2] ON THE PERTURBATIONS OF URANUS. 31 



-20-5= Se -0-9985 So;, + 0-9942 So;, -0-3671 /!,- 07304 h., 



-13-60S-0-0538S?/ 1 + 0-1074S// 2 -0-9302 4 + 0'6830 k, 



+ 0-9035 A 3 + 0-4164 ^ + 0-6928^-0-9251^ 



+ 0-4286 4-0-9092 </,- 07212 <7,-0'3796 q 3 



2-4= 8e -0-9633 Bx, + 0'8560 S^-0'2363 A.-0-8883 h, 



- 12-64 Sn- 0-2684 8^ + 0-51708^-0-97 17 4 + 0'4593 4 

 + 0-6562 /i :i + 0'4882 p, + 07327 p.- 0'8345 p, 

 + 0-7546 4-0-8727 ft-0'6806 g.,-0-5511 q 3 . 



41. The equation for finding p 3 may be formed as before, by multi- 

 plying the above equations taken in order by 



-0-8, -0-6, +1-0, +1*0, +0-9, +0-6, +0'4, + 0'3, 



beginning with the second ; and the equation for q 3 by multiplying the same 

 equations by 



1-0, 1-0, 0-5, 0-4, 0-3, 0-2, 0-1, 0-1. 



Thus we obtain 



-279 /r 64= 2'808e -3-37428^ + 0-02658^-2-9237 7^ + 2-2232 h, 



- 27-82 Sn + 3-7593 8^ -1 '0986 Sy,- 3'8471 &, + 3-6706 k, 



+ 0-1281 A :j +l-7522 ^, + 2-6081 ^.-4-9033 p t 



-1-2295 ^-3-4661 ^-2-2221 f/,+ 1'5785 q, t 



83-56= 3-60 Se +0-27148.^-0-95678^-1-5602 7^-1-3924 h a 

 -91-84Sw-O t 51168y l -279768y a + 1-0937 4 + 0-6112 k, 

 + 1-0027 7?. 3 - 1-6385 p^O'1802 ^., + 0-6529 p 3 

 -27879 4-2-4746 g-,-3'2736 5. + 0-3113 q a . 



42. Eliminate 8e and 8n by means of (e) and (n) of Articles 35 and 

 36, and these equations become 



-36172=- 4-18318^ + 0-61798^- 47839 4+ 2'0969 h, 



+ 7-1533 8^-1-53888^- 0'6909 4+ 6'4242 k., 



+ 0-7410 h 3 - 0-7000 p,- 0-0153^0- 6'0258 p 3 



- 1-2508 4-1-3068 q,- 0'6369 q t + 5'0525 q t 



