SURFACES OF DISCONTINUITY 517 



not parallel to the surface but normal to it. As stated above, it 

 is by reason of this that the enormous kinetic pressure in the 

 interior (the intrinsic pressure) never manifests itself to our 

 senses or our measuring instruments. Only a small fraction of 

 the molecules, whose kinetic energy is sufficiently above the 

 average and whose direction of motion is sufficiently near to the 

 direction of the outward normal, will manage to effect their 

 escape and impinge on an enclosing solid wall or enter into a 

 vapor phase. Thus it is chat, apart from artificially produced 

 thrusts on the surface of the liquid mass and the effects of 

 gravity, the observed pressure of the liquid is just the saturated 

 vapor pressure. 



This picture of the surface conditions enables us to make a 

 calculation of the surface potential energy in a manner alterna- 

 tive to that suggested earlier. The basic idea of it is just the 

 same as that employed in calculating the potential energy of a 

 body raised above the ground ; perhaps the potential energy of a 

 wall of given height is a better analogy. The details are again 

 too troublesome to reproduce here, but once more we reach the 

 same result as before for this energy per unit area of surface, 

 viz., the expression (3). 



This second method of analyzing the situation also enables us 

 to obtain a formula for the "cohesion," i.e., the amount by which 

 the intrinsic pressure of the liquid exceeds the observed pres- 

 sure. It can be shown that the attraction of the interior liquid 

 on all the molecules contained in the amount of surface layer 

 which lies under unit area of surface is 



4>(r)dr. (4) 



- 27rn2 



(This happens to be expression (2) with the sign reversed.) 

 This is the well-known result of Laplace, and this expression 

 (4) for the "cohesion" is usually denoted by the letter K. It is, 

 of course, as well to remember that this expression, like the 

 previous results, is derived on the assumption of a liquid so fine- 

 grained in structure as to be practically continuous, and there- 

 fore these expressions can only be regarded as approximate 

 representations of the proper formulae in the case of an actual 



