6o8 Albert P. Mathews 



the following assumption was made based on van der Waals' 

 conclusion that the surface film is infinitely thick at the critical 

 temperature. At absolute zero, where the molecules are 

 presumably in contact, it may be assumed that the surface 

 film is only a single molecular diameter deep. At the critical 

 temperature, on the other hand, it must be infinitely deep. 

 That is, no matter how many layers of molecules one passes 

 over, one can never, at that temperature, get to a region of 

 differing density. Between absolute zero and the critical 

 temperature the depth of the surface film must lie between 

 these two values, increasing with the temperature, and pre- 

 sumably in all normal substances at corresponding tempera- 

 tures it will be the same number of molecular layers thick. 

 I accordingly made the guess that it would be equal to 

 (T C /(T C T)) 2/3 molecular diameters since this fraction is equal 

 to (d /(di dj) 2 (see page 617). This guess turned out to be 

 correct if Eotvos surface-tension figures are used, but if Ram- 

 say and Shields' are taken the fraction must be raised to the 

 0.76 power and even then the value of "a" computed by this 

 assumption runs down near the critical temperature. Since 

 Eotvos measured the surface tension by a method which en- 

 tirely avoided any assumption as to the angle of contact and 

 Ramsay and Shields used the capillary method, which involves 

 such an assumption, I believe Eotvos figures and his statement 

 of the law is to be preferred. That his formula of TV* /3 = 2.27 

 (T c T) is to be preferred on other accounts is shown by the 

 calculations which follow: 



The total surface energy gained by passing a gram mol 

 through the surface is hence : 



(3) S - TV' /3 N 1/3 (T C / (T c T)) o.76 ergs ; or 



(4) 2 - TV; /3 N 1/3 (T C / (T c T)) 2/3 ergs. 



Formula (4) is to be preferred, when the surface tension is 

 measured by methods which do not involve the angle of 

 contact. 



We only have left to find the relation between the amount 

 of energy thus lost and the difference in the cohesive energy 



