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" extend considerably beyond the Science to which they 

 " primarily belong, and no proposition is so purely theo- 

 " retical as to be incapable of being applied to practical 

 " purposes. There is no apparent connexion between 

 " duration and the cycloidal arch, the properties of which 

 *' have furnished us with the best method of measuring 

 " time ; and he who has made himself master of the 

 " nature and affections of the logarithmic curve has ad- 

 " vanced considerably towards ascertaining the propor- 

 " tionable density of the air at various distances from the 

 *' earth. The researches of the Mathematician are the 

 " only sure ground on which we can reason from experi- 

 " ments ; and how far Experimental Science may assist 

 *' commercial interests is evinced by the success of manu- 

 " factures in countries where the hand of the artificer 

 " has taken its direction from the Philosopher. Every 

 " manufacture is in reality but a chemical process, and 

 " the machinery requisite for carrying it on, but the 

 " right application of certain propositions in rational 

 " mechanics." So far your Academician. Every sub- 

 ject, therefore, whether in its usual acceptation scientific 

 or otherwise, may have a mathematical aspect ; as soon, 

 in fact, as it becomes a matter of strict measurement, 

 or of numerical statement, so soon does it enter upon 

 a mathematical phase. This phase may, or it may not, 

 be a prelude to another in which the laws of the 

 subject are expressed in algebraical formulae or repre- 

 sented by geometrical figures. But the real gist of the 

 business does not always lie in the mode of expres- 

 sion ; and the fascination of the formulae or other 

 mathematical paraphernalia may after all be little 

 more than that of a theatrical transformation scene. 

 The process of reducing to formulas is really one of abs- 

 traction, the results of which are not always wholly on 



