Dec. 13, 1888] 



NATURE 



63 



majority of the problems which arise in regard to the motions of 

 the solar system should liave their origin in an effort to confirm 

 that law. 



The first attempt to apply Newton's law to all the motions 

 of the solar system was made by Laplace. When, however, 

 Lindenau and Rouvard undertook to compute their tables of the 

 motions of the planets, a complete revision of Laplace's theory 

 was found necessary. So enormous is the labour involved, that 

 there exists, besides those mentioned, only one other coirplete 

 set of theories and tables of the motions of the principal planets 

 — that of Leverrier. Leverrier's tables of the inner planets are 

 now nearly thirty years old. His tables of the outer planets are 

 much later, having employed his attention almost to the day of 

 his death. His tables of Jupiter and Saturn were published in 

 1876, and those of Uranus and Neptune in the year following. 

 Xewcomb's tables of Neptune were published in 1865 ; those of 

 Uranus, in 1874. Hill's theorj- of Jupiter and Saturn, which 

 has for years occupied his attention, has at last been completed, 

 and he is now engaged in preparing tables therefrom. These 

 are intended to form a part of a complete series of tables of the 

 principal planets now being prepared under the direction of 

 Prof Newcomb at Washington. Another such series is a'so 

 being prepared by Prof. Gylden at Stockholm. 



The values of the coefficients of the terms of short period in 

 the motions of the principal planets are now pretty well known ; 

 and the same might be said of the secular variations, were it not 

 for the difference between theory and observation which exists 

 in regard to the ntotion of the perihelion of Mercury, which was 

 discovered by Leverrier, and has been confirmed by Newcomb, 

 in a discussion of the observations of the transits of Mercury 

 extending over a period of more than two centuries. The cause 

 of this difference still remains unknown. The completion and 

 comparison with observations of the new theory of the four 

 inner planets, now being prepared under the direction of Prof. 

 Newcomb, will be awaited with interest, with the hope that it 

 may throw new light on this interesting subject. 



The only recent original tables of the moon's motions are 

 those of Hansen. These, like Leverrier's tables of the inner 

 planets, are now more than thirty years old. These tables have 

 been compared with observations, and agree fairly well with 

 those made during the century preceding their publication, but 

 not with those made before or since that time. The theoretical 

 value of the acceleration of the moon's longitude is 6" ; that 

 found by Hansen from accounts of ancient total eclipses of the 

 sun, 12". Newcomb, however, considers these accounts as 

 unreliable, and, limhing himself to the Ptolemaic eclipses of the 

 "Almagest " and the Arabian eclipses of the " Table Hakemitc," 

 obtains the value 8" "3, or, from the Arabian eclipses alone, 7" 

 — a value but Httle greater than the theoretical value. Dr. 

 Ginzel, from an extended examination of accounts of ancient 

 and mediaeval total eclipses of the san, concludes that Hansen's 

 value requires a change of only a little over i". His solution, 

 however, in reality depends upon the ancient eclipses alone. 

 The only other theory of the moon comparable with Hansen's is 

 that of Delaunay. This theory, however, is limited to a deter- 

 mination of the inequalities in the motion of the moon due to 

 the action of the sun, on the hypothesis that the orbit of the 

 earth is a pure ellipse, and differs from that of Han-en in that 

 the inequalities determined are not expressed numerically, but 

 only symbolically in tenns of arbitrary constants. 



. While the coefficients of the inequalities upon which Hansen's 

 tables are based seem to be pretty well knmvn, I am not aware 

 that the tables themselves have been sufficiently checked, except 

 by comparison with observations. Apparently the great de- 

 sideratum now is a set of tables computed from Delaunay's 

 theory in a completed form, or computed in some other way 

 entirely independently of Hansen's. Until Hansen's tables are 

 thus checked, it is questionable whether it can be safely said 

 that the mclion of the moon cannot be completely accounted 

 for by the law of gravity. 



The detection of the two satellites of Mars by Prof. Hall may 

 be considered the most interesting recent achievement in pure 

 di>covery. It was not till the discovery of these satellites that a 

 means was offered for the accurate determination of the mass of 

 that planet. No satellites of \'enus and Mercury have as yet 

 been detected, and the values at present assumed for the masses 

 of those planets are very uncertain. 



