SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 801 



Sectiox IV.— on the FUNDAMENTAL CHEMICAL EQUATIONS. 



(1) xy is the symbol of a single weight which is composed of the same weights as those 

 of which that group of weights is constituted of which x-\-y is the symbol. Now 

 according to the definition which I have given of chemical identity, two weights are said 

 to be identical which consist of the same weights (Sec. I. Def. 6). Hence the weight of 

 which xy is the symbol is identical with the weight of which x-\-y is the symbol ; and 



xy—x+y. 



In like manner, since - is the symbol of a single weight composed of the same weights 

 as that of which the group of weights x—y is constituted, 



X 



These equations may justly be termed the fundamental equations of the Chemical 

 Calculus, for from them chemical symbols derive their distinctive character, and, through 

 the limitations thus imposed upon them, are discriminated from numerical symbols, which 

 in many respects they resemble*. 



(2) If, in the equation xy=x-\-y, y=l, A'l=a.- + 1 ; whence since x=x\ and x—x=.Q, 

 we infer that 



0=1. 



This equation informs us of the identity of the ponderable matter of which and 1 are 

 the symbols, which has already been shown. 



The same point may be proved in a similar manner as regards the other forms of 

 the symbol 1. For since 



and 

 Or, since 



And again, since 



0=0*. 



mx=cif, 

 0=0^. 



X 



* This equation occupies a somewhat similar place in the chemical calculus to that held in the logical s3-stcm 

 by the equation x^=x (Boole, 'Laws of Thought,' p. 31), as being expressive of a characteristic property by 

 which the symbols are distinguished. The possibility of the existence of a claas of symbols, other than the 

 symbols of the logarithms of numbers, which should satisfy the condition 



■was indicated by D. F. Gkeqort in his paper " On the Real Nature of Svmbolical Algebra" (Edin. Phil. Trans, 

 vol. xiv. p. 208). This anticipation is hero realized. 



