CAPILLARY ACTION. 



This then expresses the work done by the attractive forces when a particle 

 M M brought from an infinite distance to the point P at a distance z from 

 a stratum whose suHkce-density is <r, and whose principal radii of curvature 

 mn R t and J(. 



To find the work done when m is brought to the point P in the neigh- 

 liourhood of a solid body, the density of which is a function of the depth v 

 Mow the surface, we have only to write instead of <r pdz, and to integrate 



2irm j pj (:) dz + * hr+ ft) I f^ ( z ) dz > 



where, in general, we must suppose p a function of z. This expression, when 

 integrated, gives (1) the work done on a particle m while it is brought from 

 an infinite distance to the point P, or (2) the attraction on a long slender 

 column normal to the surface and terminating at P, the mass of unit of 

 length of the column being m. In the form of the theory given by Laplace, 

 the density of the liquid was supposed to be uniform. Hence if we write 



K=2ir\ ^i(z)dz, H=2irt zt/(z)efe, 

 the pressure of a column of the fluid itself terminating at the surface will be 



mid the work done by the attractive forces when a particle m is brought to 

 the surface of the fluid from an infinite distance will be 



If we write 



"*(*)&-*(*), 



then 2irmp0(z) will express the work done by the attractive forces, while a 

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

 surface of a mass of the substance of density p and infinitely thick. The 

 function 9(z) is insensible for all sensible values of z. For insensible values it 

 may become sensible, but it must remain finite even when z = 0, in which case 

 6(0) = K. 



