

1862, Nov. 12

Peters

Clinton

78.   Diana

1863, Mar. 15

Luther

Bilk

79.   Eurynome

1863, Sept. 14

Watson

Ann Arbor

80.   Sappho

1864, May 2

Pogson

Madras

81.   Terpsichore

1864, Sept. 30

Tempel

Marseilles

82.   Alcmene

1864, Nov. 27

Luther

Bilk

83.   Beatrix

1865, Apr. 26

De Gasparis

Naples

84.   Clio

1865, Aug. 25

Luther

Bilk

85.   Io

1865, Sept. 19

Peters

Clinton

86.   Semele

1866, Jan. 14

Tietjen

Berlin

87.   Sylvia

1866, May 16

Pogson

Madras

88.   Thisbe

1866, June 15

Peters

Clinton

89.   Julia

1866, Aug. 6

Stephan

Marseilles

90.   Antiope

1866, Oct. 1

Luther

Bilk

91.   Ægina

1866, Nov. 4

Borelly

Marseilles

92.   Undina

1867, July 7

Peters

Clinton

93.   Minerva

1867, Aug. 24

Watson

Ann Arbor

94.   Aurora

1867, Sept. 6

Watson

Ann Arbor

95.   Arethusa

1867, Nov. 24

Luther

Bilk

96.   Ægle

1868, Feb. 17

Coggia

Marseilles

97.   Clotho

1868, Feb. 17

Coggia

Marseilles

98.   Ianthe

1868, Apr. 18

Peters

Clinton

99.   Dike

1868, May 28

Borelly

Marseilles

100.   Hecate

1868, July 11

Watson

Ann Arbor

101.   Helena

1868, Aug. 15

Watson

Ann Arbor

102.   Miriam

1868, Aug. 22

Peters

Clinton

103.   Hera

1868, Sept. 7

Watson

Ann Arbor

104.   Clymene

1868, Sept. 13

Watson

Ann Arbor

105.   Artemis

1868, Sept. 16

Watson

Ann Arbor

106.   Dione

1868, Oct. 10

Watson

Ann Arbor

107.   Camilla

1868, Nov. 17

Pogson

Madras

108.   Hecuba

1869, Apr. 2

Luther

Bilk

109.   Felicitas

1869, Oct. 9

Peters

Clinton

110.   Lydia

1870, Apr. 19

Borelly

Marseilles

111.   Ate

1870, Aug. 14

Peters

Clinton

112.   Iphigenia

1870, Sept. 19

Peters

Clinton

113.   Amalthea

1871, Mar. 12

Luther

Bilk

114.   Cassandra

1871, July 23

Peters

Clinton

115.   Thyra

1871, Aug. 6

Watson

Ann Arbor

116.   Sirona

1871, Sept. 8

Peters

Clinton

117.   Lomia

1871, Sept. 12

Borelly

Marseilles

118.   Peitho

1872, Mar. 15

Luther

Bilk

119.   Althea

1872, Apr. 3

Watson

Ann Arbor

120.   Lachesis

1872, Apr. 10

Borelly

Marseilles

121.   Hermione

1872, May 12

Watson

Ann Arbor

122.   Gerda

1872, July 31

Peters

Clinton

123.   Brunhilda

1872, July 31

Peters

Clinton

124.   Alceste

1872, Aug. 23

Peters

Clinton

125.   Liberatrix

1872, Sept. 11

Prosper Henry

Paris

126.   Velleda

1872, Nov. 5

Paul Henry

Paris

127.   Johanna

1872, Nov. 5

Prosper Henry

Paris

128.   Nemesis

1872, Nov. 25

Watson

Ann Arbor

129.   Antigone

1873, Feb. 5

Peters

Clinton

130.   Electra

1873, Feb. 17

Peters

Clinton

131.   Vala

1873, May 24

Peters

Clinton

132.   Æthra

1873, June 13

Watson

Ann Arbor

133.   Cyrene

1873, Aug. 16

Watson

Ann Arbor

134.   Sophrosyne

1873, Sept. 27

Luther

Bilk

135.   Hertha

1874, Feb. 18

Peters

Clinton

136.   Austria

1874, Mar. 18

Palisa

Pola

137.   Melibœa

1874, Apr. 21

Palisa

Pola

138.   Tolosa

1874, May 19

Perrotin

Toulouse

139.   Juewa

1874, Oct. 10

Watson

Pekin

140.   Siwa

1874, Oct. 13

Palisa

Pola

141.   Lumen

1875, Jan. 13

Paul Henry

Paris

142.   Polana

1875, Jan. 28

Palisa

Pola

143.   Adria

1875, Feb. 23

Palisa

Pola

144.   Vibilia

1875, June 3

Peters

Clinton

145.   Adeona

1875, June 3

Peters

Clinton

146.   Lucina

1875, June 8

Borelly

Marseilles

147.   Protogenea

1875, July 10

Schulhof

Vienna

148.   Gallia

1875, Aug. 7

Prosper Henry

Paris

149.   Medusa

1875, Sept. 21

Perrotin

Toulouse

150.   Nuwa

1875, Oct. 18

Watson

Ann Arbor

151.   Abundantia

1875, Nov. 1

Palisa

Pola

152.   Atala

1875, Nov. 2

Paul Henry

Paris

153.   Hilda

1875, Nov. 2

Palisa

Pola

154.   Bertha

1875, Nov. 4

Prosper Henry

Paris

