792 SIB B. C. BEODIE OX THE CALCULUS OP CHEMICAL OPEEATIONS, 



the mind recognizes at once when stated, by some special intuition, as " flowing from 

 the idea of substance"*. As to the nature of this process we are left in the dark. 

 However, such assumptions are happily as unnecessary as they are unmeaning, and it is 

 sufficient for all the objects of science if we admit this axiom to be the undoubted 

 acquisition of those combined processes of reasoning and observation which are the only 

 sources of exact knowledge. 



7. A " compound weight" is a single weight of which the whole is identical with two 

 or more weights. Such weights are termed the components of the compound weight, 

 whicli is said to be composed of them. 



It follows from this definition that every part, individually or separately considei'ed, 

 of a compound weiglit is proportionally identical with the same weights of which the 

 totality is composed ; that is to say, if the whole of a compound weight be identical with 



the weights A and B, -th part of that compound weight, in whatever way the division 



into parts be effected, is identical with -th part of tlie weight A and -th part of the 



waight B, and is similarly composed of those parts ; and also it is to be inferred that if 



every -th part of a single weight be identical with -th part of a Aveight A and -th part 



of a weight B, the whole of that single weight is composed of the weights A and B. 



A group of two or more weights may, in the sense of this definition, be regarded as a 

 compound weight, if only every constituent of the group have a common component. 

 Thus, for example, a group consisting of two portions of matter, of which the one is 

 composed of A and B, and the other of A and C, may be regarded as a single weight 

 (Sec. I. Def. 4) of which the totality is composed of A and B or C ; for if, regarding the 

 group as one object, we agree not to effect the separation of its constituents, every 



-th part of that weight satisfies proportionally the same condition. 



Some difficulty may perhaps be felt in assenting to the above reasoning, from a certain 

 ambiguity in language in the use of the conjunctions " and " and " or." That these 

 conjunctions have the same meaning, so far as the purposes of enumeration are concerned, 

 is apparent on enumerating the constituents of a group with each conjunction. The 

 language of symbols is free from this ambiguity, the two conjunctions being represented 

 by one mark, as will hereafter be explained. 



8. A " simple weight" is a weight which is not compound. It may also be defined 

 as a weight which has only one component. Two weights are said to be simple in 

 regard to one another which have no common component. 



9. An " integral compound weight" is a weight which is composed of an integral 

 number of simple weights. 



* See Whe-well's ' Philosophy of the Liductive Sciences,' vol. i. chap. iv. p. 412, ed. 1847, " On the Appli- 

 cation of the Idea of Substance in Chemistry." 



