( 



520 RICE ART. L 



is carried out it yields the result that the inward attraction on a 

 small prism of the liquid at the surface, whose depth is h and 

 whose sectional area is bs, is equal to 



6s < — 27rn2 / r^<l>{r)dr — — j r^4>{r)dr > , 



where R is the radius of curvature of the spherical surface. A 

 reference to (3) and (4) shows that this is just 



(5) 



Were the surface of the liquid mass concave, we could show 

 in a similar manner that the attraction on a molecule situated at 

 P would be less than for a plane surface and that the result for 

 the total attraction on the prism would work out to be 



8. {a- -I}- (6) 



The analysis is due to Laplace, and it is customary to denote the 

 quantity 2o- by the letter H. (See, for example, Freundlich's 

 Colloid and Capillary Chemistry, English translation of the third 

 German edition, pp. 7-9, where K is called the internal pressure, 

 an unfortunate term since i^ is a cohesional attraction and not a 

 pressure, and H/R is referred to as a surface pressure, another 

 unfortunate name for what is really an additional cohesion.) 



7. Interpretation of a as a Tension 



We can now use this material to elucidate the apparent role 

 of cr in this connection. In the first place, if we consider a plane 

 surface we have the result 



Po- K = po, (7) 



where Po stands for the intrinsic pressure within a (weightless) 

 liquid bounded by a plane surface,* and po stands for the 

 external pressure on its surface which arises from its saturated 



* I.e., by a spherical surface of very large radius. 



