902 On Molecular Attraction. 



It can be strictly shown mathematically that it is impossible 

 to determine completely the law of attraction between mole- 

 cules from latent heat data, or in other words the law deduced 

 should contain an arbitrary function of the distance of 

 separation of the molecules and the temperature. It follows 

 therefore that if we assume a certain law of attraction and 

 deduce from it a formula for the latent heat and find that it 

 fits the facts, it does not therefore follow that the law assumed 

 is correct. In fact an infinite number of different laws can 

 be obtained, each of which gives a formula for the latent heat 

 agreeing with the facts. It is owing to this that different 

 investigators have obtained different laws for the attractions 

 between molecules. Attention was drawn to this point in a 

 paper read before the Sheffield Meeting of the British Asso- 

 ciation. A demonstration of the result stated cannot be 

 given here, and I therefore beg to refer to a paper on the 

 subject which will be published in this journal shortly. 



That we may deduce from latent heat data more laws than 

 one, can be shown by an example. Assuming that the 

 attraction between two molecules varies inversely as the 

 sqiitire of their distance of separation, Mills obtained for 

 the latent heat the formula A(/?J /3 — p^ 3 ), where A is a con- 

 stant and p u p 2 denote the densities'of the liquid and vapour 

 respectively. Now if we assume that the attraction varies 

 inversely as the seventh power of the distance, we obtain the 

 formula B(/^ — p? 2 ) for the latent heat, where B is a constant, 

 and this also agrees well with the facts ("Equation of State," 

 Phil. Mag., supra, pp. 678 et seq.). We may therefore with 

 equal justice assume that the attraction obeys the latter law. 



Further, it can be shown independently of the above con- 

 siderations that the law of Mills cannot possibly account for 

 the latent heat of evaporation, etc. According to Mills the 



attraction between two molecules is -y, where z is their 



z 



distance of separation and K a constant. The heat of 

 evaporation of a molecule may be taken as the energy 

 expended in bringing it from the interior of a large mass of 

 liquid to an infinite distance from the liquid ; for which I 

 have given a general formula, Phil. Mag. May 1910, p. 801. 



Substituting -y for ^(^(^^m^'m the formula we obtain 



z 



where m is the mass of a molecule and L the internal latent 

 heat in ergs. In the case of ether at 273° this gives 

 K = 8*9xl0" 21 dyne, K being the attraction between the 



