SEQUEL TO THE EPOCH OF N*EWTON. 233 



and the strength of Euler, D'Alembert, Lagrange, 

 and Laplace, was for a time foiled by this difficulty. 

 At length, in 1787, Laplace announced to the Aca- 

 demy that he had discovered the true cause of this 

 acceleration, and that it arose from the action of 

 the sun upon the moon, combined with the secular 

 variation of the eccentricity of the earth's orbit. 

 It was found that the effects of this combination 

 would exactly account for the changes which had 

 hitherto so perplexed mathematicians. A very re- 

 markable result of this investigation was, that 

 " this Secular Inequality of the motion of the moon 

 is periodical, but it requires millions of years to 

 re-establish itself;" so that after an almost incon- 

 ceivable time, the acceleration will become a re- 

 tardation. Laplace some time after (in 1797,) 

 announced other discoveries relative to the secu- 

 lar motions of the apogee and the nodes of the 

 moon's orbit. Laplace collected these researches 

 in his " Theory of the Moon," which he published 

 in the third volume of the Mecanique Celeste in 

 1802. 



A similar case occurred with regard to an acce- 

 leration of Jupiter's mean motion, and a retardation 

 of Saturn's, which had been observed by Cassini, 

 Maraldi, and Horrox. After several imperfect at- 

 tempts by other mathematicians, Laplace in 1787 

 found that there resulted from the mutual attrac- 

 tion of these two planets a great Inequality, of 

 which the period is 929 years and a half, and which 



