OF ARTS AND SCIENCES. 431 



face, caused by variations of temperature, similar results may be 

 obtained without the aid of Lippman's experiments. 



It will, for the present, be assumed that the superficial tension de- 

 creases as the temperature increases. 



When any surface of constant area is heated, a certain amount of 

 superficial energy disappears. It must be converted into some other 

 form of potential energy. This other form of energy can be made to 

 reappear, as heat, in the contraction of the surface. Equation (c) 

 shows that the evolution of heat varies directly with the temperature 

 of the surface. 



If therefore we consider unit surface at temperature T^ we can find 

 the total amount of energy in the surface by making it contract to 

 nothing at constant temperature T. 



The total heat in the body upon which the surface considered exists, 

 is 



/: 



where o- equals the total specific heat before the formation of the sur- 

 face. When this surface disappears the total heat is diminished by 



J (IT ' 



The total energy is further diminished by an amount equal to the 

 potential energy of superficial tension of the surface. 



The total potential energy of any surface is, therefore, equal to the 

 potential energy of superficial tension plus another form of potential 

 energy, which appears as heat in the contraction of the surface. 

 Hence, what we have previously understood as superficial energy is 

 but a part of the total energy of any surface. 



Let h equal the superficial tension at temperature T. Let q equal 

 the mechanical equivalent of the heat evolved in the contraction of 

 unit surface to nothing. Let P equal the total energy of unit surface. 



P=k + q. if.) 



The following consideration is based upon the fact that this value of 

 P for any surface is independent of the temperature. This can easily 

 be seen by considering the cycle on page 419. If k^ and q^ are the 

 values of k and q at tlie higher temperature, and k^ and q^ their values 

 at the lower temperature, 