155.   Scylla

1875, Nov. 8

Palisa

Pola

156.   Xantippe

1875, Nov. 22

Palisa

Pola

157.   Dejanira

1875, Dec. 1

Borelly

Marseilles

158.   Coronis

1876, Jan. 4

Knorre

Berlin

159.   Æmilia

1876, Jan. 26

Paul Henry

Paris

160.   Una

1876, Feb. 20

Peters

Clinton

161.   Athor

1876, Apr. 19

Watson

Ann Arbor

162.   Laurentia

1876, Apr. 21

Prosper Henry

Paris

163.   Erigone

1876, Apr. 26

Perrotin

Toulouse

164.   Eva

1876, July 12

Paul Henry

Paris

165.   Loreley

1876, Aug. 9

Peters

Clinton

166.   Rhodope

1876, Aug. 15

Peters

Clinton

167.   Urda

1876, Aug. 28

Peters

Clinton

168.   Sibylla

1876, Sept. 27

Watson

Ann Arbor

169.   Zelia

1876, Sept. 28

Prosper Henry

Paris

170.   Maria

1877, Jan. 10

Perrotin

Toulouse

171.   Ophelia

1877, Jan. 13

Borelly

Marseilles

172.   Baucis

1877, Feb. 5

Borelly

Marseilles

173.   Ino

1877, Aug. 1

Borelly

Marseilles

174.   Phædra

1877, Sept. 2

Watson

Ann Arbor

175.   Andromache

1877, Oct. 1

Watson

Ann Arbor

176.   Idunna

1877, Oct. 14

Peters

Clinton

177.   Irma

1877, Nov. 5

Paul Henry

Paris

178.   Belisana

1877, Nov. 6

Palisa

Pola

179.   Clytemnestra

1877, Nov. 11

Watson

Ann Arbor

180.   Garumna

1878, Jan. 29

Perrotin

Toulouse

181.   Eucharis

1878, Feb. 2

Cottenot

Marseilles

182.   Elsa

1878, Feb. 7

Palisa

Pola

183.   Istria

1878, Feb. 8

Palisa

Pola

184.   Deiopea

1878, Feb. 28

Palisa

Pola

185.   Eunice

1878, Mar. 1

Peters

Clinton

186.   Celuta

1878, Apr. 6

Prosper Henry

Paris

187.   Lamberta

1878, Apr. 11

Coggia

Marseilles

188.   Menippe

1878, June 18

Peters

Clinton

189.   Phthia

1878, Sept. 9

Peters

Clinton

190.   Ismene

1878, Sept. 22

Peters

Clinton

191.   Kolga

1878, Sept. 30

Peters

Clinton

192.   Nausicaa

1879, Feb. 17

Palisa

Pola

193.   Ambrosia

1879, Feb. 28

Coggia

Marseilles

194.   Procne

1879, Mar. 21

Peters

Clinton

195.   Euryclea

1879, Apr. 22

Palisa

Pola

196.   Philomela

1879, May 14

Peters

Clinton

197.   Arete

1879, May 21

Palisa

Pola

198.   Ampella

1879, June 13

Borelly

Marseilles

199.   Byblis

1879, July 9

Peters

Clinton

200.   Dynamene

1879, July 27

Peters

Clinton

201.   Penelope

1879, Aug. 7

Palisa

Pola

202.   Chryseis

1879, Sept. 11

Peters

Clinton

203.   Pompeia

1879, Sept. 25

Peters

Clinton

204.   Callisto

1879, Oct. 8

Palisa

Pola

205.   Martha

1879, Oct. 13

Palisa

Pola

206.   Hersilia

1879, Oct. 13

Peters

Clinton

207.   Hedda

1879, Oct. 17

Palisa

Pola

208.   Lachrymosa

1879, Oct. 21

Palisa

Pola

209.   Dido

1879, Oct. 22

Peters

Clinton

210.   Isabella

1879, Nov. 12

Palisa

Pola

211.   Isolda

1879, Dec. 10

Palisa

Pola

212.   Medea

1880, Feb. 6

Palisa

Pola

213.   Lilæa

1880, Feb. 16

Peters

Clinton

214.   Aschera

1880, Feb. 26

Palisa

Pola

215.   Œnone

1880, Apr. 7

Knorre

Berlin

216.   Cleopatra

1880, Apr. 10

Palisa

Pola

217.   Eudora

1880, Aug. 30

Coggia

Marseilles

218.   Bianca

1880, Sept. 4

Palisa

Pola

219.   Thusnelda

1880, Sept. 20

Palisa

Pola

220.   Stephania

1881, May 19

Palisa

Vienna

221.   Eos

1882, Jan. 18

Palisa

Vienna

222.   Lucia

1882, Feb. 9

Palisa

Vienna

223.   Rosa

1882, Mar. 9

Palisa

Vienna

224.   Oceana

1882, Mar. 30

Palisa

Vienna

225.   Henrietta

1882, Apr. 19

Palisa

Vienna

226.   Weringia

1882, July 19

Palisa

Vienna

227.   Philosophia

1882, Aug. 12

Paul Henry

Paris

228.   Agathe

1882, Aug. 19

Palisa

Vienna

229.   Adelinda

1882, Aug. 22

Palisa

Vienna

230.   Athamantis

1882, Sept. 3

De Ball

Bothcamp

231.   Vindobona

1882, Sept. 10

Palisa

Vienna

232.   Russia

1883, Jan. 31

Palisa

Vienna

