French National Institute. 231 



sion, and a mind capable of devising a shorter and more 

 certain road. 



Such are the qualifications which M. Poisson has dis- 

 played. By these means he has attained the interesting 

 theorem, that the products of the two dimensions of the 

 masses do not furnisii, in the surccssive integrations, any 

 term which gives a secular equation or an acceleration in 

 motion. This is enough even for astronomers; it is de- 

 monstrated that, if this acceleration exists, it can only de- 

 pend on terms of 4, 6, and 8, i. e. absolutely insensible 

 dimensions; which assures us of the stability of the plane- 

 tary system. The.question at present therefore offers no 

 real interest, if there be not an analytical difficulty to over- 

 come, which is still sufficient to excite the emulation of 

 geometricians. 



M. Poisson, in order to obtain his theorem, had only 

 pushed the approximation to -the terms affected of the 

 squares, or of the products of the masses : having regard 

 to the variation of the elements which M. Lagrange had 

 regarded as constant, he knew how to give to the terms 

 which form the second approximation, a disposition which 

 admitted of demonstrating that none of these terms can 

 give to the grand axis a term proportional to the time. The 

 terms which ought to proceed from the variations of the 

 elements of the perturbing planets escaped this analysis ; 

 but, by ingenious methods founded on a method of M. La 

 Place, M. Poisson has proved that these kinds of terms 

 cannot produce in the grand axis any variation which in- 

 creases as the time does. 



In geometry in particular, the route by which we attain 

 for the first time a difficult discovery is rarely the shortest 

 anTi most direct. There are propositions the truth of which 

 is apparent without our being able to demonstrate it : men 

 of science dread to involve themselves in innncnse calcula- 

 tions, the success of which is problematical, and sometimes 

 give up an inquiry which presents too many difficulties. 

 But if the truth has been ascertained, as success is from 

 that moment certain,, we take courage, and demonstrations 

 are simplified and multiplied: this is precisely what has 

 lianpencd. The instant M. Poisson had demonstrated his 

 theorem, Messrs. Lagrange and La I*laee perceived that it 

 flowed out of principles and mclhods which had been for- 

 merly explained. M. Poisson attained his discovery by a 

 calculation in which he made use of the known fornmlteof 

 the elliptic motion ; M. Lagrange ilioughl that it ought to 

 " 1' 4" " have 



