326 LAPLACE. 



jects, are no luxury of erudition. The memoir in which 

 Laplace communicated his results on the invariability of 

 the mean motions or mean distances, is dated 1773.* It 

 was in 1784 only, that he established the stability of the 

 other elements of the system from the smallness of the 

 planetary masses, the inconsiderable eccentricity of the 

 orbits, and the revolution of the planets in one common 

 direction around the sun. 



The discovery of which I have just given an account 

 to the reader excluded at least from the solar system the 

 idea of the Newtonian attraction being a cause of dis- 

 order. But might not other forces, by combining with 

 attraction, produce gradually increasing perturbations as 

 Newton and Euler dreaded ? Facts of a positive nature 

 seemed to justify these fears. 



A comparison of ancient with modern observations re- 

 vealed the existence of a continual acceleration of the 

 mean motions of the moon and the planet Jupiter, and an 



* Laplace was originally led to consider the subject of the pertur- 

 bations of the mean motions of the planets by his researches on the 

 theory of Jupiter and Saturn. Having computed the numerical value 

 of the secular inequality affecting the mean motion of each of those 

 planets, neglecting the terms of the fourth and higher orders relative 

 to the eccentricities and inclinations, he found it to be so small that it 

 might be regarded as totally insensible. Justly suspecting that this 

 circumstance was not attributable to the particular values of the ele- 

 ments of Jupiter and Saturn, he investigated the expression for the 

 secular perturbation of the mean motion by a general analysis, neglect- 

 ing, as before, the fourth and higher powers of the eccentricities and 

 inclinations, and he found in this case, that the terms which were 

 retained in the investigation absolutely destroyed each other, so that 

 the expression was reduced to zero. In a memoir which he communi- 

 cated to the Berlin Academy of Sciences, in 1776, Lagrange first showed 

 that the mean distance (and consequently the mean motion) was not 

 affected by any secular inequalities, no matter what were the eccen- 

 tricities or inclinations of the disturbing and disturbed planets. 

 Translator. 



