Surface Forces in Fluids. 357 



for an even distribution of molecules, and after self-adjust- 

 ment it will be still greater. Similarly, the difference 

 between the repulsive action of the second and third and 

 that of the first and second layers will be greater than 



F 3 + F 4 + , 



and so on. 



Therefore the difference between the repulsive action in the 

 interior and that between the first and second layers is greater 

 than 



F 2 + 2F 3 + 3F 4 + 



Similarly the difference between the repulsive action in the 

 interior and that between the second and third layers is 

 greater than 



F 3 + 2F 4 + 3F 5 + , 



and so on for greater depths. 



And we have seen that no term of any of these expressions 

 has its value sensibly altered by the curvature of the layers, 

 and consequently the value of the tension at any depth will 

 not be sensibly altered by the curvature, and the same reason- 

 ing is obviously applicable to the more general case of the 

 surface of contact of any two fluids *. 



16. We are thus led to the general conclusion that the 

 layers of a fluid near and parallel to its bounding surface are, 

 if the latter has a continuous and finite curvature, each 

 mechanically equivalent to a perfectly flexible membrane, the 

 tension or pressure on which is equal in all directions and at 

 every point, and depends for its value on the nature of the 

 substances at the two sides of the surface. When two fluids 

 are separated by a common surface of contact, the surface- 

 tension, which is the subject of observation and measurement 

 in physical experiments, is the algebraic sum of all the ten- 

 sions or pressures at the two sides of the surface acting on an 

 area of insensible depth in either fluid. 



17. If we call one fluid A and the other B, then, if the 

 mutual attraction between A and B is greater than what we 

 have called the self-attraction of A, and also is greater than 



* It is to be observed that to obtain this result we have tacitly made 

 use, for the first time, of the assumption that the number of molecules 

 ■within the sphere of molecular attraction is great; for otherwise a slight 

 curvature of the layers might cause an important alteration in the num- 

 ber of molecules, and therefore in the mass of matter constituting the 

 effective portion of each layer ; and the justification of the assumption is 

 to be found in the fact that all the phenomena of capillarity show the 

 surface-tension to be independent of the curvature of the surface so long 

 as the least radius of curvature is of sensible and measurable magnitude". 



