INEQUALITY OF JUPITER AND SA.TURX. 329 



moon around the earth is connected with the form of the 

 ellipse which the earth describes around the sun ; that a 

 diminution of the eccentricity of the ellipse inevitably in- 

 duces an increase in the velocity of our satellite, and vice 

 versa ; finally, that this cause suffices to explain the nu- 

 merical value of the acceleration which the mean motion 

 of the moon has experienced from the earliest ages down 

 to the present time.* 



The origin of the inequalities in the mean motions of 

 Jupiter and Saturn will be, I hope, as easy to conceive. 



Mathematical analysis has not served to represent in 

 finite terms the values of the derangements which each 

 planet experiences in its movement from the action of all 

 the other planets. In the present state of science, this 

 value is exhibited in the form of an indefinite series of 

 terms diminishing rapidly in magnitude. In calculation, 

 it is usual to neglect such of those terms as correspond in 

 the order of magnitude to quantities beneath the errors of 

 observation. But there are cases in which the order of 

 the term in the series does not decide whether it be small 



* Mr. Adams has recently detected a remai-kable oversight com- 

 mitted by Laplace and his successors in the analytical investigation 

 of the expression for this inequality. The effect of the rectification 

 rendered necessary by the researches of Mr. Adams will be to 

 diminish by about one sixth the coefficient of the principal term of 

 the secular inequality. This coefficient has for its multiplier the 

 square of the number of centiaries which have elapsed from a given 

 epoch; its value was found by Laplace to be 10"-18. Mr. Adams has 

 ascertained that it must be diminished by l"-66. This result has re- 

 cently been verified by the researches of M. Plana. Its effect will be 

 to alter in some degree the calculations of ancient eclipses. The As- 

 tronomer Royal has stated in his last Annual Report, to the Board of 

 Visitors of the Royal Observatory, (June 7, 1856,) that steps have re- 

 cently been taken at the Observatory, for calculating the various 

 circumstances of those phenomena, upon the basis of the more cor- 

 rect data furnished by the researches of Mr. Adams. Translator. 



