326 ef 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. 
