CAPILLARY ACTION. 551 



ness is dv, in each of which the density and other properties of the liquid 

 will be constant. 



The volume of one of these shells will be Sdv. Its mass will be Spdv. 

 The mass of the whole shell will therefore be S\ pdv, and that of the interior 



Jo 



part of the liquid (F-Se)/3 . We thus find for the whole mass of the liquid 



M=Vp t -st'(p t -p)d v ........................... (2). 



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To find the potential energy we have to integrate 



E = I \xpdxdydz ....................... ....... (3). 



Substituting yjp for p in the process we have just gone through, we find 



E=VXP*-S \(xp-xp) dv ........................ ( 4 )- 



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Multiplying equation (2) by x*> and subtracting it from (4), 



......................... (5). 



In this expression M and ^ are both constant, so that the variation of 

 the right hand side of the equation is the same as that of the energy E, 

 and expresses that part of the energy which depends on the area of the 

 bounding surface of the liquid. We may call this the surface energy. 



The symbol x expresses the energy of unit of mass of the liquid at a 

 depth v within the bounding surface. When the liquid is in contact with a 

 rare medium, such as its own vapour or any other gas, ^ is greater than ^ , 

 and the surface energy is positive. By the principle of the conservation of 

 energy, any displacement of the liquid by which its energy is diminished will 

 tend to take place of itself. Hence if the energy is the greater, the greater 

 the area of the exposed surface, the liquid will tend to move in such a way 

 as to diminish the area of the exposed surface, or in other words, the exposed 

 surface will tend to diminish if it can do so consistently with the other 

 conditions. This tendency of the surface to contract itself is called the surface- 

 tension of liquids. 



M. Dupre' has described an arrangement by which the surface-tension of 

 a liquid film may be illustrated. 



