76 On the Taylorian Theorem. 
And hence if the series (A) be arranged by the dimensions of 
the quantities, Aw, Aa’, Ax", ..... and the substitutions sug- 
gested by the series (B), (C), (D), (E), Sc., being made, the re- 
sult will be 
du Ax d2u Az \2 d3u 
eee (a2) ae 
is i aoa a da 1.2.3 
(s a a.’ Raeee 
dx 
In which the symbol S = signifies 
dx 
Ar Ax Aa’ 
dg age Ge 
The meaning of the symbols we ( e222 )' §c., is suffi- 
1.2 dx 
ciently obvious. 
Ne 8 
dx dx 
The series of Maclaurin may easily be inferred from it by sup- 
This becomes identical with Taylor’s series when S 
posing « = 0 and changing Az into a. 
a 
