152 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN 



in which the atoms of these substances are related to each other, but something 

 more than this is implied in the term constitution, as we have used it above. For 

 this involves not only the " structure," or the arrangement of the equivalents in 

 atoms and in mutually united pairs, but also what we may call the potential of 

 each pair of united equivalents.* For instance, the structural formula of formic- 

 acid is 



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 which indicates — 1st, That the four carbon equivalents form one atom, the four 

 oxygen equivalents two atoms, and the two hydrogen equivalents two atoms ; 2d. 

 that these equivalents are united in pairs, thus— co, co, co, ch, ho, but it does not 

 in any way indicate (and we do not know) what is the ffotential of each of these 

 pairs— that is, how much energy would be required to separate the equiva- 

 lents from each other. We know that this potential depends upon the structure, 

 and we can to a certain extent trace the nature of this dependence, but we cannot 

 as yet express the potential numerically, or give a rule for finding its value from 

 the structure, and till we can do this we do not fully know the constitution. 



But even the structure of the majority of substances is not at all, or only very 

 imperfectly known, and this is especially the case with those whose physiological 

 action has been most fully investigated, such as the natural alkaloids. 



Seeing, then, that we could not follow the direct road of induction, it occurred 

 to us that a by-path might be found, by making use of a method resembling in 

 its main features a mathematical calculus of finite variations. This method con- 

 sists in performing upon a substance a chemical operation which shall introduce 

 a known change into its constitution, and then examining and comparing the 

 physiological action of the substance before and after the change. We may 

 express this in mathematical language thus : — Let C represent the constitution 

 of the original substance and $ its physiological action. After the operation, C 

 becomes C + AC and $ , $ + A$. Here AC, $, and <£ + A$ are known, and by 

 applying the method to a sufficient number of substances, and by varying AC, we 

 might hope to determine what function <£ is of C. The only reason why this 

 method is not a strictly mathematical one is, that we cannot express our known 

 terms AC, $, and <£ + A$ with sufficient definiteness to make them the subjects 

 of calculation. Eut although, on this account, we cannot obtain an accurate 

 mathematical definition of/ in the equation <£ = /C, we may be able, in an approxi- 

 mate manner, to discover the nature of the relation. 



In applying this method, w r e must select a chemical operation which satisfies 



* More correctly, " the exhaustion of the potential energy" of each pair of united equivalents. 

 See Thomson and T.ut's Treatise in Natural Philosophy, § 547. 



