444 HISTORY OF PHYSICAL ASTRONOMY. 



Sect. 4. — Application of the Newtonian Theory to Secular Inequalities. 



Secular Inequalities in the motions of the heavenly bodies occur 

 in consequence of changes in the elements of the solar system, which 

 go on progressively from age to age. The example of such changes 

 which was first studied by astronomers, was the Acceleration of the 

 Moon's Mean Motion, discovered by Halley. The observed fact was, 

 that the moon now moves in a very small degree quicker than she did 

 in the earlier aires of the world. When this was ascertained, the vari- 

 ous hypotheses which appeared likely to account for the fact were re- 

 duced to calculation. The resistance of the medium in which the 

 heavenly bodies move was the most obvious of these hypotheses. An- 

 other, which was for some time dwelt upon by Laplace, was the suc- 

 cessive transmission of gravity, that is, the hypothesis that the gravity 

 of the earth takes a certain finite time to reach the moon. But noue 

 of these suppositions gave satisfactory conclusions ; 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 Acad- 

 emy 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 

 remarkable result of this investigation was, that " this Secular Inequal- 

 ity of the motion of the moon is periodical, but it requires millions of 

 years to re-establish itself;" so that after an almost inconceivable time, 

 the acceleration will become a retardation. Laplace some time after 

 (in 1797), announced other discoveries relative to the secular 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 acceleration of Jupiter's 

 mean motion, and a retardation of Saturn's, w T hich had been observed 

 by Cassiui, Maraldi, and Horrox. After several imperfect attempts 

 by other mathematicians, Laplace, in 1787, found that there resulted 

 from the mutual attraction of these two planets a great Inequality, 

 of which the period is 929 years and a half, and which has acceler- 

 ated Jupiter and retarded Saturn ever since the restoration of as- 

 tronomy. 



