THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 
We also have 
1 — 
(25) 
Pm = Tn — Pin+19 
a form more convenient in the applications. 
m) 
( 
The general expression for J, . 1s 
Coy 
(m) (0) 
Te =e Pi- Pa Ps--- Pos (26) 
2 i 
where 
(0) oat, E I! 
Te =1—p+ pa pm + ete, (27) 
if we put l= Ad. 
From the expression 
oe (ty Puta A Ww) 
(GUs@) = Sizan (EO) => 7 dine (GH) 
it is evident that when h’ = 0, or when both 7? and #’ are zero, this expression cannot 
be employed. 
To find the values for these exceptional cases let us resume the equation 
When hf = 0 we have 
