1818.] Traitc de Physique expcrimentale et Mathcmaiique. 59 



the discussion of the controverted questions which necessarily 

 forms a considerable proportion of all publications of this de- 

 scription. But to those who are not in possession of the work 

 it may be impoitant to know what are the subjects on which M. 

 Biot treats, although we may be able to give little more than 

 a mere table of contents. 



This work contains about 2300 closely-printed octavo pages in 

 a small type It abounds much in theoretical discussions, and 

 in refined speculations ; and, on all occasions where they 

 could be introduced, the author employs mathematical reason- 

 ing and algebraical notation. Some extracts have already 

 been given from the dedicatoiy epistle to Berthollet, in 

 which he enters into a formal defence of the propriety of 

 this method of proceeding. He admits that it is useless to 

 employ an algebraical notation to express results which are so 

 simple that they may be announced, comprehended, and appre- 

 ciated, in simple and direct terms. It is still worse, or rather 

 positively objectionable, to combine in this way parts or ele- 

 ments which are in themselves vague or hypothetical ; for by 

 doing so, " we only realize uncertainty, and give a body to 

 error." But when we have observed with sufficient precision the 

 different modes of the same phenomena, and have obtained cor- 

 rect numerical expressions of them, what inconvenience, he 

 asks, can there be in uniting them by a formula, which may 

 embrace the whole ? When they are capable of being reduced 

 to a simple law, but when this cannot be immediately perceived, 

 is not this the best method of discovering it ? Whereas, on the 

 contrary, if the nature of their relations be essentially compound, 

 which is commonly the case, is it not the only means which we 

 possess to connect them into one whole, " and to obtain a 

 common expression, which may be afterwards introduced, with 

 all the generality of its indeterminateness, into the analysis of 

 other phenomena, in which the first may bear a part ? " To 

 these remarks every one must assent ; but they do not decide 

 the point respecting the propriety of M. Biot ? s method, because 

 it is a question of degree, rather than one of an absolute nature. 

 No one will deny the propriety of introducing mathematics into 

 all the departments of natural philosophy : in some they form 

 the necessary foundation of the whole superstructure ; and in 

 all of them there are parts which, by this means, can be placed 

 in a clearer light, and have their relations better illustrated, than 

 by any other mode of expression. We must, however, confess" 

 that we are amons; the number of those who think that the 

 sparing and cautious introduction of mathematical expressions 

 into general physics is favourable to the progress of knowledge ; 

 for, although we may gain something on the score of accuracy 

 and conciseness, we place science out of the reach of many who 

 might profit by it, and might in their turn contribute to its ad 

 vancement. 



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