370 PROCEEDINGS OF THE AMERICAN ACADEMY § 5 



A special device must be invented for approximation in 

 each particular case; and although a solution of this sort 

 is of course worthless for purposes of demonstration, 

 it will be sufficient to show whether the facts are 

 satisfied or not by the theory within reasonable limits, 

 and if the error, introduced by the complexity of a mole- 

 cule in a given case, is found to be small as compared to 

 the whole quantity, we may suppose that any small mis- 

 take in the elimination of this error will have still less 

 influence in the result. 



We have reason to expect, a priori, that in any simple 

 liquid the latent heat Avill be less than its uncorrected value 

 by not more than fifty per cent.; and if we allow for a 

 mistake of even twenty per cent, in calculating the correc- 

 tion, we ought not to be in error by more than ten per 

 cent, in the result. 



When the latent heat has been determined, we ought 

 to be able to supply either the elasticity or the coeffi- 

 cient of expansion, with the same degree of approximation, 

 wherever formula II. of § 2 applies. If a liquid be not 

 simple, but compounded (chemicall}') of two, difl:ering 

 widely in their properties, especially if the union be not 

 very intimate, we may shorten the calculation by treating 

 the compound liquid as a mechanical mixture of its com- 

 ponents. Thus ethyl h3-drate (alcohol) may be treated 

 as a mixture of 18 parts water and 74 parts ethyl oxide 

 (ether), whereas the latter (ethyl oxide) would not be 

 treated as a mixture of ethylene and water, even if we 

 possessed the necessary data. 



§ 5. In applying the rules and formulae of the preced- 

 ing sections, it must be remembered that they were estab- 

 lished on the assumption, which has not so far been 

 questioned, that the ultimate atoms are perfectly elastic. 



