Theory of Surface Forces. 215 



Since dp/p 2 ccdv, this equation, obtained by purely hydro- 

 statical methods applied to the liquid and vapour and the 

 layer of transition between them, has precisely the same sig- 

 nificance as Maxwell's theorem upon the position of the line 

 C G in J. Thomson's diagram. In that theorem w represents 

 the external pressure that would be exerted by the fluid in 

 various states of uniform density, some of which are not 

 realizable. In the subject of the present investigation all the 

 densities intermediate between those of the vapour and liquid 

 actually occur ; but, except at the extremities, ot no longer 

 represents external pressure. 



The explanation of the stable existence in the transitional 

 layer of certain densities which would be unstable in mass, 

 depends of course upon the fact that in the transitional layer 

 the complete self-attraction due to the density is not developed 

 in consequence of the rapid variation of density in the 

 neighbourho od . 



The distribution of density in the transitional layer, and the 

 tension of the surface, can only be calculated upon the basis of 

 a knowledge of the physical constitution of the fluid as ex- 

 pressed by the relation between p and p, and by the law of 

 self-attraction. Poisson's contention that the surface-tension 

 cannot be found upon the supposition of an abrupt transition 

 from the liquid to its vapour is evidently justified ; and since 

 the thickness of the layer of transition is necessarily of the 

 order of the range of the attraction, it follows that the cor- 

 rection for gradual transition is not likely to be small. A 

 complete calculation of a particular case would be of interest, 

 even on rather forced suppositions; but the mathematical 

 difficulties are considerable. An approximate investigation 

 might be conducted as follows : — 



From (1) and (3), 



J 



p r dz l 



If we neglect the terms in d^p/dz*, &c, this becomes 



2L S=J7- 2K ^=/W- 2K -^ • • (") 



where f(p) —^dp/p is a function of p given by the consti- 

 tution of the medium. 



Equation (14) may now be integrated by quadratures. 



