64 
SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
Section I. 
(1) Our total information as to the identical relation of ponderable matter is com- 
prised in a system of equations constituted upon the principles explained in Part I. 
Section VI. When we are adequately impressed with this important truth a chemical 
equation becomes a study of transcendent interest, and we are led to consider in a new 
light the purport and significance of its algebraical properties. Now even the science of 
Algebra itself has been defined as consisting but in the “ analysis of equations,” from 
which new truths are continually in process of evolution, and to the study of which all 
other objects of the science may be regarded but as accessory and subordinate. The 
same is emphatically true of the algebra of chemistry ; and the most essential and cha- 
racteristic feature of the Chemical Calculus, by which it is fundamentally discriminated 
from other modes of considering the science, is that in it we do not, as in the atomic 
theory, reason by the intervention of material images, but, setting aside all preconceived 
ideas, we base our arguments upon the equations themselves, and elicit from them, by 
the application of algebraical processes, the laws and principles which they implicitly 
contain. 
Now I have been very unwilling to introduce irrelevant matter into a complicated 
subject ; and in the first part of this Memoir, at the risk of some misapprehension, I 
have entirely confined myself to the consideration of questions the determination of 
which was essential to the end immediately in view, the “ construction,” namely, “ of 
chemical symbols.” But before proceeding further with the subject, it is necessary to 
recur to the fundamental principles of the method, and to discuss a question referred to 
in Part I. (Section IV. (5)), and there postponed, namely, under what conditions the 
operations of algebraical multiplication and division may be performed upon chemical 
equations. 
The nature of such an equation, and the principles on which such equations are to be 
constructed, have been fully explained (Part I. Section V.), and it is only necessary to 
remind the reader that by a chemical equation is here meant an equation of the form 
v=m<p +m , <p 1 +m''<p 2 +wV' , <p 3 + ... =0, 
where 
<p =a p b r 'C p 2 . . ., 
tp^a^b^ c 23 . . ., 
<p 2 =a r b r ' <f 2 . . ., 
<p, <p n <p 2 . . . being the symbols of the units of matter, a, b, c . . . the symbols of simple 
weights (Section I. (8)), and . . . q, q 2 . . . r, r u r 2 . . . positive integers, and m, m’, 
m! 1 , ml". . . numerical symbols, positive or negative, satisfying the conditions afforded by 
the system of indeterminate equations : 
