2] ON THE PERTURBATIONS OF URANUS. 23 



26. Eliminate Sx., and 8y. 2 from these equations by means of (x) and 

 (y) and they become 



(3) -4767= -2-930/^ + 7-572^ + 4'332/* 3 



- 275 U", - 6-348 k, - 20'350 k 3 

 + 0-155j9, + 0-350_p 3 - l-686p 3 

 1 -653</, 1 -074(7,, + Q'047 q 3 



(4) -485-9= -3-463/^-0-805^+ 1'3604, 



+ 8-345^-8-391 k.,-3l'9QOk 3 

 -4-525^-3-679^- 0-233^., 



+ 3-545^ + 2-286^+ 2'292g :i 



These equations, with (l) and (2) of Article 22, suffice for the solution 

 of our problem. 



27. Eliminate the left-hand members from equations (2), (3), (4), by 

 means of equation (1), and we have 



0= 0-4819 /t, 0'5950 h., 5 '0570 4 t + 0'2063j9, + 0-1475^, + 0-4300^ 3 

 -0-6812^ + 3-2982^ + 29-5618 A,- 07804 g, -0-2375 &-0'4789 /, 



0= - 1-2005 h, + 2-4466 h, - 24-0122 h. + G'9735^ + 0'9412 p, - 0'8575^ 3 

 -2-6633 ^-5-8825^-19-6219 ^-1-6362 ^-1-0648 ^ + 0-2791 </, 



= - 1 7003 /i, - 6-0294 h, - 27'5295 /t, - 3-6908p, - 3'0772_p a + 0'61 18 p t 

 + 8-4344^-7-9162^-31-1583 ^ + 3-5621 ^ + 2-2954 ft + 2'5285 q, 



28. If now we put e e' = and e nr ft, it is easily seen that 



h = - 36-99 sin ,= 58'97 sin 20 



m m 



^i-= -36-99 cos ,= 58-97 cos 20 



m 



^L= 5-80 sin 30 +0-007460^ + 0-008974^ 



-0-008974 =^ + 0-007460% 



m in 



^-,= 5 -80 cos 



^?= 0-18sin(0-j8) -0-046247 {=? cos 20- - sin 201 



m! \J n m } 



