SIR B. C. BKODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 795 



Icitter operation to be performed it is necessary that the weight A, sliould be part of the 

 weight A. 



Now since a group which is constituted of tlie weights A and Aj is identical with 

 (Sec. I. Def. 6) a group which is constituted of A, and A, .T-{-Xi=Xi-{-x. 



Also, since it is immaterial in what order the operation is performed which results 

 in the exclusion of a weight from a group x—Xi= —Wy-{-x. 



If, in the expression x — s^, Xi=x the expression becomes the symbol of a group in 

 which no weight appears ; for it is the symbol of that weight which is the result of 

 removing the weight A from the weight A, in other words, x—x is the symbol of the 

 weight A without the weight A, but the result of the successive performance of these 

 operations is no ponderable matter. By analogy of interpretation to that of the symbol 0, 

 regarded as a numerical symbol, let be the symbol of a group in wliich no weight 

 appears, and which has had its origin in the several performance of the operations x 

 and — x; so thatar— ar=0. 



The chemical symbol has the property of the numerical symbol given in the 

 identity 0-\-x=x; for the ponderable matter which results from adding the weight A 

 to a group in which no weight appears is identical with the ponderable matter A. 



Also, since a group is not affected by removing from it no weight, the symbol of a 

 group is not affected by removing from it the symbol of no weight, and 0-\-x=-\-x=x. 



The interpretation which is here assigned to the symbols + and — is strictly analogous 

 to that which has been given to them in the aritlimetical and logical systems*. They are 

 the symbols of those operations by which we form a group from its constituents, or 

 remove the constituents from a group. These operations, Avhich may be tenned the 

 operations of "aggregation" and "segregation," are found in cA'ery department of 

 thought. No uniform meaning has hitherto been attached to the symbols + and — in 

 chemistry, notwithstanding their constant use. The prevalent opinion seems to be in 

 favour of the use of the symbol •{• as the symbol of "mechanical mixture "f. It is 

 difBcult to say what may be the exact signification of this term. In the present method, 

 at any rate, no such interpretation is to be attached to the symbol, it being quite im- 

 material for the end in view whether the objects referred to be what is termed " mixetl " 

 or not. A simUar uncertainty prevails in the use of the symbol of identity J. The 

 symbol = is sometimes employed in chemistry as the symbol of numerical equality, at 



• Boole, ' Laws of Thoiiglit,' p. 32. 



t Sec Odlixq's 'ilanual of Cbemistrj-,' vol. i. p. 4. "The-sipni + signifies addition to, or ratlicr mixture 

 with." Also, "WiLUAMSoif 's ' Chemistry for Students,' p. 37. " The sign + interposed between symbols denotes 

 addition or mixture of the atoms or molecules wliich the symbols represent. Thus H + denotes a mixture of 

 1 part by weight of hydrogen with 10 parts by weight of oxj-gen." 



X OoLrao's ' Chemistry,' vol. i. p. 4. " The sign = signifies equivalency with, or rather conversion into." 

 Williamson says, p. 37, " The sign = is used in describing chemicjil changes. It only denotes equality in 

 weight between the sum of the atoms of each kind on one side of it, and the sum of the atoms of the same kind 



on the other side of it H'- + 0=H-0 means that 2 parts by weight of hydrogen added to lO parts by 



weight of oxygon; can bo made to combine to form 18 parts by weight of water." 



