OF URANUS AND NEPTUNE. xliii 



d*P (PP* - 



log a 2 — : — = 1-91155 -, log a 2 —7— = 1 '94481 - ; 



° deda deda 



.-. $6 - (+ l"-306 + 0"'438 + 0"-378 + 0"-21l) sin X, 

 + (- 0"-053 - o"-022) COsX, 

 = + 2"-333 sin X, 

 the coefficient of the cosine may be neglected. 

 The corresponding formula for Neptune is 

 <- d (lR') 

 /, da 



2n'a'*f 



2mm nn aa 



f fdP fP^ dP^ <PP[\ s . n \ 

 ' 2 \ \de deda' de deda' J [ 



a> 2 sinl" j tdP d^Pl _dP <PI\\ f 



\ \de deda' de deda' J ) 



( (W **L *$L ^A sin y\ 



Zmrn'^a' 3 J \de deda' de deda) I 



+ « 2 sin 1" A idQ. d?P£ _ dQ' rf 2 P 2 \ ( 



( \de' de'da' de' deda') ) 



( l<PQ_ dl\ + £<f_ dPj\ gin 1 



mm'nn'aa' 2 j \deda' de deda' de ) \ 



) + f_*£. **± _ *# ^ cosX ( 

 I \deda' de deda' de J ) 



f ld?Q_d]\ d*Q' dP t \ J 

 \ \de'da de' de'da' de ) \ 



\ + [de'da' de' de'da' de')™ 5 *) 



*&— i(*S*.£). -Mog = 0-04856, 

 deda a \ aeaa ae / 



,. tfP/ 1 / . d 2 P 2 ' dP 2 '\ 



a' 2 — ^ U -j-p + a -T 1 ; •*• lo 8 " r43837 "' 



deda a \ deda de J 



de'da' a \ de'da de' ) 



, 8 (PP/ 1 / , tPP/ dP 2 ' \ - 



de'da' a \ de'da de ) ' 



log «' 2 t-tj = 0-66346, log a' 2 — -^ = 1-98373 -, 



deda deda 



d?Q d 2 Q' 



log a' 2 -vt^j = 0-61850, log a' 2 -p^h = 0-65176 ; 



deda deda 



.: 3V- (- l"-l26 - 0"-394 - o"-367 - o"-49l) sin X, 

 = - 2"-378 sin X, 

 neglecting the coefficient of cos X which is very small. 



w 2 sin f 



rwW 3 

 a) 2 sin l" 



f2 



