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LXIIL On the Theory of Surface Forces. 

 By G. Barker *. 



§ 1« nnjTE potential function. — One can study capillarity 

 either by imagining a liquid to be a system of 

 olecules in movement, or by supposing some homogenic 

 agent, which produces the same external effect as the liquid ; 

 we will follow the second method. 



The force exercised between the parts of the liquid acting 

 only through a very small range f,, the potential V at some 

 internal point depends only on the elements embraced in the 

 sphere of action o£ which it is the centre, and should be pro- 

 portionate to the density p ; thus q 2 and /being constants 



q*Y=-brfp (1) 



As to the interior of the liquid, the derivatives 

 dY dV ^V 

 dx' dy' dz> 



may be regarded as nul. Let us refer the liquid to any set 

 of rectangular axes. 



Suppose on the left of the plane of the y- and c-axes an 

 infinite mass of liquid limited to this plane; this plane is then 

 a level plane and the lines of the capillary force adjacent to 

 this plane are parallel to the .r-axis ; thus we should have : — 



dy U ' dz 



The character of the capillary forces demands that the force 

 parallel to the w-axis is annulled very rapidly on leaving the 

 #~ -plane ; this condition may be stated by supposing : 



V=Ab-«* (2) 



in which A and q are constants, where q may be very large. 

 Further, 



Differentiating the equation (2) twice, one finds 



a* 1 



By reversing the coordinate- axes, one arrives at two other 

 relations of the same form. These relations and the conditions 



* Communicated by the Author. 



| Young, « On the Cohesion of Fluids/' Phil. Trans. 1805. See Ray- 

 leigh, " On the Theory of Surface Forces," Phil. Mag. Oct.-Dec. 1890. 



= </v. 



