OF ARTS AND SCIENCES. 421 



The second law of thermodynamics gives for this case 



Q Q—dQ _ 

 T T—dT~' 



.'. QdT=:TdQ = — ~Ty^dT; 



" V—— J J- ^T- 



This last equation is a special form of (c). It gives the quantity 

 of heat absorbed in increasing, by A, the area of a film at constant 

 temperature T. The application of Carnot's cycle to this special case 

 was made by Thomson. (Proc, Roy. Soc, IX. 255.) It is obvious 

 that the latent heat of extension of unit of area is equal to the absolute 

 temperature into the decrement of superficial tension per degree of 

 temperature. 



Equation (e) may be written : 



u = -Tf(x)li. 



From this form it is obvious that, if y^, is minus, there must be an 



absorption of heat when x is increased, and an evolution when x is 

 diminished. 



Experiment has shown that the surface energy between two media 

 is a function not only of the temperature, but also of the difference of 

 electrical potential across the surface. Faraday observed that a large 

 drop of mercury, in contact with dilute sulphuric acid, changed its 

 form when connected with the electrode of a battery. And Lipp- 

 mann * has made a series of experiments upon the relation between 

 superficial tension and electrical phenomena in the case of mercury in 

 contact with various substances. 



The results of Lippmann's experiments may be summed up as 

 follows : — 



I. The superficial tension between two liquids is not a specific con- 

 stant depending merely upon the nature of the substances in contact. 

 The superficial tension is a function of the difference of electrical 

 potential between the two liquids ; and for every value of the difference 

 of potential, there is one, and only one, value of the superficial tension. 



* Annales de Chimie et de Physique, 1875 and 1877. 



