90 Dr. R. D. Kleeman : Determinations of the Law of 



molecules, it should be identical with the attraction we are 

 considering. Now the gravitational attraction of two ether 

 molecules one cm. apart is 1*84 x 10~ 51 dyne, which is a 

 much smaller quantity than K 2 . Thus the gravitational 

 attraction would have to be about 10 3i times its actual 

 value to account for the latent heat o£ evaporation. It 

 follows therefore that the molecular attraction must decrease 

 at a much greater rate with the distance from the molecule 

 than that given by the inverse square law. 



That Mills 5 law cannot be true follows also from surface- 



tension considerations. If — | is substituted for <£(z)(2 ^m^) 2 



in the general formula for the surface-tension given by the 

 writer * we obtain \ = D(p l <~-p 2 ) i where D is a constant which 

 varies only with the nature of the liquid. In the case of 

 chlorobenzene we have Dt=l'84 at 423° C. and D = '89 at 

 533° C D is thus by no means constant, and the law there- 

 fore not true. 



Several investigators of the law of attraction between 

 molecules have assumed that it must be such as will make 

 the internal heat of evaporation per gram of liquid inde- 

 pendent of the mass of liquid allowed to evaporate completely. 

 But it is not at all necessary that this condition need be 

 fulfilled. Consider a spherical mass of liquid to evaporate 

 till none is left. It is evident then that the energy expended 

 to remove a molecule to infinity depends on the mass of the 

 liquid only when the diameter of the sphere of liquid is 

 equal to the radius of the sphere of action of a molecule, 

 which is taken to be the distance of separation between two 

 molecules for which their potential energy is small in com- 

 parison with that corresponding to the distance the molecules 

 are separated in the liquid state. Now the writer f has 

 shown that the radius of the sphere of action of a molecule is 

 of the same order of magnitude as the distance of separation 

 of the molecules in the liquid state. It follows, therefore, 

 that the latent heat will depend on the mass of liquid allowed 

 to evaporate only when it is equal to about 10 -24 gram, and 

 the latent heat of a gram of liquid therefore independent of 

 external conditions, as has been found to be the case. 



The law deduced from surface-tension or latent heat we 

 have seen should contain an arbitrary function. But still the 

 law may contain a good deal of useful information. Thus it 

 might happen that the arbitrary function is an arbitrary 

 function only of certain quantities or of definite functions 



* Phil. Mag. May 1010, pp. 789-792. 

 t Phil. Mag. June 1910, p. 840. 



