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



ill portions). The usual method (of varying two mean distances, actually computing 

 three orbits) would not only have required more operations, but these must, many of 

 them, have been carried to seven decimals, in order to obtain with any degree of accu- 

 racy the coefficients of the unknown quantities in the equations (41). At least one 

 third the labor appears to be saved by this process, while a differential method, in gen- 

 eral much better than the rule of false position, is substituted for the latter. 



Moreover, the general relations developed in the first part of this paper are not with- 

 out very interesting aspects with regard to the general problem of representing long 

 series of geocentric observations by an orbit, by the method of least squares ; and it 

 is not impossible that further calculations may be made upon the theory of Aglaja, 

 using the numbers and formulae already obtained, and approximating more and more 

 closely to the true elements, when the observations requisite shall have been made. 



