The Internal Pressures of Liquids 607 



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energy per square cm. of the surface film. For each con- 

 centric shell of the surface one molecular diameter deep, the 

 surface energy is, then, T times the surface, or TV* 73 ; and the 

 total energy in the surface or a, will be equal to this amount 

 multiplied by the number of shells, which we shall represent 

 by the letter n, thus we have the equation : 



(1) a = TVl /3 n 



If now a gram mol of liquid passes from liquid to vapor it 

 must pass through this surface in which surface energy is 

 gained at the expense of the cohesive energy which is lost. 

 To determine the total amount of energy which is thus changed 

 in passing the whole gram mol through the surface, it is only 

 necessary to determine how many times we shall have to make 

 a new surface shell until the whole of the gram mol has passed 

 through. Since the total number of molecules in the gram 

 mol is N, and there are in a surface shell N 2/3 molecules, we 

 shall have to make a new surface N/N 2/3 times, or N 1/3 times. 

 The total energy then which will be gained as surface tension 

 energy will be S, or 



(2) S = TVY*NY*n. 



This same value may be obtained, also, in the following 

 way: The surface tension measures the force necessary to 

 overcome the surface tension pressure along a line i cm long 

 and a molecular diameter deep. The surface-tension pressure 

 per sq. cm acting in the plane of the surface is hence T/v 1 / 3 , 

 i) being the volume of a single molecule. Multiplying numera- 

 tor and denominator by N 1/3 we have the pressure per square 

 cm N 1/3 T 1/3 /V; /3 . If this pressure work through the volume V t , 

 the volume of one gram mol, we have the surface tension energy 

 if a whole gram mol were present as a surface shell, or N 1/3 TV* /3 . 

 Multiplying this by the number of shells, or n, we have our 

 former expression. 



Equation (2) contains the unknown factor "n," that is the 

 number of layers one molecular diameter thick constituting 

 the surface film. Since I knew of no way of measuring this, 



