The Internal Pressures of Liquids 609 



in a gram mol of liquid and vapor, respectively. I think that 

 the total surface-tension energy must be one- third of the total 

 difference in cohesive energies in equal weights of the two phases 

 separated by the surface. The energy in the surface is an 

 expression of the difference in cohesive pressure in one direction 

 only, whereas the two phases differ in their cohesion in three 

 dimensions. That the value one- third is correct is shown by 

 the computations which follow. The value one-third was that 

 adopted also by Young more than a century ago, but his 

 reasoning is so condensed that it is hard to follow. His 

 statement is as follows i 1 



"Upon these grounds we may proceed to determine the 

 actual magnitude of the contractile force derived from a given 

 cohesion extending to a given distance. Supposing the cor- 

 puscular attraction equable throughout the whole sphere of 

 its action, the aggregate cohesion of the successive parts of 

 the stratum will be represented by the ordinates of a parabolic 

 curve; for at any distance x from the surface, the whole in- 

 interval being a, the fluxion of the force will be as dx(a x), 

 since a number of particles proportional to dx will be drawn 

 downwards by a number proportional to a, and upwards by 

 a number proportional to x, and the whole cohesion at the 

 given point will be expressed by ax * 2 / 2 ; and this at last 

 becomes a 2 / 2 , which must be equal to the undiminished co- 

 hesion in the direction of the surface. Consequently the dif- 

 ference of the forces acting on the sides of the elementary 

 cube will everywhere be as a 2 / 2 ax + x 2 / 2 and the fluxion 

 of the whole contractile force will be dx(a 2 / 2 ax + * 2 / 2 )> 

 the fluent of which when x == a becomes a 3 / 6 , which is V 3 of 

 a xa*/ 2 , the whole undiminished cohesion of the stratum." 

 "We may, therefore, conclude, in general, that the contractile 

 force is one- third of the whole cohesive force of a stratum of 

 particles equal in thickness to the interval to which the primi- 

 tive equable cohesion extends," or T = aK/3. 



Accepting this coefficient of 1 / 3 of Young in place of that of 



1 Young, T: "Article on Cohesion," collected works, p. 460. 



