90 
SIB B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
which may be written thus 
a { a ^)X + an* = a(ax 2 t; 2 )&)x + cuofo 
whence 
a (a* 2 f 2 ~ *>)(% — ®)= 0. 
In this event, therefore, a is necessarily to be regarded as “ constant,” and the event 
is to be referred to one of two “ causes,” namely, the exchange of ax 2 £ 2 for co or of 
for a. 
If also x=y , the equation becomes 
A(x—af=0, 
the two causes of the event being identical, and 
Ax 2 + A a 2 = 2 A ax. 
Such an event is the following : — 
Example : — A unit of chlorine and a unit of iodine are identical with two units of 
chloride of iodine ; thus 
ax 2 + au 2 =2axcu, 
whence 
a U—‘ *) 2 =0- 
In this event a is “ constant ; ” the event occurs by the substitution of u for and occurs 
in two ways by that substitution, as is evident on inspecting the equation. 
(9) If in the above equation a= 1, so that the equation becomes 
A{x-l){y-b) = 0, 
one of the “causes” of the event is the substitution of 1 for x. Now the symbol 1, 
being interpreted as the symbol of the “weight” or matter which occupies an empty 
unit of space, is the symbol of “ no weight and this “ cause,” therefore, is the substi- 
tution of “ no weight ” for the weight which results from the performance of the 
operation x. A substitution of this kind will be termed “ a transference.” Thus we 
should say that the above event occurred either by the “ substitution ” of b for y, or by 
the “ transference ” of x. 
In introducing this term it is necessary to guard against the supposition that “ a 
transference ” is here regarded as a new and peculiar phenomenon distinct from a 
“ substitution.” This is not the case ; every “ transference ” is a “ substitution,” although 
every substitution is not a “ transference.” This distinction is, however, really inherent 
in the received theory of “substitution” or “double decomposition,” as explained even 
by the most competent chemists. Thus Kekule indicates as a blot on the theory of 
“ double decomposition,” that this theory is inapplicable to cases of “ direct addition,” 
or applicable only with the greatest violence “ nicht (oder nur hochst gezwungen) 
anwendbar ” [Kekule, vol. i. p. 142]. In this Calculus the distinction is not abolished, 