233.   Asterope

1883, May 11

Borelly

Marseilles

234.   Barbara

1883, Aug. 13

Peters

Clinton

235.   Caroline

1883, Nov. 29

Palisa

Vienna

236.   Honoria

1884, Apr. 26

Palisa

Vienna

237.   Cœlestina

1884, June 27

Palisa

Vienna

238.   Hypatia

1884, July 1

Knorre

Berlin

239.   Adrastea

1884, Aug. 18

Palisa

Vienna

240.   Vanadis

1884, Aug. 27

Borelly

Marseilles

241.   Germania

1884, Sept. 12

Luther

Dusseldorf

242.   Kriemhild

1884, Sept. 22

Palisa

Vienna

243.   Ida

1884, Sept. 29

Palisa

Vienna

244.   Sita

1884, Oct. 14

Palisa

Vienna

245.   Vera

1885, Feb. 6

Pogson

Madras

246.   Asporina

1885, Mar. 6

Borelly

Marseilles

247.   Eukrate

1885, Mar. 14

Luther

Dusseldorf

248.   Lameia

1885, June 5

Palisa

Vienna

249.   Ilse

1885, Aug. 17

Peters

Clinton

250.   Bettina

1885, Sept. 3

Palisa

Vienna

251.   Sophia

1885, Oct. 4

Palisa

Vienna

252.   Clementina

1885, Oct. 27

Perrotin

Nice

253.   Mathilde

1885, Nov. 12

Palisa

Vienna

254.   Augusta

1886, Mar. 31

Palisa

Vienna

255.   Oppavia

1886, Mar. 31

Palisa

Vienna

256.   Walpurga

1886, Apr. 3

Palisa

Vienna

257.   Silesia

1886, Apr. 5

Palisa

Vienna

258.   Tyche

1886, May 4

Luther

Dusseldorf

259.   Aletheia

1886, June 28

Peters

Clinton

260.   Huberta

1886, Oct. 3

Palisa

Vienna

261.   Prymno

1886, Oct. 31

Peters

Clinton

262.   Valda

1886, Nov. 3

Palisa

Vienna

263.   Dresda

1886, Nov. 3

Palisa

Vienna

264.   Libussa

1886, Dec. 17

Peters

Clinton

265.   Anna

1887, Feb. 25

Palisa

Vienna

266.   Aline

1887, May 17

Palisa

Vienna

267.   Tirza

1887, May 27

Charlois

Nice

268.

1887, June 9

Borelly

Marseilles

269.

1887, Sept. 21

Palisa

Vienna

270.

1887, Oct. 8

Peters

Clinton

271.

1887, Oct. 16

Knorre

Berlin

3. Remarks on Table I.

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

Palisa

60

Peters

47

Luther

23

Watson

22

Borelly

15

Goldschmidt

14

Hind

10

De Gasparis

9

Pogson

8

Paul Henry

7

Prosper Henry

7

Chacornac

6

Perrotin

6

Coggia

5

Knorre

4

Tempel

4

Ferguson

3

Olbers

2

Hencke

2

Tuttle

2

Foerster (with Lesser)

1

Safford (with Peters)

1

and Messrs. Charlois, Cottenot, D'Arrest, De Ball, Graham, Harding, Laurent, Piazzi, Schiaparelli, Schulhof, Stephan, Searle, and Tietjen, each

1

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

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

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

Asteroids.

1879

20

1875

17

1868

12

1878

12

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

January

13

February

23

March

19

April

35

May

21

June

13

July

14

August

28

September

46

October

28

November

26

December

5

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

4. Mode of Discovery.

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

NAMES AND SYMBOLS.

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

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

5. Magnitudes of the Asteroids.

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

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

6. The Orbits of the Asteroids.

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

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

2. The eccentricity, e.

3. The longitude of the perihelion, π.

4. The longitude of the ascending node, ☊.

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

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

6. Its period, P, and

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

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

TABLE II.

Elements of the Asteroids.

