60 LECTURES ON THE LUNAR THEORY. [LECT. 



and 



'?- = r - (2 - 2m) a., sin (2 - 2m) 6 + ^ e sin (6 - OT) 

 at h~a v tfa 



= T (2 - 2m) a, sin (2 - 2m) + wa [1 + /t, cos (2 - 2m) 0] e sin (0 - nr), 

 J = (2- 2m) 2 , cos (2 - 2m) ^ - (2 - 2m) A 2 sin (2 - 2m) e sin (0 - m) ~ 



+ -? [1+ A, cos (2 - 2m) 0] e cos (9 - w) C , 

 nadh . . . ., dd 



na r rde . dm 



^-fl+A. cos (2- 2m) ^] 7 ,,sm (d-is)-e in cos (^- -,-. 

 h L J |_rfy dd ' at 



Multiply by t^/n~a 3 ; then since 



^d6 



dt 



-=11= hnd- [ 1 + /;., cos (2 - 2m) ff], 



we have 



nv f~/" / t' t 



3 -T, = (2 - 2m) 2 a s cos (2 - 2m) - (2 - 2m) h, sin (2 - 2m) e sin (0 - 



% Of 6tt 



+ e cos (0 zr) + 2A 2 cos (2 2m) e cos (0 OT) 

 j -T7.(2 2m) a, sin (2 2m) 



+ [ 1 + A. 2 cos (2 - 2m) 0T [~ sin (0 - CT ) - e ^ cos (0 - CT )] 



|_ac/ etc/ 



and this is equal to 



IP p. I ,r^ 3 ,r^ 

 n 2 aV w'a 1 2 a 3 + 2 a 3 LC ^ 



+ 2me cos (3 2m ar 

 = I l+~^ + 2h,cos(2-2m) 0}[l+a,cos(2-2m)0 + ecos(0 



-tftf + 2 m * h '[ l - 3a ^ cos ( 2 - 2m) - 3e cos (0 - sr)] 



3 r 



+ - m% 6 1 cos (2 - 2m) + 6a 2 e cos (0 - w) 



- (- + 2m) e cos (l-2md + CT ) - (| - 2m) e cos (3-2m0- 



\^ / \z / 



