OF ARTS AND SCIENCES. 419 



If the body is supposed to pass through a reversible cycle, 



•••/ 



a_jl^A£I^O. IV. 



Equation IV. only holds if all the steps of the transformation are of 

 a perfectly reversible character, and if the body is finally brought back 

 to its primitive state in every respect. That the part of the transfor- 

 mation depending upon changes in the superficial energy may be con- 

 sidered reversible is shown by the following example : — 



I. Let a soap film be stretched, at temperature T, to area A. 

 II. Let it then be cooled to temperature T — d T. 

 in. Let it then contract at temperature T — d T to its original me- 

 chanical state. 

 IV. Let it then be heated to temperature T. 



Every step of this process is obviously reversible, and the body is 

 finally brought back to its original state in every respect. The work 

 done by the film is equal to that which would have to be done upon it 

 in order to go through the cycle in the reverse direction. 



In equation IV. the expression under the integral sign must be an 

 exact differential : 



dT \t) ~ dx \Tj' 

 substituting from (a), 



(5.) 



This equation gives the variation of the coefficient of capillarity with 

 the temperature. The experiments of Wolff on the ascent of water in 

 capillary tubes give : 



k = 76.08(1 — 0.002 T-\- 0.00000115 T'), 



