794 SIE B. C. BBODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 



A " distiibuted weight " is a weight which, in such a system of events, is resolved into 

 two or more weights or made up from such weights. 



An " undistributed weight " is a weight which, in the same system of events, is not so 

 resolved or so made up. An undistributed weight may also be defined as a weight 

 which is resolved into one weight, or made up from one weight alone. 



This division of weights into distributed and undistributed weights is coextensive with 

 the previous division of the same into compound and simple weights. A distributed 

 weight is necessarily a compound weight, for we can always assert its identity as a whole 

 with the parts into which it is distributed; and a weight which is not distributed 

 can only be regarded as a simple weight, for, by hypothesis, no information is supplied 

 to us from the system of events under consideration, which enables us to assert its 

 identity with any other weights, such an assertion in every case being purely relative to 

 the facts before us, and open to modification by the acquisition of further knowledge. 



It is essential to remark that the previous definitions are definitions of abstract con- 

 ceptions, which have immediate reference to the symbolic method developed in the fol- 

 lowing section, for the construction of which they afford an adequate basis, and which 

 is necessarily more comprehensive than those special subjects of physical investigation 

 to which it is hereafter to be applied. 



Section II.— ON THE SYMBOLS OF CHEMICAL OPEKATIONS. 



Having explained the nature of those objects and relations which fall under the con- 

 sideration of the chemist as the investigator of the laws of the distribution of weight, I 

 proceed to consider their symbolic expression. 



(1) Let a chemical operation be defined as an operation performed upon the unit of 

 space, of which the result is "a toeight" (Sec. I. Def. 3), and let x, x^, x^ be the symbols 

 of such operations, of which the weights A, A,, Ag are the results. Then the symbols 

 of operation, x, x-^, a^g, are termed (for bre^dty and convenience) the symbols of the 

 weights A, Aj, A2. 



Any symbolic expression into which the symbols of chemical operation enter is termed 

 a chemical function. 



(2) Two chemical operations are said to be identical of which the results are identical 

 as regards weight (Sec. I. Def. 6). Now let the symbol = be the symbol of identity. 

 Hence if the weight A be identical with the weight Aj, x=Xi. 



(3) Further, let the symbol + be the symbol of that operation by which a weight is 

 added to a weight so as to constitute with it one group (Sec. I. Def. 5) ; and let the symbol 

 — be the symbol of that operation by which a weight is removed from a group of weights. 

 These operations are expressed in language by the words " and" and "without." 



From these definitions x-\-x-^ is to be regarded as the symbol of a group constituted 

 of the two weights A and Aj, and x-\-x, that is, 2x, is the symbol of two weights A, and 

 x—X]^ is to be regarded as the symbol of the weight A without the weight Aj. For this 



