JANDAEY 19, 1900.] 



SCmNGE. 



85 



A question of intense interest to astron- 

 omers in the early part of the century is 

 that of the stability of the solar system. 

 Lagrange, Laplace, and Poisson thought 

 they had demonstrated that, whatever may 

 have been the origin of this system, the 

 existing order of events will go on indef- 

 initely. This conclusion seems to have 

 been alike satisfactory to scientific and 

 unscientific men. But with the growth of 

 the doctrine of energy and with the devel- 

 opments of thermodynamics, it has come to 

 appear highly probable that the solar sys- 

 tem has not only gone through a long series 

 of changes in the past, but is destined to 

 undergo a similarly long series of vicissi- 

 tudes in the future. In other words, while 

 our predecessors of a century ago thought 

 the 'system of the world' stable, our contem- 

 poraries are forced to consider it unstable.* 



But interesting as this question of sta- 

 bility still is, there is no pressing necessity, 

 fortunately, for a determination of the ul- 

 terior fate of our planet. A more impor- 

 tant question lies close at hand, and merits, 

 it seems to me, immediate and serious in- 

 vestigation. This question is the funda- 

 mental one whether the beautifully simple 

 law of Newtonian attraction is exact or 

 only approximate. No one familiar with 

 celestial mechanics or with the evidence for 

 the law of gravitation as marshalled by 

 Laplace in his ' Systeme du Monde ' can fail 

 to appreciate the reasons for the profound 

 conviction, long held by astronomers, that 



Dr. S. C. Chandler and was announced in the Astro- 

 nomical Journal, No. 248, November, 1891. For the 

 mathematical theory of this subject and for titles of 

 the principal publications bearing on this theory, refer- 

 ence may be made to the author's paper on ' Mechan- 

 ical interpretation of variations of latitudes,' Astro- 

 nomical Journal, No. 345, May, 1895 ; and to a paper 

 by S. S. Hough on ' The rotation of an elastic 

 spheroid,' Philosophical Transactions, No. 187, 1896. 

 *See a review of this subject by M. H. Poincare, 

 "Sur la stability du systeme solaire, " in Annuaire du 

 Bureau des Longiiudes, for 1898. 



this law is exact. But on the other hand 

 no one acquainted with the obstinate 

 properties of matter can now be satisfied 

 with the Newtonian law until it is proved 

 to hold true to a much higher degree of 

 approximation than has been attained 

 hitherto.* For, in spite of the superb ex- 

 perimental investigations made particularly 

 during the past quarter of a century by 

 Cornu and Baille,t PoyntiDg,;|; Boys,§ Rich- 

 arz and Krigar-Menzel,|| and Braun,^ it 

 must be said that the gravitation constant 

 is uncertain by some units in the fourth 

 significant figure, and possibly by one or 

 two units even in the third figure ;** thus 

 falling, along with the sun's parallax, the 

 annual stellar abeiTation, and the moon's 

 mass, amongst the least well determined 

 constants of the solar system. Here then 

 is a fruitful field for research. The direct 

 measurement of the gravitation constant to 

 a much higher degree of precision seems to 



*As to the degree of precision with which the New- 

 tonian law is established by astronomical data, see 

 Professor Newcomb's "Elements of the four inner 

 planets and the fundamental constants of astronomy, ' ' 

 Supplement to American Ephemeris and Nautical 

 Almanac for 1897, "Washington, 1895. 

 ^ Comptes rendus, LXXVI., 1873. 

 JThe Mean Density of the Earth, by J. H. Poyn- 

 ting, Chas. Griffin & Co., London, 1894. 

 'i Philosojihical Transactions, No. 186, 1895. 

 li Sitzungsberichte, Berlin Academy, Band 2, 1896. 

 \ Denkschriften, Math. Natur. Classe, Vienna 

 Academy, Band LXIV., 1897. 



** The results of the investigators mentioned for 

 the gravitation constant are, in C. G. S. units, as fol- 

 lows, the first result having been computed from data 

 given by MM. Cornu and Bailie in the publication 

 referred to : 



Cornu and Bailie (1873) 6668X10-" 



Poynting (1894) 6698X10-" 



Boys (1894) 6657X10-" 



Richarzand Krigar-Menzel (1896) 6685 X10-" 



Braun (1897) 6658X10"" 



Regarding these as of equal weight, their mean is 

 6673 X 10 - " with a probable error of =t 5 units in 

 the fourth place, or l/1330th part. This is of about 

 the same order of precision as that deduced by Pro- 

 fessor Newcomb from astronomical data. 



