THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 91 
Differentiating relative to 7, we have 
at 
GH dv’ ; 
dt 
The differentiation of (23) also relative to t gives 
CGO WENAG 
d@ d& dt 
hy 2B dp 
aly ib” (1-Ep)8 dz : 
Eliminating = by means of (24), we have 
ae 
de dW 28 dg 
Lr ee de 1+8° dr* 
dt ; 
Substituting in the expression for ae we have 
LT 
dp dw 
dt ” Ge 
Since » is an ideal codrdinate, we get from this 
es 8 if (© at, (25) 
IV being the constant of integration, and the dash having the same signification as 
before. 
This expression for » is a transformation of that given in the equation 
1 — 2e,€ — cos *g,.€’— cos *¢y.7? 
ITtyv= G@LEpyi@e mera coseen 
a 
“im 7) 
ay 
Since z is also an ideal coordinate, we have from (23) 
es is ea 
raj = rob + G+ mf 1 W +5) \ dt (26) 
g being the constant of integration and being the mean anomaly for ¢= 0. 
