551 ' VPILLARY ACTION. 



A piece of sheet metal is cut out in the form A A (fig. 1). A very fine 

 idip of metal U laid on it in the position BB, and the whole is dipped into 



a solution of soap, or M. Plateau's glycerine mixture. 

 When it is taken out the rectangle AACC is filled up 

 by a liquid film. This film, however, tends to contract 

 on iteelf, and the loose strip of metal BB will, if it 

 is let go, be drawn up towards A A, provided it is 

 sufficiently light and smooth. 



Let T be the surface-energy per unit of area; then the energy of a 

 sur&ce of area S will be ST. If, in the rectangle AACC, AA=a, and (7(7=6, 

 it* area is S=al, and its energy Tab. Hence if .F is the force by which 

 the alip BB is pulled towards A A, 



F-^Tab-Ta ( 6 ), 



..r the force arising from the surface-tension acting on a length a of the strip 

 is Tti, so that T represents the surface-tension acting transversely on every 

 unit of length of the periphery of the liquid surface. Hence if we write 



r = J 4 (x-X.)/**" (7), 



we may define T either as the surface-energy per unit of area, or as the 

 surface- tension per unit of contour, for the numerical values of these two 

 quantities are equal. 



If the liquid is bounded by a dense substance, whether liquid or solid, the 

 value of x ma 7 be different from its value when the liquid has a free surface. 

 If the liquid is in contact with another liquid, let us distinguish quantities 

 belonging to the two liquids by suffixes. We shall then have 



(8), 

 (9). 



Adding these expressions, and dividing the second member by S, we obtain 

 for the tension of the surface of contact of the two liquids 



f'i f't 



(x.-X".)/>A+ (x~x-)/vki (10). 



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