142 LAPLACE. 



Although the iuvariabilrty of the mean distances of the planetary 

 orbits has been more completely demonstrated since the appearance of 

 the memoir above referred to, that is to say, by pushing the analytical 

 approximations to a greater extent, it will, notwithstanding, always 

 constitute one of the admirable discoveries of the author of the Meca- 

 niqne Celeste. Dates, in the case of such subjects, are no luxury of eru- 

 dition. The memoir in which Laplace communicated his results on the 

 invariability of the mean motions or mean distances is dated 1773.* It 

 w'as in 1784 only that he established the stability of the other elements 

 of the system from the smallness of the planetary masses, the incon- 

 siderable eccentricity of the orbits, and the revolution of the planets 

 in one common direction around the sun. 



The discovery of "whicli 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 disorder; 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 revealed the ex- 

 istence of a continued acceleration of the mean motions of the moon 

 and the planet Jupiter, and an equally striking diminution of the mean 

 motion of Saturn. These variations led to conclusions of the most 

 singular nature. 



In accordance with the presumed cause of these perturbations, to say 

 that the velocity of a body increased from century- to century, was equiv- 

 alent to asserting that the body coutinuall}' approached the center of 

 motion. On the other hand, when the velocity diminished the body 

 must be receding from the center. 



Thus, by a strange arrangement of nature, our planetary system 

 seemed destined to lose Saturn, its most mysterious ornament, to see 

 the planet, accompanied by its ring and seven satellites, plunge gradually 



pended. In this way he found the limitinj^ values of the eccentricity aud inclination for 

 the orbit of each of the principal planets of the system. The results obtained by that great 

 geometer have been mainly confirmed by the recent researches of Lo Verrier on tlie same 

 subject. (Connaissance des Temps, 1843.) — TRANSLATOR. 



* Laplace was originally led to consider the subject of the perturbations of the mean mo- 

 tions of the planets by liis researches on thetheory of Jupiter and Saturn. Having computed 

 the numerical value of the secular inequality afiecting the mean motion of each of those 

 plants, neglecting the terms of the fourth aud higher orders relative to the eccentricities aud 

 inclinations, lie found it to bo so small that it might be regarded as totally insensible. 

 Justly suspecting that this circumstance was not attributable to the particular values of the 

 elements of Jupiter and Saturn, he investigated the expression for the secular perturbation 

 of the mean motion by a general analysis, neglecting, as before, the fourth and higher 

 powers of the eccentricities and inclinations, aud 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 communicated to the Berlin Academy of Sci- 

 ences, in 1776, Lagrange first showed that the mean distance (aud consequently the mean 

 motion) was not atfected by any secular inequalities, no matter what were the eccentricities 

 or inclinations of the disturbing and disturbed planets. — Translator. 



