HENRI POINCARE NORDMANN. 751 



other branch of natural philosophy which provides to the meditation 

 or to esthetic revery such grandeur. Astronomy is the mother of all 

 the sciences and it is still today the most advanced, that in which we 

 can best predict the future. 



The study of the stability of our universe has been for two centuries 

 the fundamental problem of celestial mechanics for the solution of 

 which the genius of mathematicians has striven. This portion of 

 space wherein we are placed, the solar system, is it stable? WiU 

 those planets which we have observed from time immemorial con- 

 tinue to describe invariably the same immense orbits with only a few 

 periodic oscillations from their mean positions, will they continue 

 thus indefinitely in the future? Or wUl this machine so harmo- 

 niously contrived, and wherein We at present see no apparent sign of 

 possible destruction, never become imstable and disappear some day ? 

 That is the problem. 



When Newton demonstrated that gravity acted not only between 

 the sun and the planets but also between the planets themselves, it 

 was seen that there must result irregularities in the harmony of the 

 solar system, that the reciprocal attraction of the planets must 

 slightly deform the perfect ellipses which the attraction of the sun 

 alone would have made them describe. Truly these deformations are 

 small because of the smallness of the masses of the planets compared 

 with the central smn (Jupiter's mass is 300 times that of the earth but 

 only one one-thousandth that of the sun). But might not these 

 planetary pertm-bations, accumulating thi-ough centuries the effects 

 already observable in the time of Newton, finally destroy the Kepler 

 elhpses ? At any rate, the simple harmony of the world of Kepler no 

 longer is real. Newton, strongly embarrassed by the foresight of the 

 impending catastrophe, has made, in his optics, this allusion to the 

 planetary inequaUties, "which probably," he says, ''will become so 

 great in the long course of time that finally the system will have to be 

 put in order by its Creator." 



In 1772 Laplace believed he was able to demonstrate that these 

 fears were groundless. He showed that the secular inequalities of 

 the planetary elements compensated themselves periodically at the 

 end of a sufficiently long period and the terms of the first order of the 

 perturbations would disappear in the calculations. That implies a 

 stability of our system at least for a very long time, thousands of 

 secular periods. Consequently, Laplace criticized the deus ex 

 machina invoked by Newton and somewhat haughtily believed he 

 could affirm, arguing from his results, that the macliincry of our 

 world had had no need of the initial fillip and that it would go ahead 

 indefinitely without the need of outside assistance. Is it necessary to 

 note that there must be some fault in logic on the part of one who 

 could suppose that when the solar system had so beautifully evolved 