Name

a

P

e

π

☊

i

149.   Medusa

2.1327

1137.7d

0.1194

246°37  ´

342°13  ´

1°6  ´

244.   Sita

2.1765

1172.8

0.1370

138

20837

250

228.   Agathe

2.2009

1192.6

0.2405

32923

31318

233

8.   Flora

2.2014

1193.3

0.1567

3254

11018

553

43.   Ariadne

2.2033

1194.5

0.1671

27758

26435

328

254.   Augusta

2.2060

1196.8

0.1227

26047

289

436

72.   Feronia

2.2661

1246.0

0.1198

30758

20749

524

40.   Harmonia

2.2673

1247.0

0.0466

054

9335

416

207.   Hedda

2.2839

1260.7

0.0301

2172

2851

349

136.   Austria

2.2863

1262.7

0.0849

3166

1867

933

18.   Melpomene

2.2956

1270.4

0.2177

156

1504

109

80.   Sappho

2.2962

1270.9

0.2001

35518

21844

837

261.   Prymno

2.3062

1278.4

0.0794

17935

9633

338

12.   Victoria

2.3342

1302.7

0.2189

30139

23535

823

27.   Euterpe

2.3472

1313.5

0.1739

8759

9351

136

219.   Thusnelda

2.3542

1319.4

0.2247

34034

20044

1047

163.   Erigone

2.3560

1320.9

0.1567

9346

1592

442

169.   Zelia

2.3577

1322.3

0.1313

32620

35438

531

4.   Vesta

2.3616

1325.6

0.0884

25057

10329

78

186.   Celuta

2.3623

1326.2

0.1512

32724

1434

136

84.   Clio

2.3629

1326.7

0.2360

33920

32728

922

51.   Nemausa

2.3652

1328.6

0.0672

17443

17552

957

220.   Stephania

2.3666

1329.8

0.2653

33253

25824

735

30.   Urania

2.3667

1329.9

0.1266

3146

30812

26

105.   Artemis

2.3744

1336.4

0.1749

24238

1883

2131

113.   Amalthea

2.3761

1337.8

0.0874

19844

12311

52

115.   Thyra

2.3791

1340.3

0.1939

432

3095

1135

161.   Athor

2.3792

1340.5

0.1389

31040

1827

93

172.   Baucis

2.3794

1340.6

0.1139

32923

33150

102

249.   Ilse

2.3795

1340.6

0.2195

1417

33449

940

230.   Athamantis

2.3842

1344.6

0.0615

1731

23933

926

7.   Iris

2.3862

1346.4

0.2308

4123

25948

528

9.   Metis

2.3866

1346.7

0.1233

714

6832

536

234.   Barbara

2.3873

1347.3

0.2440

33326

1449

1522

60.   Echo

2.3934

1352.4

0.1838

9836

1925

335

63.   Ausonia

2.3979

1356.3

0.1239

27025

33758

548

25.   Phocea

2.4005

1358.5

0.2553

30248

20827

2135

192.   Nausicaa

2.4014

1359.3

0.2413

34319

16046

650

20.   Massalia

2.4024

1365.8

0.1429

997

20636

041

265.   Anna

2.4096

1366.2

0.2628

22618

33526

2524

182.   Elsa

2.4157

1371.4

0.1852

5152

10630

20

142.   Polana

2.4194

1374.5

0.1322

21954

31734

214

67.   Asia

2.4204

1375.4

0.1866

30635

20247

559

44.   Nysa

2.4223

1377.0

0.1507

11157

13111

342

6.   Hebe

2.4254

1379.3

0.2034

1516

13843

1047

83.   Beatrix

2.4301

1383.6

0.0859

19146

2732

50

135.   Hertha

2.4303

1383.8

0.2037

32011

3443

219

131.   Vala

2.4318

1385.1

0.0683

22250

6515

458

112.   Iphigenia

2.4335

1386.6

0.1282

3389

3243

237

21.   Lutetia

2.4354

1388.2

0.1621

3274

8028

35

118.   Peitho

2.4384

1390.8

0.1608

7736

4730

748

126.   Velleda

2.4399

1392.1

0.1061

34746

237

256

42.   Isis

2.4401

1392.2

0.2256

31758

8428

835

19.   Fortuna

2.4415

1394.4

0.1594

313

21127

133

79.   Eurynome

2.4436

1395.2

0.1945

4422

20644

437

138.   Tolosa

2.4492

1400.0

0.1623

31139

5452

314

189.   Phthia

2.4505

1401.1

0.0356

650

20322

510

11.   Parthenope

2.4529

1403.2

0.0994

3182

12511

437

178.   Belisana

2.4583

1407.8

0.1266

2780

5017

25

198.   Ampella

2.4595

1408.9

0.2266

35446

26845

920

248.   Lameia

2.4714

1419.1

0.0656

24840

24634

41

17.   Thetis

2.4726

1420.1

0.1293

26137

12524

536

46.   Hestia

2.5265

1466.8

0.1642

35414

18131

217

89.   Julia

2.5510

1488.2

0.1805

35313

31142

1611

232.   Russia

2.5522

1489.3

0.1754

20025

15230

64

29.   Amphitrite

2.5545

1491.3

0.0742

5623

35641

67

170.   Maria

2.5549

1491.7

0.0639

9547

30120

1423

262.   Valda

2.5635

1496.4

0.2172

6142

3840

746

258.   Tyche

2.5643

1499.8

0.1966

1542

2084

1450

134.   Sophrosyne

2.5647

1500.3

0.1165

6733

34622

1136

264.   Libussa

2.5672

1502.4

0.0925

07

5023

1029

193.   Ambrosia

2.5758

1510.0

0.2854

7052

35115

1139

13.   Egeria

2.5765

1510.6

0.0871

12010

4312

1632

5.   Astræa

2.5786

1512.4

0.1863

13457

14128

519

119.   Althea

2.5824

1515.7

0.0815

1129

20357

545

157.   Dejanira

2.5828

1516.1

0.2105

