268 Researches on some important Points 



degree of probability, and sure methods of determining the truth 

 among different, equally probable, hypotheses. 



By directing our observations in a suitable manner we have 

 discovered simple relations between pheenomena, the connexion 

 of which had not been previously attended to. The many points 

 of view under which these phaenomena may be considered, pre- 

 clude our embracing the whole at one time ; but we have thought 

 that it might be useful, in the interim, to make knovvn the results 

 we have obtained. 



These first results relate to specific heats. The determination 

 of this has been the object of the labours of many philosophers. 

 The attempts hitherto made to discover some laws in the specific 

 heats of bodies have all been unsuccessful. It is not uncommon,for 

 example, to meet with numbers, in the best tables, three or four 

 times as great as they ought to be. 



Our first cure was directed to what could render the measure- 

 ments that we were to use as accurate as possible. Among the 

 methods of determining the capacities of bodies, those in which 

 the melting of ice, or the mixing of bodies with water, are em- 

 ployed, may doubtless, if properly conducted, lead to very exact 

 results ; but most of the substances on which it is indispensable to 

 operate, can seldom be obtained in sufficient volume to enable us 

 to apply these methods; and it was therefore necessary that we 

 should have recourse to a different one. That which we have 

 chosen appears to unite all the requisite conditions. It is founded 

 upon the law of cooling. 



It is well known that there exist between the times of cooling 

 of different bodies placed in the same circumstances, and the 

 specific heats of the same bodies, relations in consequence of 

 which the ratio of the capacities may be deduced from that of the 

 times of cooling. Mayer first applied this principle, and satisfied 

 himself that the capacities determined in this way differ little from 

 those obtained for the same bodies by the method of mixture. 

 Leslie, who adopted this method, pointed out an additional pre- 

 caution, of which Mayer did not suspect the necessity; viz. to in- 

 close the body operated on in an envelope, which must always be 

 the same, to prevent the error which would result from inequa- 

 lity in the radiating power of the surfaces. The most important, 

 however, of all th.e causes of uncertainty, and to which neither of 

 these philosoj)hers paid any attention, is that^vhich results from 

 the unequal conductibility of the substances that are compared. 

 This cause has the less influence the smaller the volume of the 

 bodies on which we operate, and the slower the heat is permitted 

 to make its escape. The aim then should be to fulfil both of 

 these conditions ; but it is difficult to reconcile them, because, 

 when we diminish the volume of the body, we augment the velo- 

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