LECTURE V. 



THE VARIATION, (continued). 



WE will now proceed to substitute in the differential equations the 

 values of l/r and 6 which we have obtained, retaining terms of the order 

 of the squares and products of a 2 , 6., and m- or mf. 



The values to be thus substituted are 



- ; = -(l+a 2 cos2t/), 



6 = nt + e + i., sin 2\jt, 



where \(i nt + e (n't + e 7 ), 



3 2 + m, 



2 1 



3-2m 1 + -w, 2 



Hence r = a\ 1 2 cos 2$ + - a, 2 (1 + cos 4i/) , 



-j = 4a ft n' a,- cos 2if 2a 2 2 cos 



= 4 w - n - < + a 2 cos 2^ - - a/ cos 4/J ; 



32 