10724

6231

122

101.   Helena

2.5849

1518.0

0.1386

32715

34346

1011

32.   Pomona

2.5873

1520.1

0.0830

19322

22043

529

91.   Ægina

2.5895

1522.1

0.1087

8022

117

28

14.   Irene

2.5896

1522.1

0.1627

18019

8648

98

111.   Ate

2.5927

1524.8

0.1053

10842

30613

457

151.   Abundantia

2.5932

1525.3

0.0356

17355

3848

630

56.   Melete

2.6010

1532.2

0.2340

29450

1941

82

132.   Æthra

2.6025

1533.5

0.3799

15224

2602

250

214.   Aschera

2.6111

1541.1

0.0316

11555

34230

327

70.   Panopea

2.6139

1543.6

0.1826

29949

4818

1138

194.   Procne

2.6159

1545.4

0.2383

31933

15919

1824

53.   Calypso

2.6175

1546.8

0.2060

9252

14358

57

78.   Diana

2.6194

1548.5

0.2088

12142

33358

840

124.   Alceste

2.6297

1557.6

0.0784

24542

18826

256

23.   Thalia

2.6306

1558.4

0.2299

12358

6745

1014

164.   Eva

2.6314

1559.1

0.3471

35932

7728

2425

15.   Eunomia

2.6437

1570.0

0.1872

2752

18826

256

37.   Fides

2.6440

1570.3

0.1758

6626

821

37

66.   Maia

2.6454

1571.6

0.1750

488

817

36

224.   Oceana

2.6465

1572.6

0.0455

27051

35318

552

253.   Mathilde

2.6469

1572.9

0.2620

33339

1803

637

50.   Virginia

2.6520

1577.4

0.2852

109

17345

248

144.   Vibilia

2.6530

1578.4

0.2348

79

7647

448

85.   Io

2.6539

1579.2

0.1911

32235

20356

1153

26.   Proserpine

2.6561

1581.1

0.0873

23625

4555

336

233.   Asterope

2.6596

1584.3

0.1010

34436

22225

739

102.   Miriam

2.6619

1586.3

0.3035

35439

21158

54

240.   Vanadis

2.6638

1588.0

0.2056

5153

11454

26

73.   Clytie

2.6652

1589.3

0.0419

5755

751

224

218.   Bianca

2.6653

1589.3

0.1155

23014

17050

1513

141.   Lumen

2.6666

1590.5

0.2115

1343

3197

1157

77.   Frigga

2.6680

1591.8

0.1318

5847

20

228

3.   Juno

2.6683

1592.0

0.2579

5450

17053

131

97.   Clotho

2.6708

1594.3

0.2550

6532

16037

1146

75.   Eurydice

2.6720

1595.3

0.3060

33533

35956

51

145.   Adeona

2.6724

1595.4

0.1406

11753

7741

1238

204.   Callisto

2.6732

1596.4

0.1752

25745

20540

819

114.   Cassandra

2.6758

1598.8

0.1401

1536

16424

455

201.   Penelope

2.6764

1599.3

0.1818

33421

1575

544

64.   Angelina

2.6816

1603.9

0.1271

12536

3114

119

98.   Ianthe

2.6847

1606.7

0.1920

14852

3547

1532

34.   Circe

2.6864

1608.3

0.1073

14841

18446

527

123.   Brunhilda

2.6918

1613.2

0.1150

7257

30828

627

166.   Rhodope

2.6927

1613.9

0.2140

3051

12933

122

109.   Felicitas

2.6950

1616.0

0.3002

561

456

83

246.   Asporina

2.6994

1619.9

0.1065

25554

16235

1539

58.   Concordia

2.7004

1620.8

0.0426

18910

16120

52

103.   Hera

2.7014

1621.8

0.0803

3213

13618

524

54.   Alexandra

2.7095

1629.1

0.2000

29539

31345

1147

226.   Weringia

2.7118

1631.2

0.2048

28446

13518

1550

59.   Olympia

2.7124

1631.7

0.1189

1733

17026

837

146.   Lucina

2.7189

1637.5

0.0655

22734

8416

136

45.   Eugenia

2.7205

1639.0

0.0811

2325

14757

635

210.   Isabella

2.7235

1641.7

0.1220

4422

3258

518

187.   Lamberta

2.7272

1645.0

0.2391

2144

2213

1043

180.   Garumna

2.7286

1646.3

0.1722

12556

31442

054

160.   Una

2.7287

1646.4

0.0624

5557

922

351

140.   Siwa

2.7316

1649.0

0.2160

30033

1072

312

110.   Lydia

2.7327

1650.0

0.0770

33649

5710

60

185.   Eunice

2.7372

1654.1

0.1292

1632

15350

2317

203.   Pompeia

2.7376

1654.5

0.0588

4251

34837

313

200.   Dynamene

2.7378

1654.6

0.1335

4638

32526

656

197.   Arete

2.7390

1655.8

0.1621

32451

826

848

206.   Hersilia

2.7399

1656.5

0.0389

9544

14516

346

255.   Oppavia

2.7402

1656.6

0.0728

16915

146

933

247.   Eukrate

2.7412

1657.7

0.2387

5344

020

257

38.   Leda

2.7432

1659.6

0.1531

10120

29627

657

125.   Liberatrix

2.7437

1660.0

0.0798

27329

16935

438

173.   Ino

2.7446

1660.8

0.2047

1328

14834

1415

36.   Atalanta

2.7452

1661.3

0.3023

4244

35914

1842

128.   Nemesis

2.7514

1666.9

0.1257

1634

7631

616

93.   Minerva

2.7537

1669.0

0.1405

27444

54

837

127.   Johanna

2.7550

1670.3

0.0659

12237

3146

817

71.   Niobe

2.7558

1671.0

0.1732

22117

31630

2319

213.   Lilæa

2.7563

1671.4

0.1437

2814

12217

647

55.   Pandora

2.7604

1675.1

0.1429

1036

