26] ACCELERATION OF THE MOON'S MEAN MOTION. 209 



1 or 2 3 o-;- 2 

 Or, p r = _- 2 _ + __ COB (2,,_27) > 



Tr= -|^8b(2*-2F). 



Now, by the formulae of elliptic motion, we may find 



~ 

 ~ 



-1 sin (2,, -27) 



A 



neglecting terms involving 2S, and powers of E above the second. 



Substituting, and then taking the variation, we have 

 ~ r 8r + 3 ^ rSr cos (2v - 2 V) - 3 ~ 



(Pr) = ~ r 8r + 3 rSr cos (2v - 2 V) - 3 ~ r%v sin (2v - 2 V ) 



1 \ - 5E8E cos (2^ - 2L) + 1 8E cos (2i> -2L- S) 



S (Tr) = - 3 - rSr sin (2v - 2 F) - 3 - rv cos (2v -2V) 



in which ^Sf-) may be written for r8r, and the expressions given by 

 A. 27 



