THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 43 
To transform from ((4, h, c)) into (2, 7, c) 
we have 
(—i') _(W=7) 
(2,0,@0) =O (2, lo c)) = Dhow KG h’,¢)). 
Here, 7 is the constant, and /’ the variable; and for the different values of /’, begin- 
ning with h’ = 7, 
we find 
(0) ((’—1) —7)) 
(40,6) =JSyv (4,0 6)) + Serax  ((47—1,¢)) + ete. 
((/+1)—v)) 
> Fussy ((%, v +-1, ¢)) + ete. 
The expression 
(mm jm nei aii re 
= weet (1 soe _— : + ete.) 
1. .2..m 1.m-+1 1.2.m-+_1l.m--2 1.2.3.m+1.m—+2.m-+3 
(m) 
enables us to find the value of -/,, for all values of m. 
A simpler method can be obtained in the following manner : 
Patting c's -Y) in the form 
(1) (-1) (2) 
aie) ges © (—2) 
JEP? = Y—S,.-¥! +5.c-Y tJ .-y + ete. 
— é e€ 
hy hy 
we have, for the differential coefficient relative to y, 
e ae nety—y) (1) (2) (1) - be (2) A 
he(lt+y) c's HJ, 2.+2.5,..yrete +S ..y?— 2S, ey ete. 
If we multiply the second member of the first equation by h{ (1+ y~), we have 
an expression equal to the second member of the second expression, and by comparing 
the two we find 
(22) 
