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XL VI. — On an Application of Mathematics to Chemistry. By Alexander 



Crum Brown, M.D., D.Sc. 



(Read 18th February 1867.) 



Prefatory Note, added June 24, 1867. 



Since reading this paper, I have seen Sir Benjamin Brodie's paper on " The 

 Calculus of Chemical Operations," read before the Royal Society of London. 



The two papers resemble one another, merely in being applications of mathe- 

 matical language to chemistry. They entirely differ in method, object, and 

 result. 



I may here mention, what I have omitted to state explicitly in the paper, that 

 I have no idea of attempting to substitute a functional notation for that in common 

 use. I only propose to use a functional notation to express certain general and 

 serial relations in those cases where the common atomic notation is inconvenient 

 or obscure. 



The full application of Mathematics to Chemistry can only be made when a 

 fundamental physical hypothesis is discovered, from which, by means of mathe- 

 matical methods, results may be deduced which coincide with the observed facts 

 of chemistry. In the meantime, however, a profitable application of mathematics 

 may be made in another direction. Mathematics is the science by means of 

 which consequences are deduced from laws ; and although we have not, as yet, 

 discovered the laws of chemistry, we have what may represent them, — approxi- 

 mate generalisations. To these we can apply mathematical methods, or at 

 least we can express them in mathematical language. 



I. — Definition of Symbols. 



The objects of chemical study are of two classes — 1st, substances; and 2d, 

 processes performed on these substances. In this paper I shall represent the former 

 as operands, and the latter as operators ; where the contrary is not specially 

 mentioned, a single operand symbol will be used to indicate one molecule, or 

 chemical unit of a homogeneous substance. 



An operator <p is defined by the chemical equation or equations connecting a, 

 and (p-a, a being a molecule of a substance, and cp-a the result of applying the 

 process (p to it. Thus if the chemical equation be a + KHO = (p'a + H 2 0, the 

 process <p as applied to a, is the union of a with a molecule of caustic potash and 

 the simultaneous elimination of a molecule of water. 



VOL. XXIV. PART ITT. 9 B 



