30 ON THE PERTURBATIONS OF URANUS. [2 



40. Again, the equations of condition given by the ancient observations 



are 



62-6= Se -0-8776 8^ + 0-5402 So;, +0-7923 A, +0-2554 A, 



- 39-31 S- 0-4795 8y, + 0-84158y s + 0'6101 4 + 0-9668 4 



-0-3875 lt, t - 0-9877 p 1 -0'6870p.,-0-W09p t 

 + 0-9-219 4+0-1566 </,- 07267 </ a -0'9949 & 



84-5= Se + 0-49758^- 0-5050 Sa;.,- 0-0887 4 -0-9843 /* 



-32-30 S/i-0-867582/,-0-8631 82/3 + 0-9961 4-0'1767 4 



+ 0-2634 />,- 0-9085 ^ -0'3355 p, + 0'9681p 3 



-0-9647 4-0-4178 </,- 0'9420 </ 2 -0'2506 r/ 3 



67-2= Se + 0-6732 So;,- 0'0935 8ar s - 0'2243 /t 1 -0'8994 /t. 



- 31-34 871- 0-7394 8//,- 0-9956 //, + 0-9745 *,- 0-4371 /:. 



+ 0-6277 7^-0-8720 ^ -0'2815 j9 2 + 0'9982p 3 

 -0-7785 ^-0-4895 (/,- 0'9596 (/ 2 -0'0591 7., 



-51-8= Se -0-2616 Sas, -0-8631 8ic,-0'9436 ^ + 07809 fi t 



- 19-59 8 + 0-9652 8//, - 0'5050 8y 2 - 0'3310 *, + 0'6247 4 



-0-5301 /i a - 0-0731 p, + 0-3991 /> 2 - 0'6801 ^ 

 -0-8479 4-0-9973 </,-0'9169 7-. + 07331 (/ s 



-43-2= Se -0-4741 8^-0-55058^-0-8861 /< 1 + 0'5704 A, 



- 18-58 8n + 0-8805 By, - 0'8348 By*- 0'4634 4 + 0'8213 4 



-0-1248 A 3 + 0'0115 J > 1 + 0-4532_p,-0-8147j) 3 

 -0-9922 4-0-9999 </, - 0'8914 fy 2 + 0'5798 ^ s 



-50-1= Se -0-64308^-0-1731 S^-0'8191 4 + 0*3420 h., 



- 17-68 8w + 07659% a - 0-9849 8t/ a - 0-5736 4 + 0-9397 4 



+ 0-2588 /, + 0-0871 p, + 0-5001p 2 -0'9063p s 



-0-9659 4-0-9962 ^-0-8660^ + 0-4225^ 



-37-8= Se - 0-9492 8aj, + 0-80218^-0-5743^ -0-3404 A, 



-15-25 8w + 0-31458y 1 -0-59728y s -0-8l86 A, + 0-9403 4 



+ 0-9652 ^ + 0-2872 p l + 1 6192p s -0-9984p, 



-0-2613 4-0-9579 9, -0'7852 ^-0-0560 q 3 



