420 PROCEEDINGS OF THE AMERICAN ACADEMY 



for a tube .02346 cm. in diameter. And 



/; = 77.34(1 — 0.00181 T), 



for a tube .03098 cm. in diameter. 

 The equation may also be written : 



dp dk . , . a 



dT~'~ dl'J K^) — T' 



Thomson has shown (Proc. Roy. Soc. Edin., 1870) by considera- 

 tions regarding the equilibrium between a liquid and its saturated 

 vapor, that the pressure on the surface of the liquid depends upon the 

 form of the surface. 



In certain cases the part of the external work, p d x, may be con- 

 sidered equal to zero ; the chief external work being done against 

 superficial tension. The extension of the soap film represents such a 

 case. Here 



dk 1 r«"[ , . 



In considering the case of the soap film mentioned on page 419, it 

 will be seen that the work done against superficial tension in Part I. 

 of the process is 



A represents the area, and Z;y the value of k for temperature T. 



Experiment has shown that the coefiicient of capillarity in general 

 decreases as the temperature increases. The work done in the con- 

 traction of the film — Part III. of the process — is 



2^[i,_^rfr]. 



This exceeds the work done upon the film by : 



Consequently, from thermodynamic considerations, a certain quan- 

 tity of heat, Q, must be absorbed at temperature 7*, and a quantity, 

 Q — d Q, must be evolved at temperature 2' — d T, and 



2Adk 

 dQ = -^j^dT. 



