SIR B. C. BEODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
39 
(I. Sec. II. (1)), is an operation with one variety of which chemists are familiar under 
the name “ chemical combination.” I have not employed this language, for the terms 
are by no means coextensive ; and we should be led into unnecessary difficulties by 
restricting “ a chemical operation ” to that particular kind of “ chemical operation ” 
implied in the term “ combination ” with all the ideas which have grown up around it. 
If, however, we are willing to discard material images, and consider “ combination ” in 
a more general and abstract sense, the term will work. Let x, y, z ... be the symbols 
of the operations of chemically combining the “weights” or bits of matter, 
A, B, C, . . ., at 0° and 750 millims. pressure, then x, y, z . . . are termed the chemical 
symbols of A, B, C . . . respectively at that temperature and pressure. Also let xy 
he the symbol of the “combination” of A and B, and xyz... the symbol of the 
“combination” of A and B and C . . ., then xxx . . . is the symbol of the “combi- 
nation ” of A and A and A . . . Further let z be the symbol of the “ weight ” or 
matter contained in an empty unit of space, then zz (or z 2 ) is the symbol of the 
combination of the “ weights ” (or matter) contained in two empty units of space, and 
z v is the symbol of the combination of the “ weights ” in p empty units of space. But 
the “ weights ” in two empty units of space are collectively identical with the “ weight ” 
in one empty unit of space, being in both cases “ no weight,” and the weights in p 
empty units of space are collectively identical with the “ weight ” in one empty unit ; 
we have, therefore, z p =z, and generally xy . . . z v —xy . . . Now among the symbols 
of number we have one symbol, and one symbol alone, which satisfies the condition 
satisfied by the symbol z, namely, the symbol 1. If, therefore, we put I as the symbol 
of the “weight” contained in an empty unit of space, and work with this symbol (as a 
factor) in the algebra of chemistry, according to precisely the same rules as in general 
algebra we work with the numerical symbol 1, we shall never be led into error. My 
object in these remarks is to point out the intimate connexion which subsists between 
the principles of this Calculus and those fundamental ideas which have been developed 
by the requirements of the science*. I shall not pursue the subject, as it has been fully 
treated in Part I. Sec. III. 
The symbols of the units of hydrogen, oxygen, water, and binoxide of hydrogen, as 
thus expressed, are : — 
* The objects of chemistry, considered as an art and as a science, were defined by the illustrious Stahl 
in the following words : — “ Chymia alias Alchymia et Spagirica, est ars corpora yel mixta vel composita vel 
aggregata etiam in principia sua resolvendi aut ex principiis in talia comhinandi. 
“ Subjectum ejus sunt omnia mixta et composita quae resolubilia et comhinabilia. Objectum est ipsa resolutio 
et combinatio, seu corruptio et generatio.” — Stahl, Fundamenta Chymice, Norimbergse mdccxxiii. 
The “resolubilia” and “comhinabilia” of Stahl correspond to what is here termed ponderable matter 
[I. Sec. I. Def. (1)], while the “ ipsa combinatio ” and “ ipsa corruptio ” represent, in bis order of ideas, what 
is here termed a “ chemical operation ” [I. Sec. II. Def. (1)]. 
