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XLVI.—On an Application of Mathematics to Chemistry

  • Alexander Crum Brown

Extract

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 mathematical 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.

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page 693 note * It is not by any means certain that this is true, even in the case of the simplest operands; it is almost certain that it is not true in the case of complex operands; but as we have not sufficient data to enable us to form a theory connecting the order in which operators are applied to a molecule with the parts of the molecule upon which they act, I have provisionally assumed the simplest possible law.

page 695 note * There is an obvious and important difference between direct and inverse operators, which I may mention here.

If we represent as direct those operators only which express direct processes which can be performed so as to get ϕ·a by acting on a, it is plain that if ϕ includes the physical conditions of the process, ϕ·a can have only one value. It may have a number of conceivable values, and it is the business of the experimental chemist to find out which of these is the real one; but ϕ −1a may have more than one real value, for ϕ −1 is not restricted to mean one actual process capable of being performed, but any process, such that ϕ −1a shall be by the process ϕ (performed on the part of the molecule, introduced or modified by ϕ −1) reproduce a. Thus, if ϕ be the addition of H2, and a be alcohol, ϕ −1a may represent either aldehyde or oxide of ethylene, for both of these give a when treated by the process ϕ. Examples of this kind might be multiplied to any extent.

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Earth and Environmental Science Transactions of The Royal Society of Edinburgh
  • ISSN: 1755-6910
  • EISSN: 1755-6929
  • URL: /core/journals/earth-and-environmental-science-transactions-of-royal-society-of-edinburgh
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