27. 



INVESTIGATION OF THE SECULAR ACCELERATION OF THE MOON'S 

 MEAN MOTION, CAUSED BY THE SECULAR CHANGE IN THE ECCEN- 

 TRICITY OF THE EARTH'S ORBIT. 



[From the Monthly Notices of the Royal Astronomical Society, Vol. XL. (1880).] 



As the question of the Moon's secular acceleration has lately been 

 again brought before the Society, I have thought that it might not be 

 useless or without interest to communicate an investigation of the two 

 leading terms of that acceleration which I gave many years ago in my 

 lectures on the lunar theory. 



1 . Let r, be the polar coordinates of the Moon at time t, u - , 



r 



dO 



H = r* -j- , p. the sum of the masses of the Earth and Moon ; also let m' 



be the mass of the Sun, r', 6' its polar coordinates, a' the Sun's mean 

 distance, n' its mean motion, and e' the eccentricity of its orbit, A.' = n't + e' 

 its mean longitude, and $' = n't + e' a/ its mean anomaly. 



Then the equations to be satisfied are 



d"u u. 1m' 3m' 



.,,, 



3 m' du 



c l ( Tf"-\ o' 



272 



