LEWIS. — FREE ENERGY AND EQUILIBRIUM. 19 



^ -,._/(,.) ^ T, dv ^ ^ dv 



It is probable from the derivation of F' {v) that this is a function of the 

 same general nature as the preceding term, and will vary with the volume 



d c p d c^, , 



in the same way that -— ^ does. Then, since the coefficient of -7— is 



■' dv u I' 



not a volume function, we may write, not as a complete expression, but 

 as an approximation one step nearer the truth than the equations pre- 

 viously obtained, the following isothermal equation of condition, 



« = _-^^-^ + .^, (30a) 



P V -/{!■) do ^ dv' ^ ' 



or, after the type of the van der Waals equation, 



^==J^_4 + c^, (305) 



^ V — b v' d V 



where c is a third constant to be determined by experiment, and which 

 differs with different temperatures. 



Equation (29) gives the corresponding equation isochore, which may 

 be written for moderate ranges of temperature, 



IL^ C -^^\nT. (31) 



dT dv ^ ^ 



These equations, (30) and (31), should furnish a more exact statement 



of the behavior of gases and liquids than the equation of van der Waals 



or the corresponding ones developed in this paper. Since the degree of 



dc^, 

 accuracv is not known in the values of -r-^ at present determined, I 



d 



have not yet attempted an application of these equations. 



Returning to the consideration of f(v) or h, it may be stated at once 

 that this quantity is always a function of the volume and decreases with 

 decreasing volume, for usually tlie total volume in the liquid state is less 

 than b calculated for the gaseous state, and if b were constant then 

 V — b would have a negative value, which would be meaningless, v — b 

 must always have a positive value. 



The way in which the quantity a varies with the volume cannot be 

 predicted. If it represents the attraction between the molecules, then it 

 will vary inversely with the volume if the attraction between the molecules 

 varies inversely with the distance. But since the attraction observed is 

 probably the resultant of forces attractive and repulsive acting between 



