802 am B, C. BRODIE ON THE CALCULUS OF CHEMICAL OPEEATIOXS. 



and 



^—x—x, 



X 



We thus arrive from the general properties of chemical symbols at the same result as 

 regards the forms of the symbol 1, and the interpretation of that symbol, as was infen-ed 

 from the special interpretations of each form of that symbol. 



(3) If, in the equation xy=x-\-y, x=-l and y=\, 



12=1 + 1 



and 



1 = 2. 



From this and the previous equation, = 1, it is to be infeiTed that 



0=1=2=3= n. 



It hence follows that any number of numerical symbols of this class may be added to a 

 chemical function without affecting its interpretation ; a property which will hereafter 

 be shown to admit of important applications. The reason of this is that in every inde- 

 pendent symbol of number which enters into a chemical function the chemical synnbol 1 

 is understood as the subject of operation, so that 2=2x1, and that this symbol has 

 no interpretation in weight. We have a parallel to this property of chemical symbols 

 in the property conferred upon numerical symbols by the factor 0, where 

 0=1x0=2x0=3x0= MXO. 



The chemical equation 0=1 may at the first glance appear paradoxical. But this 

 apparent paradox arises merely from the associations connected with the interpretation 

 of these symbols in those symbolic systems with which wc are most familiar. In these 

 systems there is a profound antithesis between the symbols, which reaches its climax 

 in the logical system, where is the symbol of nothing and 1 the symbol of the universe 

 of thought*. It need not, however, be a matter of surprise that in the chemical system 

 we should have two symbols for " no weight," since in that system the same ponderable 

 matter maybe denoted by xy anda:+y. Indeed it might even be expected from analogy 

 that as a real weight may have several symbols, so the absence of weight should be 

 expressed in more than one way. Nor is it, in truth, more singular or paradoxical that 

 in chemistry and 1 should be symbols denoting the same object, than that in geometry 

 af^ and 1 should have the same interpretation. 



Now it would appear that the symbols and 1 may occur in a chemical function 

 with two distinct interpretations, as chemical symbols and as arithmetical symbols, and 

 that to prevent ambiguity, it might be desirable to make evident by some special nota- 

 tion the meaning to be assigned to them. But this is not necessary. The chemical 

 symbol 1, although implicitly contained as the subject of operations in every chemical 



* Boole, « Laws of Thought,' p. 48. 



