790 SIR B. C. BKODIE 0^• THE CALCULUS OF CHEMICAL OPEKATIO>'S. 



other times as the symbol of chemical transmutation. So far as I am aware it has never 

 yet been employed with the signification which I have assigned to it, nor has the rela- 

 tion which it here expresses been recognized in the conceptions of the science, among 

 which it occupies so fundamental a position. 



(4) Furtlier, let x+xl or (x+Xj) be the symbol of the two weights A and Aj collec- 

 tively considered as constituting a single weight. Then x+x^+y+y^ will be the symbol 

 of a group of which two such weights are the constituents, and {x+Xi)-{-{y+yi) will be 

 the symbol of two such weights collectively considered, and as constituting a single 

 weight. 



Now, since the result is the same whether we add or remove a group of weights collec- 

 tively, or add or remove the constituents of the group severally, 



x-y^^=a;—y—yi, 



From this we may infer that the chemical symbols + ^^^ — have the properties of 

 the numerical symbols + and — , so that 



+ +x=+x, 

 — \-x=—a', 



a-=+^'- 



(5) Now, let W be a compound weight, of which certain portions of matter named 

 A and B are the components (Sec. I. Def. 7). Let <p be the symbol of the weight W, 

 and .r and y the symbols of the weights A and^B respectively. Further, let xy be 

 selected as the symbol of the weight W, so that 



(f)=xy; 



xy is termed a composite symbol, of which x and y are the factors. The symbol xy is 

 also termed a combination of x and y, which are said to be combined in it. 



li y=x, then (p=xx, which may also be written x-; and generally if <p be the symbol 

 of a compound Aveight of which the component weights are n weights named A, «j Aveights 

 named Aj, n.^ weights named Ag , of which x, A'j, X2, are the symbols, then 



(p=:X"x''Xt' 



If in this expression x=Xi=x.2 , 



Now, recurring to the symbol xy, since a portion of ponderable matter composed of 

 A and B is identical Avith a portion of ponderable matter composed of B and A, 



xy=yx, 

 that is to say, the order in which apposed symbols of chemical operations are written is 

 indifferent. Symbols possessing this property are termed " commutative". 



