On the Potential Energy of Liquid Surfaces, 451 



From this we deduce 



dT c/' 2 T 



and consequently the variation of the heat Q contained in the 

 mass m will be given by 



^Q=AT^/S+A^S^=A^(S^) . . (1) 



I have supposed the liquid surface in contact with air ; but 

 equation (1) evidently applies to the case of the surface of 

 separation of two liquids which do not mix, or to that of the 

 surface of contact of a solid and a liquid. I shall speedily 

 treat the case in which S represents either the free surface of 

 a solid body, the surface of separation of two solid bodies, the 

 free surface of a gas, or the surface of contact of a solid and 

 a gas. At present I shall deduce from this equation several 

 consequences which appear to be of great import. 



I. If we impart to a liquid mass m an increment dS of 

 free surface, then the potential energy T is a positive quantity; 

 that is to say, the total initial potential energy has received a 

 positive increment Td$. It follows that the mass m, having 

 acquired a greater potential energy, must have lost a certain 

 quantity of heat; that is, dQ is negative. This is shown 

 more simply still by the sign of 



(«a 



dt' 



the tension T diminishing when the temperature t increases, 



dT 



— and consequently also dQ must be negative. It was from 

 at 



this point of view that Sir W. Thomson investigated the 



thermal effect produced when a liquid film is stretched * ; but 



he has given only the term 



At-r-dS 

 dt 



of the second member of equation (1). 



I purpose to submit this formula to the test of numerous 

 experiments ; in this preliminary note I will merely say that 

 equation (1) appears to me to account for a great number of 

 phenomena yet unexplained. In order to judge of this by 

 particular instances, let us replace dQ by mgkdt, k being the 

 specific heat of the mass m at the temperature t ; we shall 



* " On the Thermal Effect of drawing out a Film of Liquid " (Phil. 

 Mag. 1859, [4] vol. xvii.p. 61). Compare the article entitled " Influence 

 de la temperature sur les forces de reunion" (Theorie mecanique de la 

 chaleur, par A. Dupre, p. 266 : Paris, 1869). 



2 a 2 



