and Electronic Potential Energy. 265 



the whole expanded till it fills the volume which it would 

 have as saturated vapour. Let the distance between neigh- 

 bour pairs be r 2 , and suppose the electric moment ea- 2 now 

 proportional to r 2 , so that the medium in its second state is 

 geometrically similar to what it was in the first, then on 

 account of ecr, and therefore es changing in the proportion 

 of 1\ to r 2 , and therefore of R^ to R 2 the corresponding 

 molecular distances, the change of attractional potential 

 energy is not proportional to p l — p 2 but to pi l/z — p 2 ' d - Now 

 in the second state suppose that the electrons fall together in 

 groups so as to form the actual molecules of the saturated 

 vapour. The potential energy lost in this collapse will be con- 

 verted into translatory kinetic energy of the electron pairs, for 

 we have seen that their rotational energy seems to be constant. 

 The relation of Mills shows that none of this kinetic energy 

 appears as heat, for our imaginary operations have simply 

 converted the liquid into vapour at the same temperature. 

 The loss of potential energy during the imagined collapse 

 has become kinetic energy required by the pairs of electrons 

 to maintain dynamical equilibrium in the non-uniform state 

 when they are collected in groups to form molecules. This 

 kinetic energy may be regarded as internal molecular potential 

 energy. AVhen there is a change of molecular state the total 

 change of potential energy is equal to the difference of the 

 changes occurring when all the electrons forming the mole- 

 cules fall from one and the same imaginary uniform distri- 

 bution to each of the non-uniform distributions forming a 

 molecular state. The total energy required to change one 

 heterogeneous distribution of pairs of electrons into another 

 is equal to the differences between the changes required to 

 transform the heterogeneous states into the same homogeneous 

 one, it is equal to the work required to change the distance 

 apart of the molecules from the one heterogeneous state to 

 the other against the attraction of neighbours according to 

 the inverse fourth power law, together with the supply of 

 internal energy required to maintain dynamical equilibrium 

 under the changed conditions of heterogeneity. The sum of 

 these two quantities of energy forming the total internal 

 latent heat is subject to the law discovered by Mills. This 

 law could be explained by itself by supposing that each 

 molecule attracts its six immediate neighbours with a force 

 varying inversely as the square of the distance between them, 

 and that no internal change takes place in molecules when 

 their distance apart is changed. But the large mass of 

 evidence gathered in my papers on molecular attraction is 

 quite against this simple hypothesis, while it all supports the 

 Phil. Mag. S. 6. Vol. 20. No. 116. Aug. 1910. T 