In 1788, just one hundred years ago, Laplace published his 

 theory of Jupiter's satellites. This theory is still the basis of the 



tables now in use. Souillart's analytical theory of these satellites 

 appeared in 1881. The numerical theory. was completed only 

 within the last year, and the tables therefrom remain still to be 

 formed. 



Bessel made a careful investigation of the orbit of Titan ; but 

 the general theory of the Saturnian system which he commenced, 

 he did not live to finish. Our knowledge of the motions of 

 Saturn's satellites, with the exception of Titan, was very meagre 

 until the erection of the great equatorial at Washington. A 

 difficulty in the determination of a correct theory of the motions 

 of Saturn's satellites is the fact that there are a number of cases 

 of approximate commen-urability in the ratios of their mean 

 motions. The most interesting case is that of Hyperion, whose 

 mean motion is very nearly three-fourths that of Titan. In this 

 case there is the additional difficulty that theif distance from one 

 another is only about one-seventh as great at conjunction as at 

 opposition. 



Our knowledge of the motions of the satellites of Uranus and 

 Neptune depends almost entirely on the observations made at 

 Washington. Quite accurate determinations of the masses of 

 these two planets have been obtained. The large secular motion 

 of the plane of Neptune's satellite, to which M art h has called 

 attention, needs confirmation. . . 



The number of the asteroids, is so great that they have been 

 the frequent subject of statistical investigation. The systematic 

 grouping of the nodes and perihelia which exists was shown by 

 Newcomb -fo be the effect of perturbation. Glauser finds that 

 the grouping of the nsdes on the ecliptic is a result of a nearly 

 uniform distribution on the orbit of Jupiter. Prof Newton had 

 previously found that the mean plane of the asteroid orbits lies 

 nearer to the plane of Jupiter's orbit than to the orbit plane of 

 any individual asteroid. Eighty- five per cent, of the asteroids 

 hav« mean motions- greater than twice and less than three times 

 that of Jupiter ; and the mean motions of none approximate 

 closely either of these, the two simplest ratios possii le. The 

 next simplest ratios lie beyond the limits of the 7one ; that is, 

 there are no asteroids having mean motions nearly equal to or 

 less than one and a half times that of Jupiter, and none nearly 

 equal to or greater than four times that of Jupiter. The labour 

 of determining the general perturbations and computing tables of 

 an asteroid is as great as in the case of a major planet. It is 

 no wonder, therefore, that tables have been prepared for scarce 

 a dozen of these small bodies, and that these are already out of 

 date. 



Of well-known comets of short period, Encke's, which has 

 the shortest period of any, possesses the greatest interest to the 

 student of celestial motions, since it was from a discussion of the 

 orbit of this comet that Encke detected evidence of the existence 

 of a resisting medium which produces an acceleration in the 

 comet's mean motion. This acceleration has been confirmed by 

 the investigations of Von Asten and Backlund. The investiga- 

 tions of Oppolzer and Haerdtl indicate that there is an accelera- 

 tion also in the mean m tion of Winnecke's comet. 



We have thus glanced briefly at the present condition of our 

 knowledge of the motions of the principal bodies of the solar 

 system. Only four cases have been found in which we cannot 

 fully explain these motions, so far as known, by Newton's law 

 of gravity. The unexplained discordances are the motion of the 

 penhelion of Mercury, and the accelerations of the mean motions 

 of the moon and the two periodic comets just named. 



If we go beyond the solar system, we cannot tell whether 

 Newton's law does or does not apply without modification to all 

 parts of the universe. It is principally in the hope of answering 

 this question that double-star observations are carried on ; and, 

 in the case of the many binary systems already detected, 

 Newton's law is satisfied within the errors of observation. 

 Nevertheless, this evidence is purely negative, and its value, it 

 seems to me, not at all commensurate with the labour expended 

 upon it, unless it be in the case of such objects as Sirius, whose 

 observation may assist in the solution of the problem of irregular 

 so-called proper motion. The angles subtended are in general 

 so small that relatively large personal errors are unavoidable ; 

 so that, even though their motions be controlled by a law or 

 laws of gravity widely different from that of Newton, it is not 

 likely that such differences can be proved with any degree of 

 certainty. It is rather to the study of the proper motions of the 

 fixed stars and of the nebula;, and then only after a lapse of 

 hundreds and perhaps thousands of years, that we must look for 

 a solution of this question. 



