CAPILLARY ACTION. 



Tha nmf substance may be able to exist in two different states at the same 

 temperature and pressure, as when water and its saturated vapour are con- 

 tained in the same vooool The conditions under which the thermal and 

 iMffihan^l equilibrium of two fluids, two mixtures, or the same substance in 

 two physical states in contact with each other, is possible belong to thermo- 

 dynamics. All that we have to observe at present is that, in the cases in 

 which the fluids do not mix of themselves, the potential energy of the system 

 mu*t be greater when the fluids are mixed than when they are separate. 



It is found by experiment that it is only very close to the bounding 

 Atirfkce of a liquid that the forces arising from the mutual action of its parts 

 have any resultant effect on one of its particles. The experiments of Quincke 

 and others seem to shew that the extreme range of the forces which produce 

 capillary action lies between a thousandth and a twenty thousandth part of 

 a millimetre. 



We shall use the symbol e to denote this extreme range, beyond which 

 the action of these forces may be regarded as insensible. If x denotes tl it- 

 potential energy of unit of mass of the substance, we may treat x as sensibly 

 constant except within a distance e of the bounding surface of the fluid. In 

 the interior of the fluid it has the uniform value x<>- I n l^ e manner the 

 density, p, is sensibly equal to the constant quantity p,, which is its value 

 in the interior of the liquid, except within a distance e of the bounding surface. 

 Hence if V is the volume of a mass M of liquid bounded by a surface whose 

 area is S, the integral 



(1), 



where the integration is to be extended throughout the volume V, may be 

 divided into two parts by considering separately the thin shell or skin extend- 

 ing from the outer surface to a depth c, within which the density and other 

 properties of the liquid vary with the depth, and the interior portion of the 

 liquid within which its properties are constant. 



Since e is a line of insensible magnitude compared with the dimensions of 

 the mass of liquid and the principal radii of curvature of its surface, the 

 volume of the shell whose surface is S and thickness e will be Se, and that 

 of the interior space will be V ' Se. 



If we suppose a normal v less than e to be drawn from the surface S 

 into the liquid, we may divide the shell into elementary shells whose thick- 



