24 ON THE PERTURBATIONS OF URANUS. [2 



(L ]=- 0-1 8 cos (8-/3) + 0-046247 j^j sin 20 + % cos 201 

 ?ft' [m TO J 



^== 24-91 sin(20-/3) + 0-13055 ft cos -% sin 01 

 TO' [TO m' J 



-^;= 24-91 cos (20-/3) + 0-13055 ft sin + ^ cos 01 



TO' [-' m' J 



29. Substituting these expressions in the equations of Article 27, and 

 putting for /3 its value 50 15''8, we obtain, after a slight reduction, 



0= - (1 -24782) sin 6 + (1-40248) cos 0-( 1-57155) sin 26 + (2'27388) cos 29 

 -(1-46746) sin 30 + (2-23430) cos 30 + (9-10380) ^-(9'48254)% 





+ (8-28455) ft cos d- -^ sin 0} - (8'49138) ft sin 0+ -% cos B\ 

 v ' \m m! I v ' \m m! J 



- (7-97958) -fc cos 29- ^ sin 201 - (8'55742) fe sin 20 + -% cos 201 

 v ; \m m J v 7 [m m } 



= (1 -G5083) sin + (1 -99378) cos 9 + (2- 1 4259) sin 20- (2'58192) cos 20 

 -(2-14400) sin 30-(2'05631) cos 30- (9'93475) ^- (8'91803) ^ 



+ (9-08947) fe cos 0- ^ sin 01 - (9-14306) fe sin + -% cos 01 



7 [?VZ' 9H J ' [m' TO' J 



-(8-65341) -fe cos 20- * sin 20| - (8'87892) fe sin 20 + ^ cos 20] 



' [m 111! } ' [TO m J 



- (1 -79213) sin - (2'49403) cos - (2'55700) sin 20 - (2'56972) cos 20 

 - (2-20337) sin 30- (2-25714) cos 30 + (9'83632) ^, 3 + (0-31156) q '-, 



-(9-60395 {-^cos0-- y > sin 0} + (9'47665) ft sin +-% cos 01 

 (m m' } v x \mf m J 



+ (9-23220) fe cos 20 - % sin 201 + (9 "2 1679) { P ] sin 20 + -% cos 20) 

 ' [TO' m' J v ; [m' m J 



where the numbers enclosed within parentheses denote the logarithms of the 

 corresponding coefficients. 



