518 RICE ART. L 



liquid. This, however, does not invalidate the general tenor 

 of the argument. The expression (4) for K represents the 

 van der Waals' cohesion a/v"^. If the constant a is reckoned 

 for unit mass of the liquid it is easy to see that 



a = — 



where m is the mass of a molecule. 



III. The Quasi-Tensional Effects at a Curved Surface 



6. Modification of the Previous Analysis 



Hitherto we have regarded the surface of a liquid mass as 

 plane. When we consider the situation in a surface layer at a 

 curved surface we have to modify the calculation of the inward 

 attraction on this layer. In the same broad manner as before 

 we can indicate the modification and thereupon it will be clear 

 how it comes about that the quantity represented by a, which is 

 manifestly an energy per unit area, appears to take on the 

 role of a surface tension, i.e., a force per unit length. (It is, of 

 course, obvious that energy/area and force/length have the 

 same physical dimensions.) To make this clear we shall have 

 to indicate in a little more detail how the calculation which 

 leads to (4) is effected. In Figure 1, ^ is a point in the surface 

 (supposed plane) and C a point at the distance h below. If P 

 represents the position of a molecule in the layer, we consider 

 another point B such that AP = PB; it is then clear that the 

 layer of liquid between the surface of the liquid mass and the 

 parallel surface through B produces no resultant force on the 

 molecule at P. Thus the inward attraction on P will arise 

 from the layer of liquid between the surfaces through B and C, 

 and a little thought will show how this attraction increases as P 

 approaches A . This argument is made use of in the calculation 

 of the entire force on all the molecules lying between the surface 

 through A and that through C, — a calculation which, as stated, 

 leads to (4). Supposing, however, that the surface of the liquid 

 were spherical and convex, and that we were proceeding as 

 before to determine the attraction inwards on a molecule 



