664 Mr. W. Sutherland on the Electric 



But a most interesting problem arises when we extend 

 these ideas from a solid at absolute zero to a gas at ordinary 

 temperatures. The gas still shows cohesion, but how are we 

 to imagine the axes of electrization of neighbour molecules 

 in a gas to be related in a manner similar to that shown in 

 figs, 2 and 3. Fessenden assumed that in a gas the mole- 

 cules behave as if each molecule has an electric charge 

 opposite to that of its immediate neighbours, and so he 

 proposed to replace the equation of van der Waals 

 (p + a/?; 2 )(u — 5) = RT by a form in which the cohesional 

 term a/v 2 is replaced by a/v*/ 3 . I do not know of any ex- 

 perimental evidence that he ever submitted in support of 

 this change. In " The Laws of Molecular Force " (Phil. 

 Mag. [5] xxxv. 1893) I have shown that the equation of 

 van der Waals applies to the element gases and methane, 

 but not to compound gases in general, for which the co- 

 hesional virial tends to the form l/(v + Jc) instead of l/v or 

 the a/v of van der Waals. Now although it has just been 

 proved that Fessenden's assumption is a convenient and 

 proper simplification for a number of uniformly electrized 

 molecules in contact, there is no warrant for it in the case of 

 gases when we are studying the mutual potential energy 

 of molecules. We shall see it apply to total potential energy. 

 It does apply to the ions of a solution as the electrical 

 evidence shows. 



Since gases do not behave as completely ionized substances, 

 the electrical evidence is also directly opposed to the literal 

 truth of Fessenden's assumption for gases. As a fiction it 

 has no schematic convenience in the study of characteristic 

 equations, because it implies that the uniformly electrized 

 spherical molecule of a gas converts the whole of its domain 

 into a uniformly electrized sphere. We shall see that the 

 whole potential energy, not merely the mutual, is that of 

 a uniformly electrized spherical domain. Yet although there 

 is no theoretical or experimental justification of the literal 

 truth of Fessenden's assumption for gases, there has been 

 discovered by J. E. Mills a remarkable relation which seems 

 to verify it completely. This paradox contains matter of 

 importance for the whole of molecular physics, and the rest 

 of the present communication will be devoted to an attempt 

 to elucidate it. This is the relation of Mills : Let L be the 

 latent heat in calories for the evaporation of a liquid of 

 density p = d at temperature T to the state of saturated 

 vapour of density p = D at T, and let E be the thermal 

 equivalent of the work done in changing the density from d ' 

 to D against the saturation pressure, so that L— E is the 



