258 



Dynamically we may regard this medium as consisting of" 

 molecules so moving that the relative orbit of two neighbours 

 is a closed orbit o£ infinite range similar to the parabolic 

 orbit of comets. Let the liquid and vapour be at absolute 

 temperature T, then the difference between this fictitious 

 medium of transition and the substance at the critical tem- 

 perature T c is that at kinetic energy corresponding with T, 

 and at density associated with 2 R 2 two neighbour molecules 

 in the medium could just separate to an infinite distance 

 apart and come to rest. Let p s be the density associated 

 with 1 R 2 , then p s corresponds with that distance between 

 neighbours which allows their kinetic energy proportional 

 to T just to oive them a relative orbit of infinite range, while 

 p c corresponds with that distance between neighbours at the 

 critical point which allows their kinetic energy proportional 

 to T c just to give them a relative orbit of infinite range. 

 Thus the difference of the potential energy of a molecule in 

 our fictitious medium of density p s , and that of a molecule in 

 the critical state is equal to that of their kinetic energies. 

 Let us now return to equations (8) and (10) and derive from 

 them the average potential energy of a molecule amongst 

 those in the surface layer of liquid and the surface layer of 

 vapour, namely 



4^V(l/R 1 3 -2/ 1 R 2 3 H-l/R 2 3 )/6, . . (11) 

 and 

 4^{l/2E 1 3 -2/ 1 R 2 3 2Kl+p/pc)' + l/B/(l + p/Pc)}/0. (12) 



The first and the last terms taken together are the mean 

 energy of a molecule in the liquid and a molecule in the 

 vapour, which we may identify with the potential energy of 

 a molecule in our fictitious medium of density p s . Again 

 the middle term becomes the potential energy of a molecule 

 at density p c , if we identify jRg 3 "with w\p c in elements, and 

 with ??i/22(l-|- pjp c )*pc in compounds. To this definition of 

 X R 2 I have been led by the consideration that it is the simplest 

 one which will give the relation discovered by Eotvos, which 

 we shall obtain at once, for the last expression is now equal 

 to the difference between the kinetic energy of a molecule 

 at T c and at T. So, passing from molecules to gram-mole- 

 cules, we have the result that the surface energy or tension 

 per gram-molecule a(M/(u) 2/3 is equal to the difference between 

 the translatory kinetic energy of N 2/3 molecules (N being the 

 number of molecules in a gram-molecule) at T c and at T, 

 namely 3R(T C — T)/2N 1/ ' 3 where R is the gas constant when 