1056

714

237.   Cœlestina

2.7607

1675.5

0.0738

28249

8433

946

143.   Adria

2.7619

1676.6

0.0729

22227

33342

1130

82.   Alcmene

2.7620

1676.6

0.2228

13145

2657

251

116.   Sirona

2.7669

1681.1

0.1433

15247

6426

335

1.   Ceres

2.7673

1681.4

0.0763

14938

8047

1037

88.   Thisbe

2.7673

1681.5

0.1632

30834

27754

1611

215.   Œnone

2.7679

1682.0

0.0390

34624

2525

144

2.   Pallas

2.7680

1682.1

0.2408

12212

17245

3444

39.   Lætitia

2.7680

1682.1

0.1142

38

15715

1022

41.   Daphne

2.7688

1682.8

0.2674

22033

1798

1558

177.   Irma

2.7695

1683.5

0.2370

226

34917

127

148.   Gallia

2.7710

1684.8

0.1855

367

14513

2521

267.   Tirza

2.7742

1687.6

0.0986

2645

7359

62

74.   Galatea

2.7770

1690.3

0.2392

818

19751

40

205.   Martha

2.7771

1690.4

0.1752

2154

21212

1040

139.   Juewa

2.7793

1692.4

0.1773

16434

221

1057

28.   Bellona

2.7797

1692.7

0.1491

1241

14437

922

68.   Leto

2.7805

1693.5

0.1883

34514

451

758

216.   Cleopatra

2.7964

1708.0

0.2492

32815

21549

132

99.   Dike

2.7966

1708.3

0.2384

24036

4144

1353

236.   Honoria

2.7993

1710.7

0.1893

35659

18627

737

183.   Istria

2.8024

1713.4

0.3530

450

14246

2633

266.   Aline

2.8078

1718.5

0.1573

2352

23618

1320

188.   Menippe

2.8211

1730.7

0.2173

30938

24144

1121

167.   Urda

2.8533

1760.4

0.0340

2964

16628

211

81.   Terpsichore

2.8580

1764.8

0.2080

491

225

755

174.   Phædra

2.8600

1766.6

0.1492

25312

32849

129

243.   Ida

2.8610

1767.5

0.0419

7122

32621

110

242.   Kriemhild

2.8623

1768.7

0.1219

1231

20757

1117

129.   Antigone

2.8678

1773.9

0.2126

2424

13737

1210

217.   Eudora

2.8690

1774.9

0.3068

31441

16410

1019

158.   Coronis

2.8714

1777.2

0.0545

5656

28130

10

33.   Polyhymnia

2.8751

1780.7

0.3349

34259

919

156

195.   Euryclea

2.8790

1784.2

0.0471

11548

757

71

235.   Caroline

2.8795

1784.7

0.0595

26829

6635

94

47.   Aglaia

2.8819

1786.9

0.1317

31240

4020

51

208.   Lachrymosa

2.8926

1796.9

0.0149

12752

543

148

191.   Kolga

2.8967

1800.8

0.0876

2321

15947

1129

22.   Calliope

2.9090

1801.0

0.0193

6243

447

145

155.   Scylla

2.9127

1815.7

0.2559

821

4252

144

238.   Hypatia

2.9163

1819.0

0.0946

3218

18426

1228

231.   Vindobona

2.9192

1821.7

0.1537

25323

35249

510

16.   Psyche

2.9210

1823.4

0.1392

159

15036

34

179.   Clytemnestra

2.9711

1870.6

0.1133

35539

25313

747

239.   Adrastea

2.9736

1873.0

0.2279

261

18134

64

69.   Hesperia

2.9779

1877.0

0.1712

10819

18712

828

150.   Nuwa

2.9785

1877.5

0.1307

35527

20735

29

61.   Danaë

2.9855

1884.2

0.1615

3444

33411

1814

117.   Lomia

2.9907

1889.1

0.0229

4846

34939

1458

35.   Leucothea

2.9923

1890.6

0.2237

20225

35549

812

263.   Dresda

3.0120

1909.3

0.3051

30849

21756

127

221.   Eos

3.0134

1910.7

0.1028

33058

14235

1051

162.   Laurentia

3.0241

1920.8

0.1726

14552

3815

64

156.   Xantippe

3.0375

1933.7

0.2637

15558

24611

729

241.   Germania

3.0381

1934.0

0.1013

3407

27228

530

256.   Walpurga

3.0450

1940.8

0.1180

24017

18335

1244

211.   Isolda

3.0464

1942.2

0.1541

7412

26529

351

96.   Ægle

3.0497

1945.3

0.1405

16310

32250

167

257.   Silesia

3.0572

1952.5

0.2555

5416

3431

441

133.   Cyrene

3.0578

1953.0

0.1398

24713

3218

714

95.   Arethusa

3.0712

1965.9

0.1447

3258

24417

1254

202.   Chryseis

3.0777

1972.1

0.0959

12946

13747

848

268.   ——

3.0852

1973.9

0.1285

18448

12153

225

100.   Hecate

3.0904

1984.3

0.1639

3083

12812

623

49.   Pales

3.0908

1984.7

0.2330

3115

29040

38

223.   Rosa

3.0940

1987.9

0.1186

10248

490

159

52.   Europa

3.0955

1988.0

0.1098

10657

12940

727

245.   Vera

3.0985

1992.1

0.1950

2529

6237

510

86.   Semele

3.1015

1995.1

0.2193

2910

8745

447

159.   Æmilia

3.1089

2002.2

0.1034

10122

1359

64

48.   Doris

3.1127

2005.9

0.0649

7033

18455

631

196.   Philomela

3.1137

2006.8

0.0118

30919

7324

716

130.   Electra

3.1145

2007.7

0.2132

2034

1466

2257

212.   Medea

3.1157

2008.8

0.1013

5618

31516

416

120.   Lachesis

3.1211

2014.0

0.0475

2140

34251

71

181.   Eucharis

3.1226

2015.4

0.2205

