800 SIR 11 C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 



tions upon the unit of space, the result of one of which is to cause " a weight," and of 

 the other to remove the same. A correct system will take cognizance, not of one only, 

 but of every way in which a given result can be attained. 



There is considerable difficulty in the use of language for the expression of such 

 abstract ideas, and these points would hardly become clearer by fuller explanation. Let 

 it be sufficient, in conclusion, to state that the chemical symbol 1, while it is a necessary 

 constituent of the system of chemical symbols, and may be and indeed must be employed 

 to give effect to the purposes of the chemical calculus, is not to be interpreted in weight. 



(3) An inquiry not without theoretical interest is immediately suggested by the pre- 

 vious considerations. We have ari'ived at the symbol of no ponderable matter, regarded 

 as a component of a compound weight ; what is the symbol of all ponderable matter, 

 similarly regarded 1 Now all ponderable matter is characterized by the property that 

 the addition to it of any finite weight does not alter our conception of it. Hence a 

 compound weight, of which all ponderable matter and a finite weight are the compo- 

 nents, is the same as a compound weight of which all ponderable matter is the single 

 component. Hence, if y be the symbol of all ponderable matter thus regarded, 



Now the numerical symbols and oo satisfy this condition, since 0^=0, and co^=oo ; 

 and either symbol, so far as this equation is concerned, may be with equal propriety 

 selected as the symbol of all ponderable matter. This is by no means contrary to 

 analogy. As the numerical symbols and co are symbols of which aU numbers are 

 factors, so the chemical symbols and co are symbols of which all other chemical symbols 

 are components, 



CO =XXiX2 00 , 



0=araria'2 0. 



In the same sense as the symbol 1 is to be interpreted as the symbol of space, so it Avill 

 appear, on consideration, that the symbol oo is to be interpreted as the symbol of the 

 ponderable universe regarded as a whole. Neither object can be presented to the ima- 

 gination, but, nevertheless, they are to be treated as realities in the order of ideas, and 

 appear in the chemical system as the necessary limits of our conceptions. 



(4) Similar ideas occur in every symbolic method. In symbolic chemistry 1, as the 

 symbol of the unit of space, the subject of chemical operations, occupies the place held 

 in the geometric calculus by 1, the symbol of the unit of length considered as the subject 

 of the operations of geometry. Again, the chemical symbol co holds a position analogous 

 to that occupied by the symbol 1 in the calculus of probabilities, as denoting the total 

 subject matter of the science, and the chemical symbols 1 and oo , the symbols of space 

 and of the ponderable universe, represent in the calculus of chemistry the limits between 

 which the values of all other symbols are comprised, precisely as in arithmetical algebra 

 the corresponding limits are represented by the symbols and oo , and in the calculus 

 of logic by the symbols and 1 *. 



* Booi^, 'Laws of Thought,' p. 47. 



