SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
105 
operations of which the result is the mutual exchange of the simple weights of which 
the units of matter are constituted. Here, again, if we would reason correctly, it is 
essential to discriminate between the operation and the result of the operation. The 
symbol (x—a) occurring among the factors of a chemical equation is an interpretable 
symbol, which is defined, not by reference to a hypothetical process, but as the symbol 
of an operation of which the result is the exchange of the bit of matter resulting from 
the operation a for the bit of matter resulting from the operation x. As, for example, 
the expression — £) is the symbol of the operation of which the result is the exchange, 
between two units of matter, of the bit of the matter of oxygen resulting from the 
operation £ which weighs 0715 grm., for the bit of the matter of chlorine resulting 
from the operation % which weighs T592 grm., the exchange occurring between two 
portions of matter the nature of which is not specified, hut which severally occupy in 
the gaseous condition at standard temperature and pressure the space of 1000 cubic 
centims. But this symbol cannot be interpreted as the symbol of a portion of ponder- 
able matter, for there is no reason to believe the simple weight w(<§) to be contained in 
the simple weight «;(%), and there is no external reality, as far as we are aware, corre- 
sponding to the difference w{%) — w(f). Nor, again, are we to imagine that the process 
by which this result is attained consists in the actual exchange, in their totality, of 
these hits of matter the one for the other, as we may exchange a white ball for a red 
ball. On the contrary, when the unit of hydrochloric acid ax passes into the unit of 
water a| by the process of which the final result is the substitution in that unit of £ 
for £, that unit must be regarded as passing by a process of continuous change through 
every value intermediate between a% and of, an assumption in perfect accordance with 
what we know of the gradual character of chemical changes, which are not instanta- 
neous events, but events occurring in definite periods of time. This question first comes 
under our notice when we pass from the consideration of things and of events to the 
consideration of the chemical relations of things and the chemical relations of events. 
Certain relations of the units of matter are the necessary consequence of the nature 
of those simple chemical events in which they have their origin. If we consider the 
symbols of the four units of ponderable matter which appear in a simple event of the 
second order, 
A.(x — a){y — b) = 0, 
namely, 
A xy, 
A ay, 
A xb, 
A ab, 
it appears that these symbols are the combinations of the letters x, y , a, b, taken two 
and two, combined with a constant A, and are necessarily derived by substitution the 
one from the other — A ay being derived from A xy by the substitution of a for x. 