9525

14445

1838

62.   Erato

3.1241

2016.9

0.1756

390

12546

212

222.   Lucia

3.1263

2019.0

0.1453

2582

8011

211

137.   Melibœa

3.1264

2019.1

0.2074

30758

20422

1322

165.   Loreley

3.1269

2019.6

0.0734

22350

3046

1012

251.   Sophia

3.1315

2024.1

0.1243

777

1576

1020

24.   Themis

3.1357

2028.1

0.1242

1448

3549

049

152.   Atala

3.1362

2028.6

0.0862

8423

4129

1212

10.   Hygeia

3.1366

2029.1

0.1156

2372

28538

349

259.   Aletheia

3.1369

2029.3

0.1176

24145

8832

1040

227.   Philosophia

3.1393

2031.6

0.2131

22623

33052

916

147.   Protogenea

3.1393

2031.6

0.0247

2538

25116

154

171.   Ophelia

3.1432

2035.4

0.1168

14359

10110

234

209.   Dido

3.1436

2035.9

0.0637

25733

20

715

31.   Euphrosyne

3.1468

2039.0

0.2228

9326

3131

2627

90.   Antiope

3.1475

2039.7

0.1645

30115

7129

217

104.   Clymene

3.1507

2042.7

0.1579

5932

4332

254

57.   Mnemosyne

3.1510

2043.0

0.1145

5325

2002

1512

250.   Bettina

3.1524

2044.3

0.1302

8728

2612

1254

252.   Clementina

3.1552

2047.1

0.0837

3558

20819

102

94.   Aurora

3.1602

2052.0

0.0827

4846

49

84

106.   Dione

3.1670

2058.6

0.1788

2557

6314

438

199.   Byblis

3.1777

2069.0

0.1687

26120

8952

1522

92.   Undina

3.1851

2076.3

0.1024

33127

10252

957

184.   Deiopea

3.1883

2079.4

0.0725

16922

33618

112

176.   Idunna

3.1906

2081.6

0.1641

2034

20113

2231

154.   Bertha

3.1976

2088.5

0.0788

19047

3735

2059

108.   Hecuba

3.2113

2101.0

0.1005

17349

35217

424

122.   Gerda

3.2177

2108.2

0.0415

20345

17843

136

168.   Sibylla

3.3765

2266.2

0.0707

1126

20947

433

225.   Henrietta

3.4007

2277.8

0.2661

29913

20045

2045

229.   Adelinda

3.4129

2302.9

0.1562

3327

3049

211

76.   Freia

3.4140

2304.1

0.1700

9049

2125

23

260.   Huberta

3.4212

2311.5

0.1113

31322

16848

618

65.   Maximiliana

3.4270

2317.2

0.1097

26036

15850

329

121.   Hermione

3.4535

2344.2

0.1255

35750

7646

736

87.   Sylvia

3.4833

2374.5

0.0922

33348

7549

1055

107.   Camilla

3.4847

2376.0

0.0756

11553

17618

954

175.   Andromache

3.5071

2399.0

0.3476

2930

2335

346

190.   Ismene

3.9471

2864.3

0.1634

10539

1770

67

153.   Hilda

3.9523

2869.9

0.1721

28547

22820

755

[Pg 35]

[Pg 36]

PART II.

DISCUSSION OF THE FACTS IN TABLE II.

1. Extent of the Zone.

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

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

2. The Small Mass of the Asteroids.

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

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

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

3. The Limits of Perihelion Distance.

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

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

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

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

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

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

COMMENSURABILITY OF PERIODS.

When we say that an asteroid's period is commensurable with that of Jupiter, we mean that a certain whole number of the former is equal to another whole number of the latter. For instance, if a minor planet completes two revolutions to Jupiter's one, or five to Jupiter's two, the periods are commensurable. It must be remarked, however, that Jupiter's effectiveness in disturbing the motion of a minor planet depends on the order of commensurability. Thus, if the ratio of the less to the greater period is expressed by the fraction 1⁄2, where the difference between the numerator and the denominator is one, the commensurability is of the first order; 1⁄3 is of the second; 2⁄5, of the third, etc. The difference between the terms of the ratio indicates the frequency of conjunctions while Jupiter is completing the number of revolutions expressed by the numerator. The distance 3.277, corresponding to the ratio 1⁄2, is the only case of the first order in the entire ring; those of the second order, answering to 1⁄3 and 3⁄5, are 2.50 and 3.70. These orders of commensurability may be thus arranged in a tabular form, the radius of the earth's orbit being the unit of distance:

Order.

Ratio.

Distance.

