CAPILLABY ACTION. 



the snAce-tension the whole upward force will be 



If thi* quantity is of the aame sign as z, the displacement will be increased, 

 and UM equilibrium will be unstable. If it is of the opposite sign from z, 

 the equilibrium will lie stable. The limiting condition may be found by put- 

 ting it equal to *ero. One form of the solution of the equation, and that 

 which is applicable to the case of a rectangular orifice, is 



Substituting in the equation we find the condition 



!+" stable. 

 neutral. 

 " unstable. 



Tlat the surface may coincide with the edge of the orifice, which is a 

 rectangle, whose sides are a and b, we must have 



pa = mir, qb = HIT, 



when m and n are integral numbers. Also, if in and n are both unity, the 

 displacement will be entirely positive, and the volume of the liquid will not 

 be constant. That the volume may be constant, either n or m must be an 

 number. We have, therefore, to consider the conditions under which 



cannot be made negative. Under these conditions the equilibrium is stable for 



all small displacements of the surface. The smallest admissible value of ^+^ 



a o 



is , + ^ , where a is the longer side of the rectangle. Hence the condition of 

 stability is that 



_ 



is a positive quantity. When the breadth 6 is less than -2fp the length 

 a may be unlimited. 



