S30 French National InsLilute^ 



In order to give an idea of the three memoirs which we 

 are about to mention, it is necessary to recur to a remote 

 aera in the historv oh science. 



Astronomers had jemarkcd a sensible acceleration in the 

 course of the moon : the other planets and the eaith might 

 consequently have a similar ahhough less rapid acceleration 

 in their motions. This question may perhaps appear indiffe- 

 rent to those who are not auare of its consequences. If the 

 earth be accelerated, it must be owing to its closer approach 

 to the centre of motion ; and if so, will it not end by being 

 precipitated on the sun ? This danger to be sure is far di- 

 stant. If this acceleration existed, it would be prodigiously 

 slow, and it would not be until after an almost infinite num- 

 ber of centuries that the catastrophe could happen, suppos- 

 ing it to be possible ; for it is proved by the example of the 

 moon, tha,t the acceleration only lasts a certain time, and af- 

 terwards becomes slower: but although future generations 

 have nothing to fear from this event, and if the planet, after 

 coming closer to the sun, afterwards removes from it, it 

 must nevertheless be confessed that the question is not less 

 important: it peculiarly interests those astronomers who 

 suppose, in all their calculations, an invariability of the 

 ellipses described by the planets. 



M. La Place was the first who examined this question. 

 By alearned but simply approximative calculation he attained 

 this result, ascertaining that the axes and mean movements 

 are in reality invariable, at least when we consider them as 

 the first powers of the masses only, and the second of the 

 eccentricities and inclinations ; which is already sufficient 

 for tranquillizing astronomers with regard to the fate of our 

 planet, or rather vvirh regard to their tables. 



M. Lagrange, struck with this conclusion, endeavoured 

 to extend it ; and by a curious theorem he proved the pro- 

 position to be correct, even on considering all the succes- 

 sive powers of the ecceiitricities ; but, in connnon with 

 M. La Place, he had only considered in the masses the 

 terms of a single dimension. 



Could the terms of the two dimensions produce an ac- 

 celeration ? It would, indeed, be much slower ; but the 

 question deserved examination, and this was undertaken by 

 M. Poisson. The calculation was uninviting on account 

 of its length; it required all the resources of analysis, and 

 the knowledge of all the laws of tiie celestial motions : it 

 required a peculiar degree of attention, and a penetrating, 

 eye, which at the first glance should be able to perceive 

 all the forms thai could be assumed by a complex expres- 

 sion. 



