82 Prof. G. Quincke on the Constants of 



the force mm!<j)(d). The direction of this -pig. 1. 



force is the line joining the particles. The 

 function of the distance depends on the re- 

 sultant of attracting and repelling forces, and 

 disappears when d is larger than the radius 

 of their sphere of action, which is a barely sen- 

 sible magnitude. The plane through A. and 

 the normal at P to the lluid surface, cuts the 

 latter in a curve which, near P, coincides 

 with a circle whose radius is p. 



A second particle, m v symmetrically situ- 

 ated at B on the other side, exerts the same force as A. The 

 components of these two forces perpendicular to the normal de- 

 stroy one another ; the sum of the components parallel to the 

 normal, which is the resultant of the two forces, is 



2mm 1 ^)(d) cos (r, d)=mm l (p(d) -• 



r 



We obtain the action of all the molecules of the normal section 

 on the particle m situated at P by summing up these expressions 

 from d=0 to d=. a certain value exceeding the indefinitely small 

 radius of the sphere of molecular action. Neglecting the con- 

 stant, we have for this sum 



-%mm'd>(d) . d= — 

 .9 9 



Calling p ] the radius of curvature of a second normal section 



which is perpendicular to the former, similar considerations give 

 a similar result, and the whole action of the particles in two 

 normal sections perpendicular to each other on a particle at the 

 point P is ,-i i \ 



where k is the attraction which the particles of two normal sec- 

 tions perpendicular to each other exert on an element of the 

 plane surface of the size of the unit surface. The well-known 

 principle of Euler gives 



1 , I 1 1 ■ l 



- + — = -— + — = constant, 



9 Pi ll R i 



where R is the greatest and Rj the least radius of curvature on 

 the surface. The entire action of the mass of fluid on P, or the 

 capillary pressure (p) at the point P of the fluid-surface, is 

 therefore / 1 -j n 



or, introducing two new constants for these summations, 



*= K+ !(i-4,) tD 



