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LVI. On the Application of Thermodynamics to the Study of 

 the Variations of Potential Energy of Liquid Surfaces. 

 Divers Consequences. (Preliminary Communication.) 

 By G. Van der Mensbrugge, Correspondent of the Royal 

 Academy of Belgium *. 



SUPPOSE a liquid mass m, of which t is the absolute tem- 

 perature, S the free surface, and T the potential energy 

 per unit of surface ; the total potential energy of the surface 

 will be TS, exclusively of all other energy, such as that due 

 to weight, to a change of volume, &c. Let us search out the 

 quantity of heat dQ which the mass must supply for the sur- 

 face S to receive an increment rfS. dQ will evidently be a 

 function of S and of t. Now, from the second principle of 



thermodynamics, — must be an exact differential dp ; let, 



then, 



^=dfi=XdBA-YBdt } 



X being the variation of \x when S is increased by the unit of 

 surface, the temperature t remaining constant, Y the variation 

 of fi by unit of surface when S remains constant and t be- 

 comes t + 1 ; it is not difficult to see that X and Y are inde- 

 pendent of S, and consequently we shall have 



dX 

 dt - ' 



whence dQ = tXd$ + t—Sdt. 



If the increment dS is produced by the external work Tg?S, 

 it is clear that dQ may be decomposed into two parts : — one 

 ATcZS, corresponding to this external work ; and the other, 



tXdS + t^Sdt—ATdS, 



dt ' 



which corresponds to the internal work ^U, equivalent to 

 AdJJ, A being the thermal equivalent of the unit of work. 

 We have therefore 



AdJJ= (tX- AT)dS + t^Sdt, 

 together with the condition 



d(tX-AT) ^dX ^ X _ A ^T =0 

 dt dt dt 



* Translated from a separate impression, communicated by the Author, 

 from the Bulletins de VAcademie royale de Belyiqiie, 2 ne serie, tome xli. 

 no. 4, April 1876. 



