IgQ THE ORBIT OF URANUS. 



_ 1 '^ I (/,' _ U-Ir) cos 3^ + (3/r7t — 7t') sin Sg \ 



_ ^^\ (/,' _ GJrIr + A') cos % + {-ikVi — Uh') siu 4(/ I 

 1)6 [ I 



In computin<j these expressions it Avill be sufficient for several centuries before 

 or after 1850 to develop h, U', and II to their first dimensions: it will, however, be 

 more convenient to correct the mean anomaly <j for the perturbation H before obtaiu- 

 ino- the equation of the centre. Developnig tlie perturbations of h and I to terms 

 of the fii'st order, we have for the effects of the perturbations of those elements: 



(....!)= (2-|e,= )cV. 



(r.c.l) = -(2--^v)^/* 



(,,,,2) = - (2^0 - ^i^o^ c^^ 

 13 



(r.c.3) = — -jef hh 



103 , ,, 

 (?'.5.4) = -9! ^0 ok 



103 , ,, 

 (r.c.4) = oT'o ^'* 



24 



103 



IT 



(p.c.O) = ^» + 2^0 ^'^ 

 ((....l) = -(l-ge,/)^A 



(p.c.i) = -(i-gf,r)^/^ 



(p.-5.2) = — 2^0.71 



3 



(p.c.2) = — g^o^^"' 



17 

 (p.s.3) = — -g Co^ 5A 



17 



(p.c.3) = ^g-eo^ ^/t- 



These coefficients for p must, of course, be multiplied by the modulus 0.434294 

 to redtice the perturbations to those of tlie common logarithm of the radius vector. 



