186 THE ORBIT OP URANUS. 



cos sn 



A 1 ) cos % -f- (*/,-% 4M 3 ) sin 



In computing these expressions it will be sufficient for several centuries before 

 or after 1850 to develop h, (5/. 1 , and tl to their first dimensions: it will, however, be 

 more convenient to correct the mean anomaly g for the perturbation hi before obtain- 

 ing the equation of the centre. Developing the perturbations of Ti and Jc to terms 

 of the first order, we have for the effects of the perturbations of those elements: 



(..!)= ?- 



(v.s.2) = ( 2 e - e 3 



JO 



(v.s.3)= -e* 



10 

 ( r .c.3) = -jV 



103 



(v.c.4) = - 



(p.c.O) = 



(p.c.l) = -l-- 



g 



(p.c.2) = n e 



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

 to reduce the perturbations to those of the common logarithm of the radius vector. 



