SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 857 



posed and decomposed in the actual system of chemical transformations. The symbol 

 asserts that the unit of water is composed by two indivisible operations — indivisible, that 

 is, so far as our experience extends — operating successively upon the unit of space, which 

 are known to us through their results and are defined by their results. Again, we 

 assert that the units of certain other substances are similarly composed, the units of 

 hydrochloric acid and of hydrosulphuric acid, for example, of which a;^ and a6 are the 

 symbols, and that in this respect these substances are similar to water. Or, again, we 

 say that the units of hydrogen, of water, and of peroxide of hydrogen are connected by 

 a certain serial relation between the operations by which they are composed which is 

 given by the interpretation of the symbols a, «&, a|2, and that this relation is similar to 

 that which exists between the units of hydrogen, hydrochloric acid, and chlorine, a, u^, 

 a^^. Now these are those very relations " qui rattachent les corps entre eux sous le 

 rapport des transformations," which Gekhardt discerned to be the true object of 

 symbolic expression, but which are not indicated, except accidentally, by our present 

 system, which is based upon a different order of ideas. 



But there is another aspect of the science equally real with that in which Gekhardt 

 regarded it, and which he declined to consider. Surely we may be permitted to ask 

 with DAiiTON, not only by what operations water is composed, but what water is ? What 

 is the nature of ponderable matter as revealed to us by the science of Chemistry 1 To 

 this inquiry also, in the only form in which such an inquiry is real and intelligible, the 

 symbol supplies an answer. This answer is given by interpreting the symbol with 

 reference to the results of the operations. The unit of water (Sec. I. Def. 10), we may 

 reply to such a question, is an integral compound weight (Sec. I. Def. 7) of which the 

 whole is identical with the two simple weights (Sec. I. Def 8) a and | of Section VII., 

 which we recognize as simple weights from the fact that in the total system of chemical 

 transformations these weights are not distributed (Sec. I. Def. 12). The science of 

 Chemistry, we may add, affords no further information whatever as to the composition 

 of water than that which is comprised in this assertion, which is not only the true but 

 the only real form of answer which it is possible to give to inquiries as to the chemical 

 composition of ponderable matter. There is no difference whatever, as regards facts, 

 between this and the preceding statement ; the difference lies in the way in which the 

 facts are regarded. From the former point of view we consider the operations, from 

 the latter the result of the operations. The symbols of geometry have a similar double 

 interpretation. They may be regarded, with equal truth, as the symbols of lines and 

 surfaces, or of the operations by which lines and surfaces are generated. 



A symbol, however, should be something more than a convenient and compendious 

 expression of facts. It is, in the strictest sense, an instrument for the discovery of 

 facts, and is of value mainly with reference to this end, by its adaptation to which it is 

 to be judged. Now in the present paper I have considered not only the principles of the 

 chemical calculus, as regards the formal construction of symbols, but also the primary 

 application of these principles to the construction of a special symbolic system. In 



