4.58 MOSSOTTI ON THE FORCES WHICH REGULATE 
(1) 10, 
1 1 i 
OF eo earch. eee 
the last of these quantities will satisfy the equation (4:), and will be its 
complete integral. 
If the successive substitutions are performed, and, for brevity’s sake, 
we make 
it) a (é—4) 
Gy? oye re 1)'s (Eres pga Bia et 
i+1 
[7a] 
(0) — 
which gives, in the particular case of s = 2, a; = [ + : = a » we 
z 
shall have 
(0) @ (1) - Q” (2) e Q. ( O 
rae ae : a. r ) gq? 2; 
eee py a, io ete ular, 
r Paes rT 2 dr dr 
Now if we make 
(0) (1) (2) (i) 
a; a; a Lae ar 
! =o sed a 
Q, (7) = a A ee? Ag Stele SL "0 ee \., 
(0) (1) (2) (i) 
a; a; a; a; f —ar’ 
! aves er se z 
ao) = 4a ater iatce Syl stale + 0 fhe : 
where @ is put instead of A\ / a we shall have 
QW, = 71',2;(7') + Vi! (7), 
and the expression for /’ may take the form 
(ee) Tr 
(5) F=3% Dae f = 0, (7) Trt) de! 
° a ° °o 
7 dr! 
n oo (7 i 4 ! ! ! 
+r Pbatiet iar oem P,, sin di'dy 
* The brackets are here employed in the same way as in Vandermonde’s no- 
tation. 
