﻿A NEW METHOD FOR CORRECTING A PLANET's ORBIT. 475 



The elements will then be, 



Epoch, 1857, Nov. ICO. — M. Equinox, 1857.0. 



The remaining errors, 8 ri cos d, after the solution of the conditional equations (41), 

 were, 



C. — 0. 



n. — o".6 1 



IV. — 1".3 I ■ (42) 

 V. +1".0 J 



Substituting the new elements in the formulee for the geocentric places, we obtain 

 values of 3 a, 5 5 corresponding with them ; and from these, by (27), values oi 8^ cos 0, 

 differing from those in (42) very slightly. 



The resulting differences in the other geocentric cocirdinate, d, are nearly as follows : 



se{C. — o.) 

 n. +i".3 



IV. — 2"-.0 



V. +5".7 ; 



which is a small difference, seeing that the last normal depends upon but two observa- 

 tions, and those, as is apparent by Mr. Oeltzen's investigation [Astr. Nachr., No. 1167) 

 disagreeing largely, as indeed do the observations upon which IV. is based. 



Ten months after the date of the last of these normals, the comparison of an ephem- 

 eris computed from the above elements with a Cambridge observation, kindly furnished 

 me by Prof W. C. Bond, was as follows : ^ 



C — 0. 



/i a cos 5 /J d 



1858, Dec. 28 +1'.6 +1'.2; 



showing an agreement much more satisfactory than is usual in determinations from the 

 first apparition of an asteroid, especially considering the weakness of normals IV. and 

 v., upon which, as may be seen by (41), almost the entire Aveight of the computation 

 rests. Perturbations, too, were entirely neglected. 



The calculation of the above orbit was executed entirely with six decimal places (less 



