developement of exponential functions , &c. 45 
{ «/3 |3 y .A u, 

the number of the indices a, ( 3 , {x, being ?z — 1. 
It seems hardly necessary, after what has been said, to 
notice that the developement of any function, such as 
& c.} 
in which t, V, &c. denote any number of independent vari- 
ables, \|/, 'p, &c., any functional characteristics, and n , n\ &c., 
any indices, may be accomplished by the same means — or, 
more conveniently, derived from (33) in the same manner as 
the formula (27) was obtained from our equation (2) ; and 
the result included in a brief and simple expression. The cases 
however are few, where the results afforded appear, if I may 
so express it, in their natural form, and it would therefore be 
useless at present to extend our views farther in this direction. 
JOHN F. W. HERSCHEL. 
Cambridge, Nov. 17 , 1815 . 
