OF UHANUS AND NEPTUNE. xli 



First let lR-¥± r.+ ^'r.'' 

 de de ° 



, r d(8R) Sm'Wa* 4m ox I dP „, dP\ 



then 2wa 2 / ~V- :; — + — « 8 ) ( P— + i* -=- ) «< 



•/< da ar m \ da da I 



( ( n dP ^dP'\ ■ \ 



. '• 3 s , \ \ p ^r - i ^^-) sin2X i 



3m Va 3 4m ox J \ da da / I 



+ : — <* + ^*> , ^ ^ {« 



2w 3 sin l" m' 



.-. # e = - o"-969 sin 2X + o"-272 cos 2X, 

 omitting the secular perturbation. 



The formula for Neptune is 



, , 2 rd(8R') 3mm'nnaa' 2 4m / dQ . d<$\ 



^i do' co 2 m' V da' da'/ 



, ,,,„ , ( (p^-e**)^) 



3mm mrn a a 4m l \ da da I I 



+ 2^sinl" (1 + W a) \ / dQ" rfQ\ ( ; 



.-. <SV = + 0"-933 sin 2X - o"-268 cos2X. 

 Again, with the same value of 8R, 



-* nae J t -de- 



3m\V 4m I dP , dP\ 



( (»dP „,dP\ . \ 

 ■ Va 2 4m 1 V de de J ! 



3m 

 8w 3 sin l" ' m 



.-. ^e = + 0"-079 sin 2\ - o"-030 cos 2X, 

 which as well as the corresponding part of S'e' may be neglected. 



Next let 



5 dR, ,dRi* , dR ^ '^ dRl S„' 



bR m — — i^e + — — diW + —tt °\ e + -jzj "i* » 

 de d-sr de dsr 



then 2na 2 / \ ■ 

 J t da 



_ 2m' 2 na 3 (dP fP^ dP d*P 

 id \de deda de deda 



a secular perturbation of the epoch 



\ 2mm'ria?a (dQ. <PP d$ d*P \ 



} a) \de deda de de'daj 



[F] 



