Mr. Herschel on the 
a similar notation being used, for f(t) and/'(/), changing 
only A into a and a '. It is evident then, that 
A 
X 
a 
. a' -* 1 “ ci . a! -I- ..... <2 . a! . 
O X * I X — 1 ■ X 0 
In this equation, substituting for A^ &c., their values drawn 
from (13), we find 
F( 1 + ak=/(i 4 a y.f( 1 + A y+ 1 + Ay.f(i + a y-i 
4 &C. 
This equation may be abbreviated, upon the principles we 
have all along adopted, by a very simple and convenient arti- 
fice of notation, viz. by applying an accent to one of the A and 
also to the corresponding 0 ; these accents not altering the 
meaning of the symbols, but solely pointing out those which 
are to be applied to one another. The second number of this 
equation then becomes 
/(l+A)o°./'(x+A')o'* +y/(x+A)o./' (l+A')o' x-I +&c. 
in which the symbols of operation may now, without confu- 
sion, be separated from those of quantity, when it will take 
the form 
/ ( 1 + A ) »/ # ( 1 + A' ) [ o' x + “ • o '*— 1 4 & c - } 
And our equation becomes 
F (l+A>'=/(l+A) ./' (x+a')[H-o'}' ; (15) 
We must here notice, that the second member of this equation 
is precisely what the first would become, if, instead of F(i-}-a) 
we had written /( 1 4* A) .j* (1 4 A), its equivalent , and in- 
stead of 0 the symbolic expression 040 which is equal to it 
in quantity, and then applied the former A to the former 0, 
and the latter to the latter, by the method of accentuation 
