32 ON THE PERTURBATIONS OF URANUS. [2 



-146'-69=- 07686 8.x,- 0-1963 Sx,- 3'9519/i,- l'5548/*, 2 



+ 10-6926 Si/, -4-2508 Si/ a +ll'5128 ,+ 97013 ^ 



+ 1-7907 /> :( - 4-7913 }\- 3'1927^.,- 07902_p 3 



2-8583 & 3 + 4-6536 </,+ 1'9595 </+ 117796 <? 3 . 



43. Substituting for Sao,, Sy,,, their values in terms of Sx,, Si/,, we find 

 -4-1831 &*,+ 7-1533 S?/,+ 0-61798.^-1 '5388 8ij,= -4-16478^+ 7-14738^, 

 - 07686 Sa\+ 10'6926 Si/,-0'1963 Sx.,-4-2508 8y,= -07319 Sa:, + 10-6591 Si/,. 



Hence, if to the equations just found we add 



+ 0-60808 (as) - 5-5942 (t/) 



and + 0-07306 (x) - 8'31 10 (y) respectively, 



8a', and ST/, will be eliminated, and we shall obtain the following equations : 



(3) -476-84= -2-7630 /*, + 6'9793 /i,+ 4-6473/1, 



-2-8290 ^-5-1777 A: 2 -20'2242 k a 

 + 0-0698^ + 0-3785^- 2'5884p 3 

 - 1-7748 ^-0-8036 q,- 0'2693 q t 



(4) -486-03= -3-7091 // 1 -0'9682//,+ 2'2600 h., 



+ 8-3364 ^- 7-5348 A.-3T0457 k t 

 -4-6988^-3-1454^- G'3772^ 

 + 3-9584 (/,+ 1-71 18 q,+ 3'8734 q t . 



44. Eliminate the left-hand members from equations (2), (3), and (4), 

 of Articles 39 and 43, by means of equation (l), and we have 



0= 0-4200 /,- 0-41 14 /*.. - 4-2014 7< :i + 



- 0-4964 b + 2-3306 , + 23'3213 jfe,- 0'1567 q, - 0'0409 q, - 0'4531 q a 



0= -1-0507^, + 2-6465 //,- 21-8182 ^ + 0-9482^, + 0-8614 j9 a - 1-4023 j) s 

 -27471 ,-47334^- 19-4976 & 3 - 17569 9 ,-07972 ^- 



0= - 1-9638 /i,-5-3845/^-247l55/t 3 -3-8034p,-2-6532_p a + 



+ 8-4199 A:,-7-0819 1-30-3051 ^ + 3-9767 ^+1-7183 q,+ 4'08Ilq 3 . 



