526 RICE ART. L 



By taking logarithms we can write this in the form 



log ni + -^ = log n2 + -^ 



or, if we represent the gram-molecular gas constant by R and 

 the number of molecules in a gram-molecule by N, we can write it 

 thus: 



Rt log ni + Ne(ni) = Rt log n^ + Ndin^). (11) 



If the first phase is a vapor, so that 6(ni) approaches zero, 

 the expression on the left-hand side approaches Rt log rii. 



Now, as is well known, the chemical potential of a gram- 

 molecule of a dissolved substance, provided its concentration is 

 small, is given by Rt log ni, where rii is the concentration. In 

 seeking to discover how this formula must be generalized so as 

 to embrace more concentrated states, statistical as well as 

 thermodynamical argument may easily prove of service, and 

 the equation (11) gives a hint of a possible line of attack. 

 Equation (10) shows that the function 



Rt log n + Nd(n) 



is the same in both phases of the fluid. When we remember 

 that the chemical potential of a given component is the same in 

 all phases in equilibrium, and compare Rt log n with the formula 

 for the chemical potential of a weakly concentrated component, 

 we may well consider that the full expression just written might 

 prove to be the pattern for a formula for the chemical potential 

 under other conditions. We shall return to this point in the 

 commentary. 



In conclusion, we may point out a phenomenon at the surface 

 of a liquid which bears some resemblance to adsorption, and is 

 explained by statistical considerations, When we were treating 

 the field of force which exists at the surface separating liquid 

 and vapor it was mentioned that the field exists in a layer of 

 the vapor as well as in a layer of the liquid extending in both 

 cases as far as the radius of molecular action. Now, just as the 

 density of our atmosphere is greater the nearer we are to the 



