Mr. Herschel on various points of Analysis, 
— ] r -xdx« -I f±- 
y J \ ' 
M 
which by writing o for X, and adding a constant at each 
integration becomes, 
/ log ^ __ dx \ 
Now, if be the particular integrals of 
0 = « + 'A . Dm + "A . D”m ; (6) 
we shall have, when X= o, 
u = 'C. <'>M + . '"’m + . I’’m + &c. 
And comparing this with the expression (5), we find 
= Dlog'0„. 
= D logf 'm . . D ; 
D 
^ = Dlogf«.^«. ‘’>m.d|^.D L 
^C.)„ J 
&c = &c. 
Suppose now that by any means whatever we can discover 
n — 1 particular integrals . . . . *^w,of (6), the original 
equation deprived of its last term : then by the help of the first 
n — 1 of these equations, the values of ‘a, ... . are given. 
