Transition Layer between Two Adjacent Phases. 503 



further suggests that the average density in the surface layer 

 (call it as gram/c.c.) is larger than <7 m , the bulk value, though 

 this conclusion really widens the difference between the two 

 sets of values. As a matter of fact, as will be shown later, 

 the values of K s at ordinary temperature for water appears 

 to be of the order of 50,000 atmospheres. 



We can see the connexion between K m , K 5 , cr m , <x s most clearly 

 by making use of the Laplace expression for molecular 

 attraction. The general expression developed by Laplace for 

 the internal pressure is (employing the usual symbols) 



K 



-4 



f(z)dz 



(c is the range of molecular action) . 

 For the bulk of the liquid, therefore, 



* o 

 For the surface layer 



n oo 



K s = <Ts 2 \ 1r(z)dz, 



Jo 



and therefore, 



= <r -»vfe 



(i) 



This expression is, however, not much use to us as it stands, 

 since it contains two unknowns, <r 8 and K s . For the same 

 reason the value of a 8 cannot be obtained from what might 

 be called a corrected form of the Dupre relationship. Thus 



<r s is of course — , where v s is the average volume of 1 gram 



of the substance in the surface layer (the corresponding 

 quantities in the bulk of the liquid being a m and v m ) . It is 

 usual to call v m or v s ; ' specific volumes." Further, if 

 Xi represents the internal latent heat of vaporization of 

 1 gram, then Dupre's relationship is 



K s = 



Vs 



(2) 



To determine v t or a we must have recourse to Bakker's 

 relationship — which also requires a slight modification if we 

 are to regard v s and v m as differing in numerical value. 



