798 SIB B. C. BEODIE OX THE CALCULUS OF CHEMICAL OPERATIONS. 



Also by a strictly analogous interpretation to that assigned to the symbol t^ as a 

 symbol of operation, the symbol a:{y-\-y{) is to be interpreted as the symbol of a weight 

 which results from the successive performance upon the unit of space of the single ope- 

 rations (y+yj and X. Now the result of performing the sinyle operation (y+y,) is the 

 same as that of performing severally the two operations y and y^ ; and as regards the 

 result, it is immaterial whether we first perform severally the two operations y+yj, and 

 then perform upon these two operations the operation indicated by .x, as expressed in the 

 symbol xy-\-xyy, or whether we perform the single operation (y+yi) and then perform x 

 upon that, as expressed in the symbol a;(j/+j/j). From whichever point of view we 

 regard the symbols, whether as symbols of operation or as symbols of the results of 

 operations, we are brought to the same conclusion, that 



In like manner it may be shown that 



(^+^i)(y+yi)='^+^yi+^iy+^iyi, 



(.r+^i)(y+yi) being the symbol of a single compound weight, of which the groups A 

 or Aj and B or Bj are the components. Symbols which possess this property are termed 

 distributive symbols. 



(7) Although the selection of a symbol is in a certain sense arbitrary, it is by no means 

 a matter of indifference ; and the symbol xy which is hei'e assigned to a continuous 

 compound weight, so far from being (as might be thought from a superficial considera- 

 tion) contrary to symbolic analogy, is the only symbol by which the desired end could 

 be attained, consistently with usage. The symbol xy in its abstract interpretation is the 

 symbol of the operations x and y operating successively upon the unit or subject of ope- 

 rations ; {xy) is the symbol of the same operations but operating jointly ; x-^y is the 

 symbol of the same, operations operating upon the same subject but operating severally, 

 and {x-\-y) the symbol of the same operations but operating collectively. This funda- 

 mental distinction in operations as successively, jointly, severally, or collectively performed, 

 appears in various forms in the difierent sciences, and is found in every branch of know- 

 ledge which admits of symbolic treatment. In chemistry it expresses the various ways 

 in which we may conceive of the existence of the same ponderable matter. The language 

 of symbols supplies the means of simply and adequately expressing these conceptions, 

 isolated from every other consideration, which are not only verj^ imperfectly expressed 

 by the usual molecular representation, but are there complicated by many considerations 

 which are totally irrelevant to the real point at issue. 



Sectiok in.— on the CHEMICAL SYMBOL 1. 



(1) The preceding considerations suggest the inquiry as to the symbol of a compound 

 weight of which the weight A and no weight are the components. Now, since any 

 portion of ponderable matter is not altered by the combination with it of no ponderable 



