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INEQUALITY OF JUPITER AND SATURN. 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 remarkable 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 centuries 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 1//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. 
