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



are symbols not of quantities (which may be replaced by numbers), but of operations 

 (which cannot be thus replaced), which are defined by their results ; and the units of 

 ponderable matter are primarily conceived of in tliis calculus as made up from their 

 component weights by the successive performance upon the unit of space of the opera- 

 tions indicated by the symbols of those weights. 



It is through this order of conceptions that we are enabled to introduce into the 

 chemical calculus the zero-symbol 1, regarded as the symbol of the unit of space, the 

 subject of chemical operations, without which symbol, as will hereafter be still more 

 clearly evident, the construction of a chemical calculus would appear to be impossible, 

 and the absence of which symbol, perhaps more than any other defect, marks the radical 

 imperfection of the present notation. 



It is moreover from this point of view that it has been found possible to assign to the 

 composite symbol ay, as the symbol of a compound weight, an exact interpretation in 

 harmony with symbolic analogies, and it is as symbols of operation that chemical symbols 

 have been proved to possess the properties given in the equations 



xy=yx, 



xy=x+y, 



which aiFord an adequate basis for a symbolic method, and enable us to apply to these 

 symbols those algebraic processes through which symbols become an instrument of 

 reasoning. 



But further, symbols of this class aiFord the most real and the most obvious expres- 

 sion of the facts with which the chemist deals. That such operations as are here indi- 

 cated are the primary and immediate object of his study, and therefore the most essen- 

 tial particular to be embodied in the symbol, has been already, to a certain extent, 

 recognized by more than one master of the science, adverse to the atomic mode of repre- 

 sentation. Thus Geehardt, in the remarkable words which I have placed as a fitting 

 motto to this paper, thus defines the object of a chemical formula. "Les formules 

 chimiques, comme nous I'avons dit, ne sont pas destinees a representer I'arrangement 

 des atomes, mais elles ont pour but de rendre evidentes, de la maniere la plus simple et 

 la plus exacte, les relations qui rattachent les corps entre eux sous le rapport des trans- 

 formations"*. Now if this be the object of a formula, how unreasonable is it to attempt 

 the expression of that formula by symbols which not only permit, but even compel us 

 to regard it from the atomic point of view. We cannot adopt the atomic symbol 

 and at the same time declare ourselves free from the atomic doctrines. The symbols 

 which are here employed impose no such limitation upon our view. They are simply 

 the symbols of the operations, from whatever point of view these operations may be 

 regarded, by which chemical transformations are effected. In the symbol of the unit of 

 water a§, we assert an indisputable fact as to the operations by which that unit is com- 



* Chimio Organique, Paris, 1856, vol. iv. p. 566. 



