Hence, 



25. 



OF URANUS AND NEPTUNE. XX111 



3 (nt + e) = + l"-674 sin X - i"«785 cos X, 

 S (n't + e') = - l"-212 sin X + l"-268 cos X- 



dP. 



a — — = - a (M 3 e 3 + M i ee' i + M b e sin 2 ^ y) sin or, 



- 2aM 9 ^e' sin (2w - "&') 

 + aM l0 ee'* sin (2vr- ■nr) 

 + ali,c sin 2 1 7' sin (2 EL' - sr), 

 dP,' 



d-sr 



= - the same with cosines for sines. 



dP, _ dPi _ 



.-. log a — - = 5-53656, log a — - = 5-81345, 



dsr ° d'ar 



r-p, ^-T = - 0"-3899, r— tt ~ = - 0"-7376, 



ea> sin 1 dur em sin 1 dw 



and by last Art. 

 Again, 



m'na dP Y ., m'na dP! 



77 — = + 0"-4193, ; Tl — = + 0"'6l53. 



w sin 1 ' de w sin l" de 



, dQi a rfP, 

 efasr 



a 



, a dP, I 1 \ /3 , , . \ . , 



,dQ/ . . 



a — — ; = — same with cosines lor sines, 

 d-sr 



dPi 



a — , = - a (ilf 6 e 3 + ilf,eV + M B e'sm s ^y) sin 73-' 



+ ailf 9 e 2 e'sin (2w - ■zsr') - 2aiW 10 ee' 2 sin (2^ - tjt) 

 + aM i2 e sin 2 1-y' sin (2 II' - •ar'). 



Hence log a ~, = 5-31765, log a -^7 = 5-32552 -, 



dor dw 



wwzV dQj „ nrn'a' dQi „ „ 



■■■ , ■ ,„ j-7 = " 0' -5755, , . „ -=3 - + 0"-5860, 



e to sin 1 d^sr e w sin 1 dsr 



and by last Article, 



mn'a dQj „ mn'a dQ,' 



» ~T+ " + 0*2094, ^-„ -£L = + l"-3565. 



w sin 1 ' de' w sin l" de' 



Therefore, 



&» = - 0"-390 sin X - 0"-738 cos X, 



eSvr = - 0"-4l9 sin X - 0"-6l5 cos X, 



&»' = - 0"-575 sin X + o"-586 cos X, 



e'&sr' = - 0"-209 sin X - l"*356 cos X. 



