21. 



ON THE SECULAR VARIATION OF THE MOON'S MEAN MOTION. 



[From the Philosophical Transactions of the Royal Society, Vol. CXLIII. (1853). 

 Abstract of same, Proceedings of the Royal Society, June 16, 1853 and 

 Monthly Notices of the Royal Astronomical Society, Vol. xiv. (1853).] 



1. IN treating a gi-eat problem of approximation, such as that pre- 

 sented to us by the investigation of the Moon's motion, experience shows 

 that nothing is more easy than to neglect, as insignificant, considerations 

 which ultimately prove to be of the greatest importance. One instance of 

 this occurs with reference to the secular acceleration of the Moon's mean 

 motion. Although this acceleration, and the diminution of the eccentricity 

 of the Earth's orbit, on which it depends, had been made known by obser- 

 vation as separate facts, yet many of the first geometers altogether failed 

 to trace any connexion between them, and it was only after making repeated 

 attempts to explain the phenomenon by other means, that Laplace himself 

 succeeded in referring it to its true cause. 



2. The accurate determination of the amount of the acceleration is a 

 matter of very great importance. The effect of an error in any of the 

 periodic inequalities upon the Moon's place, is always confined within certain 

 limits, and takes place alternately in opposite directions within very moderate 

 intervals of time, whereas the effect of an error in the acceleration goes 

 on increasing for an almost indefinite period, so that the calculation of the 

 Moon's place for a very distant epoch, such as that of the eclipse of Thales, 

 may be seriously vitiated by it. 



