CAPILLARY ACTION. 



We hare next to determine the value of x in terms of the action between 

 one particle and another. Let ua suppose that the force between two particles 

 M and m' at the distance / is 



(22), 



being reckoned positive when the force is attractive. The actual force between 



the particles arises in part from their mutual gravitation, which is inversely 



n 

 as the square of the distance. This force is expressed by mm' ^. It is easy 



to shew that a force subject to this law would not account for capillary action. 

 We shall, therefore, in what follows, consider only that part of the force which 

 depends on $(f), where <f>(f) is a function of f which is insensible for all 

 sensible values of f, but which becomes sensible and even enormously great 

 when / is exceedingly small. 



If we next introduce a new function of/ and write 



(23), 



then utin'll (f) will represent (1) the work done by the attractive force on 

 the particle m, while it is brought from an infinite distance from m' to the 

 distance f from m'; or (2) the attraction of a particle m on a narrow straight 

 rod resolved in the direction of the length of the rod, one extremity of the 

 rod being at a distance / from m, and the other at an infinite distance, the 

 mass of. unit of length of the rod being m'. The function IT (f ) is also in- 

 sensible for sensible values of /, but for insensible values of / it may become 

 sensible and even very great. 



If we next write 



A(z) (24), 



then 2irm<rV(z) will represent (l) the work done by the attractive force while 

 a particle m is brought from an infinite distance to a distance z from an 

 infinitely thin stratum of the substance whose mass per unit of area is a- ; 

 (2) the attraction of a particle m placed at a distance z from the plane surface 

 of an infinite solid whose density is cr. 



