SIE B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
77 
by which a chemical equation is rendered “ normal ” is a method of effecting this 
entry. 
(8) According to the reasoning previously pursued we arrive at the numerical equation 
2m=.o-\-n, 2m=n, by successively assigning to the chemical symbols a, v the value 1, 
a value common to numerical and chemical symbols; but this method is but an 
illustration of a wider principle. We may lay down the rule, that if throughout a 
chemical equation we substitute the symbol of any one “ simple weight ” for any other 
“ simple weight,” that equation will still be true. This statement does not mean that 
the symbols of all simple weights have the same meaning, and that it is indifferent 
which we employ, or that the assertion made in the equation thus modified is the same 
as the assertion made in the original equation, but that if the original equation be true, 
the new assertion made in the equation thus modified is also true. We may compare 
the two members of a chemical equation to the two pans of a balance which is kept in 
equilibrium by a system of weights of 1 ounce, 2 ounces, 8 ounces, 1 lb., 2 lbs., 3 lbs., 
and the like in each pan, the same number of weights of each kind being in the two 
pans respectively. The equilibrium of the balance is not only unaffected by any change 
in the distribution (or arrangement) of the weights in each pan, but is also unaffected 
by the simultaneous removal from each pan of all the weights of the same kind, or by 
substituting weights weighing 1 lb. for the weights weighing 1 ounce, or any analogous 
substitutions. At first sight it would appear that the chemical symbol 1 should be 
excluded from the operation of this rule ; for it is not the case that in the normal 
equation 
1 +xy=x+y, 
where the symbol 1 appears we may write x (although where x appears we may write 1), 
and that the resulting equation should still be true. The reply to this difficulty is that, 
in order to arrive at the above equation, we have tacitly assumed the truth of the 
equation 1 P =1, and that the equation in the above form is really imperfect. If, 
however, we render the equation homogeneous, remembering that ro- p =l, whatever be 
the value of_p, we have for the complete equation 
cr 2 -f- xy — Xrs -f- y7&, 
to which the rule is applicable. 
Section II.— ON SIMPLE AND COMPOUND EVENTS. 
(1) Through the transformation of equations, described in the last section, the 
Chemical Calculus is finally constituted as a symbolical method adapted to algebraical 
reasoning. I shall now proceed to consider, in the light of these principles, the nature 
of the fundamental conceptions through which we are to reason as to the phenomena 
of chemical change. Here, again, pursuing the method employed in the first part of 
this Calculus, I shall endeavour to assign a precise meaning to the terms employed, arid 
accurately to define those conceptions. But in this case the notions themselves are so 
m 2 
