SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 787 



tional to, but not identical with, the numbers which express its density. An attempt 

 lias been made to remedy this imperfection, retaining the general features of our present 

 method, but the changes proposed have never been adopted, such alterations being always 

 attended with some inconvenience, and the question at issue being one neither of theory 

 nor of fact*. 



The following pages contain the outline of a new method for the expression, by means 

 of symbols, of the exact facts of chemistry, and for reasoning upon these facts by their 

 aid. This method is quite independent of any atomic hypothesis as to the nature of the 

 material world, and in it the symbol is placed in immediate relation with the fact, being 

 indeed its symbolic equivalent or expression. It does not, however, preclude or deny 

 such an hypothesis; the question is not raised. This method may be regarded as a 

 special application of the science of algebra, and in its construction I have been guided 

 by the similar applications of that science to geometry, to probabilities, and to logic, to 

 which it presents many curious and interesting analogies. In these branches of science 

 the symbol is not a figure of the object, nor is any resemblance attempted between the 

 symbol and the thing signified by it. The symbols which I shall have occasion to employ 

 are of the same abstract character; they pretend to no resemblance to any object in 

 nature, and are simply to be regarded as arrangements of marks which it is convenient 

 to employ for the purposes of thought. The conditions to be satisfied by such a method 

 .are fev/ and simple. It is only necessary that every symbol should be accurately defined ; 

 that every arrangement of symbols should be limited by fixed rules of construction, the 

 propriety of which can be demonstrated ; and that the symbolic processes employed 

 should lead to results which admit of interpretation. 



The object of this method may be considered to be the investigation of the laws of 

 the distribution of weight in chemical changes, and the symbols here employed repre- 

 sent "weights" in the same sense as the symbols of geometry represent lines or surfaces. 

 Now the symbol a in geometry, in its primary sense, may be regarded as the symbol of 

 the operation performed upon the unit of length, by which a line is generated, that is, of 

 which the result is a line. In like manner the symbol a, as a chemical symbol, is to 

 be regarded as the symbol of the operation performed upon a unit of space, by which a 

 weight is generated, that is, of which the result is a weight. Symbols of operation 

 have not hitherto been adopted in chemistry, and their introduction forms a distinctive 

 feature of the present method, which I have hence termed " the Calculus of Chemical 

 :Operations." 



It is my intention to divide the subject into three parts. The first part, which alone 

 is here given, relates to the construction of chemical symbols. In the second part I 



* Sco I^UREST, ' Methode dc Chimic,' p. 83, English translation, p. 67. Also Mr. J. J. Waxkeston " Ob 

 Cliemical Notation in conformity with the Dynamical Theory of Heat," Phil. ilag. vol. xxvi. pp. 248 and 515, 

 and vol. xxvii. p. 273. Also " Kemarks on Chemical Notation," by W. Odliso, Ih. vol. xxvi. p. 380, and 

 vol. xxvii. p. 380. The proposition cf Mr. W.vtebston is the san.e as that of LAimEirr, and amoimts to the 

 obvious expedient of cutting the molecules and atoms in half. 



