SURFACES OF DISCONTINUITY 521 



vapor (with the possible addition of effects arising from artificial 

 thrusts). Actually, even for a liquid under gravity, we can 

 regard Po as the intrinsic pressure just within the horizontal 

 free surface. As the depth increases, the intrinsic pressure, just 

 like the usual "hydrostatic pressure", will increase by the 

 amount gpz, where p is the density of the liquid and z the 

 depth. Now Pn arises from the momentum of the thermal 

 motion of the molecules of the hquid, and Pq — K represents this 

 kinetic pressure enormously reduced by the cohesion on the 

 surface layer. We might therefore call Pq — K the internal 

 pressure of the liquid at the surface, but care will have to be 

 taken to avoid any confusion between this use of the term 

 "internal pressure" and the use of it by Freundlich and others 

 (erroneously in the writer's opinion) to refer to the cohesion K* 

 On the other hand po is the external pressure on the surface of 

 the liquid and is the pressure actually measured by a manom- 

 eter; so that the result for a plane surface simply states that 

 the external and internal pressures at the surface are equal. 

 Turning now to a spherical surface of radius R (convex to the 

 exterior), the expression (5) yields the result 



P - 



{k+^-~)=V, (8) 



where P is the intrinsic pressure inside the liquid mass (at any 

 point if the liquid is weightless, or at the free surface if gravity is 

 supposed to act) and p is the external (observable) pressure on 

 the surface. As before, we may call P — K the internal pressure 

 of the liquid at its surface, and denoting this by p' we have 



P'-P = |- (9) 



Now this result is identical in form with that which connects 

 the gas pressure inside a membrane or liquid film and that 

 external to it. This formal identity has led to the use of the 



* Or we might use the old-fashioned phrase "vapor-tension" for 

 Pq — K, as distinct from "vapor-pressure" the term for po. 



