90 A NEW METHOD OF DETERMINING 
If in equation (21) we introduce 7 instead of ¢ we shall have 
dg cae j h, B 2 
Sait +5), (23) 
where 
ro h hy h P = h rn ee 
Ul Shs — 7 sb D8 = ots m ob 2 yo ES SN. 
; h, h hy ay h, Qy 
We have also 
dé at: h, (24) 
de ~ nh(l+p)?” 
The codrdinates of a body vary not only with the time but also with the variable 
elements. In computations where the elements are assumed constant, that part of the 
velocity of change in the coérdinates arising from variable elements must, evidently, 
be put equal to zero. Coérdinates which have the property of retaining for them- 
selves and for their first differential coefficients the same form in disturbed as in undis- 
turbed motion, HANSEN calls ideal codrdinates. 
If Z bea function of ideal codrdinates, it can be expressed as a function of the 
time and of the constant elements. Thus let the time, as it enters into quantities 
other than the elements, be itself variable and, as before, designated by tr. 
The function dependent on ¢, 7, and the elements we designate by A. Then 
ay da 
Gig — Ghe 2 
or 
dL = (--\at 
where the superposed dash shows that after differentiation 7 is to be changed into ¢. 
Let us write the equation (24) in the form 
+ BY = 7 
