28 ON THE PERTURBATIONS OF URANUS. [2 



36. Similarly the equations in the second group are 



(n) -171-27= 77-0000 Bn + 9-3938 Sy,- 1-2183 By, 

 + 87355 ,+ 7-6213 k,- 0'0590 k 3 

 + 5-9764 ,+ 4'3875 q.,+ 9"6152 q 3 



-166-33- 93-9380 Sn + 12-7179 8^+ 1-8907 Sy, 

 + 11-0393 ,+ 11-3717 & + 3'3196 k 3 

 + 7-3747 r/,+ 5-3825 r/ 3 + 12'6816 <? 3 



-181-31= 87-3550 S/i+ 11-03938^- 0'3758 By, 

 + 10-0264 k,+ 9-2740 k,+ 0'9476 & 3 

 + 6-8054 q t + 4"9866 ^+11-1971 ft 



99-51= 76-2130 S+ 11-3717 Si/, + 4-4810 8& 

 + 9-2740 &, + 10-9740 k,+ 5'6294 k 3 

 + 6-0523 q,+ 4'3916 f/,+ 11'0843 </ 



(k a ) 113-14=- 0-5900 Bn+ 3'3196 8y,+ 10'2112 &y, 

 + 0-9476 k,+ 5-6294 ^+10'0251 k 3 

 + 0-1746 q,+ 0-0454 q,+ 2'4791 </ 3 . 



37. The equations (p.^), (p 3 ) of the first group, and (</), (5-3) of the 

 second, were not formed, as our previous solution shewed that when Se, 

 8n, 8x lt and Sy t , were eliminated, the coefficients of the remaining unknown 

 quantities in these equations would be extremely small. It will be preferable 

 to combine the equations (//,), (h.!), (h 3 ), and (&,), (,), (k 3 } before, instead of 

 after, the elimination of Se, Bn, 8x lt and By t , from them. If then we change 

 the sign of the third equation in each group, and add it to the fourth 

 and fifth, we obtain 



141-07 = - 17-6009 Se + 6'0448 Bx,+ 18"2097 8x 2 



6-2965 A, + 13-6704 A 2 4-19'2974 h 3 



-13-3971 p,- 15-4639 p,+ 2'4144 p, 



194-94= -11-7320 8n+ 3"6520 By,+ 15-0680 By, 

 + 0-1951 &,+ 7-3294 yfc 3 + 147069 k 3 

 - 0-5785 q,- 0-5496 q,+ 2'3663 q t . 



