Surface-Tension with Temperature. 431 



I believe that the following proof shows that all liquids 

 satisfy MendelejefPs second condition. 



Let unit mass of liquid have a constant volume, but variable 

 surface S, and temperature t. 



In a small change of the variables, the heat absorbed is 



dK=kdt+ldS, 



h being the specific heat at constant volume, I the latent heat 

 of extension. 



The external work done on the film is 



dW = Td$. 



Therefore the gain of intrinsic energy is 



dR+dW=kdt+(l+T)d$, 



This is a perfect differential. 

 Therefore 



dk _ d(l + T) 

 d$~ dt ' 



Also — ■ is a perfect differential. 







Therefore 





dk _ dl 



d&t ~~ dtt 



Therefore 





ldk _ldl I 



tdS~tdt t 2 ' 



Therefore 





dT _ I 

 dt~ V 



And 









d*T 



dt 2 



Idl I ldk 



t It + 1 2 ~ t ds ' 



Now k does not depend on the surface unless the film is 

 very thin. 

 Therefore 



dt 2 - U ' 

 And 



T=c-bt, 



where c and b may be functions of the specific volume. 



That b does not depend on the specific volume may be 

 shown as follows. 



