CAPILLARY ACTION. 



Let us examine the case in which the particle m is 

 placed at a distance z from a curved stratum of the sub- 

 stance, whose principal radii of curvature are R 1 and R t . 

 Let P (fig. 2) be the particle and PB a normal to the 

 surface. Let the plane of the paper be a normal section 

 of the surface of the stratum at the point B, making an 

 angle at with the section whose radius of curvature is R r 

 Then if O is the centre of curvature in the plane of the 

 paper, and B0 = u, 



1 cos 2 to sin a to 



557 



Fig. 2. 



u 



Let 



= r, PQ=f, 



The element of the stratum at Q may be expressed by 



<n? sin 9 dO dco, 

 or expressing dO in terms of df by (26), 



(25). 



(26). 



<r - fdfdoi. 



Multiplying this by m and by Ilf, we obtain for the work done by the 

 attraction of this element when m is brought from an infinite distance to P, 



Integrating with respect to f from f=z to f=a, where a is a line very 

 great compared with the extreme range- of the molecular force, but very small 

 compared with either of the radii of curvature, we obtain for the work 



mcr - {\fi (z) $ (a)} do), 

 and since />() is an insensible quantity we may omit it. We may also write 



since z is very small compared with u, and expressing u in terras of <a by 

 (25), we find 