First

1⁄2

3.277

Second

1⁄3, 3⁄5

⎧

⎨

⎩2.50

3.70

Third

2⁄5, 4⁄7, 5⁄8

⎧

⎨

⎩2.82

3.58

3.80

Fourth

3⁄7, 5⁄9, 7⁄11

⎧

⎨

⎩2.95

3.51

3.85

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

I.—The Distance 3.277.

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

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

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

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

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

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

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

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

The nine cases considered are the only ones in which the conjunctions with Jupiter would occur at less than five points of an asteroid's orbit. Higher orders of commensurability may perhaps be neglected. It will be seen, however, that the distances 2.25, 2.70, 3.03, and 3.23, corresponding to the ratios of the fifth order, 2⁄7, 3⁄8, 4⁄9, and 6/11, still afford traces of Jupiter's influence. The first is in the interval between Augusta and Feronia; the last falls in the same gap with 3.277; and the second and third are in breaks less distinctly marked. It may also be worthy of notice that the rather wide interval between Prymno and Victoria is where ten periods of a minor planet would be equal to three of Jupiter. The distance of Medusa is somewhat uncertain.

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

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

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

5. Relations between certain Adjacent Orbits.

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

6. The Eccentricities.

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

The

eccentricity

of

Philomela = 0.01

"

"

"

Æthra = 0.38

"

"

"

Comet II. 1867 (ret. in 1885) = 0.41

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

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

7. The Inclinations.

The inclinations in Table II. are thus distributed:

From

0° to

4°

70

"

4° to

8°

83

"

8° to

12°

59

"

12° to

16°

32

"

16° to

20°

8

"

20° to

24°

8

"

24° to

28°

7

"

28° to

32°

0

above 32°

1

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

Asteroid.

Inclination.

Eccentricity.

Pallas

34°42  ´

0.238

Istria

2630

0.353

Euphrosyne

2629

0.228

Anna

2524

0.263

Gallia

2521

0.185

Æthra

250

0.380

Eukrate

2457

0.236

Eva

2425

0.347

Niobe

2319

0.173

Eunice

2317

0.129

Electra

2255

0.208

Idunna

2231

0.164

Phocea

2135

0.255

Artemis

2131

0.175

Bertha

2059

0.085

Henrietta

2047

0.260

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

8. Longitudes of the Perihelia.

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

9. Distribution of the Ascending Nodes.

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

I.

From

310° to

10°,

containing

61

ascending

nodes.

II.

"

120° to

180°,

"

59

"

"

Making in 120°

120

"

"

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

10. The Periods.

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

Between

1100

and

1200

days

6

periods.

"

1200

"

1300

"

7

"

"

1300

"

1400

"

43

"

"

1400

"

1500

"

13

"

"

1500

"

1600

"

46

"

"

1600

"

1700

"

54

"

"

1700

"

1800

"

20

"

"

1800

"

1900

"

13

"

"

1900

"

2000

"

19

"

"

2000

"

2100

"

33

"

"

2100

"

2200

"

2

"

"

2200

"

2300

"

2

"

"

2300

"

2400

"

8

"

"

2400

"

2800

"

0

"

"

2800

"

2900

"

2

"

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

11. Origin of the Asteroids.

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

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

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

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

12. Variability of Certain Asteroids.

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

13. The Average Asteroid Orbit.

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

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

Harrington.

Svedstrup.

Longitude of perihelion

14°39  ´

101°48  ´

Longitude of ascending node

11356

13327

Inclination

10

66

Eccentricity

0.0448

0.0281

Mean distance

2.7010

2.6435

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

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

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

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

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

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

[Pg 58]

[Pg 59]

APPENDIX.

NOTE A.

THE POSSIBLE EXISTENCE OF ASTEROIDS IN UNDISCOVERED RINGS.

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

NOTE B.

THE ORIGIN AND STRUCTURE OF COSMICAL RINGS.

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

I.

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

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

See Payne's Sidereal Messenger, April, 1885.

II.

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

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

THE END.

FOOTNOTES:

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

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

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

[4] Monthly Notices, vol. xxvii.

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

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

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

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

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

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

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

[12] Annuaire, 1886.

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Table of Contents

The Project Gutenberg eBook of The Asteroids; Or Minor Planets Between Mars and Jupiter., by Daniel Kirkwood

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)

THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER.

PREFACE.

CONTENTS.

PART I.

THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER.

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

2. Discovery of the First Asteroids.

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

3. Remarks on Table I.

4. Mode of Discovery.

NAMES AND SYMBOLS.

5. Magnitudes of the Asteroids.

6. The Orbits of the Asteroids.

TABLE II. Elements of the Asteroids.

PART II.

DISCUSSION OF THE FACTS IN TABLE II.

1. Extent of the Zone.

2. The Small Mass of the Asteroids.

3. The Limits of Perihelion Distance.

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

COMMENSURABILITY OF PERIODS.

5. Relations between certain Adjacent Orbits.

6. The Eccentricities.

7. The Inclinations.

8. Longitudes of the Perihelia.

9. Distribution of the Ascending Nodes.

10. The Periods.

11. Origin of the Asteroids.

12. Variability of Certain Asteroids.

13. The Average Asteroid Orbit.

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

APPENDIX.

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

NOTE B. THE ORIGIN AND STRUCTURE OF COSMICAL RINGS.

I.

II.

THE END.

FOOTNOTES:

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