29] DUE TO SECULAR CHANGE OF THE PLANE OF THE ECLIPTIC. 235 



and similarly ' = x', 



T/ = y' cos (t, 

 ' = y' sin a>t. 



Let r be the Moon's radius vector at time t, r' that of the Sun, m' the 

 Sun's mass, /A the sum of the masses of the Earth and Moon, and R the 

 disturbing function, then we have 



_ 



2 r' 3 - "2 r /5 



and the equations of motion, with reference to the fixed ecliptic, will be 



W.rf_ 



df r :t ~ 



dR 



/ I I t 



dt~ r* drf ' 

 d't, u, dR 



or, substituting the values of 



dR dR dR 



~ ' ~ ' 



3m' t' 



0) 



Now we have, from the values of 77 and above given, 



and 



302 



