SIR B. C. BEODIE ON THE CALCLTLUS OF CHEMICAL OPERATIONS. 811 



standard of absolute or relative weight be previously determined, so in the latter cage 

 also it is necessary tliat some one simple weight shall be selected from external consi- 

 derations as the standard of comparison, before any statement can be made upon the 

 subject. This case, however, differs from the preceding in the circumstance that the 

 selection of a simple weight is not the choice of an arbitrary unit, to be determined by 

 •considerations of convenience alone, but involves the assertion of a hypothesis as to the 

 actual composition of the chemical units of ponderable matter, which may be verified 

 and tested by experience. 



Now the hypothesis on which the present method is based, and which is the only 

 assumption of the kind which I shall have occasion to make, is that the unit of hydrogen 

 is a simple weight, that is to say, that in chemical transformations this weight is never 

 distributed (Sec. I. Def. 12). The symbol of this " weight" (Sec. I. Def. 3) will be 

 expressed by the letter a, which may be termed the " modulus " of the symbolic system, 

 it being that symbol by which the form of eveiy other symbol is regulated. The abso- 

 lute weight of the portion of ponderable matter thus symbolized, that is to say, of 1000 

 cub. centims. of hydrogen at 0° C. and 7G0 raillims. pressure, is 0-089 grm. 



In considering this question I shall select certain examples which may serve to illus- 

 trate the way in which the subject may be treated, and the difference in the result 

 anived at, according to the degree of information supplied to us by experiment. 



The first, and for the present object the most important, group of symbols to be con- 

 sidered are the symbols of those elements of which the density in the gaseous condition 

 can be experimentally determined, and which also form with one another gaseous com- 

 binations. I shall then consider the symbols of carbon and its combinations with the 

 previous group, and subsequently the symbols of certain other elements and their com- 

 binations as to which Ave possess less adequate information. 



(2) Symbol of Oxygen. — It is known from experiment that 2 units of water can be 

 decomposed into 2 units of hydrogen and 1 unit of oxygen. We hence infer the identity 

 of the weights of which these portions of ponderable matter consist, and putting 



<p as the symbol of the unit of water, 

 (pj as the symbol of the unit of hydrogen, " 

 ^2 ^s the symbol of the unit of oxygen, 

 2^=2^1+^2. 



Now, if possible, let 



?i = a, 



f2=aT', 

 where u and | are prime factors, that is to say, the symbols of simple weights, and 

 w, mj, n, «i positive integers. Then 



2a'"?'"> = 2a+aT', 

 and from the fundamental equation which connects chemical symbols, a;-{-y=d'^ 

 (Sec. IV. (1)), 



(a'"S""j2_aVf', 



