SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEIUTIOXS. 799 



matter, a weight of which the weight A and no weight are the components is the same 

 as the weight A. Hence if x be the symbol of the weight A, and y the symbol of no 

 weight, 



• xy=-x. 



Now the symbol 1 regarded as a numerical symbol, possesses the property given in the 

 equation 



x\ =x. 

 From this correspondence of symbolic properties, and guided by the same considerations 

 of analogy as those on which the symbol was selected as the symbol of no weight, 

 regarded as the constituent of a group, I shall select the symbol 1 as the chemical 

 symbol of no weight regarded as a component of a compound weight. 



Since any portion of matter whatever may be considered as a compound weight of 

 which that matter itself and no weight are the components, if <fi be the symbol of any 

 weight, 



<p=(pl. 



The symbol 1, therefore, is implicitly contained as a common factor in eveiy chemical 

 symbol, being either expressed or understood as the symbol of the common subject of 

 all chemical operations. Now this subject of chemical operations has been defined as 

 the " unit of space " (Sec. I. Def. 11), a term already appropriated to it in language, for 

 it is in space that we conceive of the existence of ponderable matter. This interpreta- 

 tion of the symbol 1, as the symbol of the unit of space, is identical with the meaning 

 before assigned to it as the symbol of "no weight;" the only property of matter under 

 consideration being weight, by the absence of which the unit of space is defined. 



(2) The correctness of the above reasoning is further evident from the identity of the 

 other algebraic forms of the chemical symbol 1 with the algebraic forms of the same 

 numerical symbol, notwithstanding the difference in interpretation. 



We have seen that x^ is the symbol of a compound weight, of which n weights A are 



the components. Hence the symbol of a compound weight, of which (or no) weights 



A are the components, is x^. But a weight of this kind is the same as "no weight ; " 



whence 



0:0=1. 



The symbols 1 and x^ correspond to the different ways in which " no weight " may have 

 originated, the result being the same whether the operation performed do not cause 

 weight or whether an operation causing weight be not perfonued; the fonner view 

 being expressed by the symbol 1, the latter by x°. 



Again, if in the expression - (Sec. II. (5)), y=x, this expression becomes the symbol 



of a compound weight composed of the weight A withoiit the weight A, that is to say, 

 which is composed of no weight ; whence also 



X 



Tliis third form of the symbol 1 corresponds to a third origin of the absence of weight, 

 which we may also regard as effected by the simultaneous performance of inverse opera- 



5q2 



