Forces of Attraction between Atoms and Molecules. 793 



In this and the foregoing investigation we have neglected 

 the influence of the surrounding vapour on the surface-tension 

 of a liquid. If condition (2) is true — namely, that matter 

 has no screening action on its attractive forces — we may 

 suppose in moving the slabs apart that an amount of matter 

 equal to the density of the vapour remains stationary. We 

 should then be dealing with matter of density (pi — P2), where 

 pi denotes the density of the liquid, and p 2 that of the vapour, 

 and to this the foregoing investigation would apply. The 

 formula for the surface-tension then becomes 



wf^/cfcj 



where k" 1 as before denotes a constant which is the same at 

 corresponding states. But since p 2 = : ap ] , where a is a con- 

 stant which is the same for corresponding states, the equation 

 may be reduced to the previous form involving p l only. 



A formula for the internal latent heat will now be developed 

 on the same lines. We will assume (1) that the kinetic and 

 internal energy of a molecule is the same in the liquid and 

 gaseous states at the same temperature, (2) that the internal 

 heat of evaporation of a molecule is equal to the work done 

 in moving the molecule from the interior of the liquid to an 

 infinite distance against the attraction of the molecules of 

 the liquid, which is supposed to be identical with that 

 producing surface-tension. 



We have seen that the work done in moving a molecule 

 at a distance nx from a liquid surface to an infinite distance 

 is 



ffO , '.J[ 



F . dm (equation 7). 



When the molecule lies initially in the surface of the liquid 

 this becomes 



(SO 1 *. J F . dn= (tc a fx a C T T T</> \z) ^ (n + w)dn 



»/0 % )o u=-oo u=-oo tc=l * 



($c a )\T a Cfl Y T U(z)- a (n + w)~\ + 4:Yh(z)^(n^w)\ = o\dn, 



Jo ^ v=1 w=1 L % Jic=o v=i L * J «•=() -J 



where 



* = *. \/{(n + wy + u* + v 2 } 



and this is one-half of the molecular internal heat of evapo- 

 ration. The other half of the heat of evaporation is expended 

 in bringing the molecule from the interior of the liquid to 



