22 ON THE PERTURBATIONS OF URANUS. [2 



- 72-'4 = 2-2815 &e a -0-3786 A, + 0-9257 A, + 2'3601 /t, 



- 4*4181 8^+0-1283 ,-07339 &- 4'1495 , 



-0-1957^-0-1428^- 0'1286^ 3 

 + 0-0283 ft + 0'0198 ft + 0'0671 ft 



- 42-0= 2-1139 8.r,-0-2652 /i, + 0-6985 h.,+ 2'1241 /* 3 



- 3-1027 S& + 0-0772 ,-0*4646 - 2*8790 3 



-0-1348.2?!- 0-0984 p.,- 0'0924^ 3 

 + 0-0154 ft + 0-01 14 ft + 0-0412 ft 



25. The largest terms depending on the eccentricity of the disturbing 

 planet occur in p 3 , q 3 ; it will he proper, therefore, to combine the above 

 equations in such a manner that these quantities may acquire the largest 

 coefficients possible. This will be done by multiplying each equation by a 

 quantity nearly proportional to the coefficient of each of the unknown quan- 

 tities p. t and ft, and adding together the several results. It was thought 

 unsafe to employ the first of the above equations, since it is derived from 

 the single observation of Flamsteed made in 1690, twenty-two years anterior 

 to any other observation. 



Hence the equation for finding p., may be formed by multiplying 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., by multiplying the 

 same equations by 



1-0, 1-0, 0-5, 0-4, 0'3, 0-2, O'l, O'l. 

 Hence we obtain 



-474-1= 4-114 8o3 s -2-817 ^ + 7-837 A a + 4'528 /, 



-20-745 By,- 2789 &,- 6-551 ,-20-666 



+ 0-193^ + 0-377^,- l-489p :i 



-1-660 $- 1-078 ft- 0-054 <? 3 



-485-0= 0-446 &c,- 3-308^-0-442^+ 1-629 A, 



-32-961 8y a + 8-267*,- 8-805 2 -32'546 3 



-4-473^-3-643^,+ 0'037^, 



+ 3-530 ft + 2-278 ft + 2'086 q. 



