544 RICE ART. L 



impression that the two equations are the same, but that is not 

 so; and both on grounds of priority and because of the wider 

 scope of Gibbs' result, there is no justification for the use of the 

 name "Gibbs-Thomson equation" which one sometimes meets 

 in the hterature, although it is doubtless true that Thomson's 

 work was independently carried out. In equations [217] and 

 [218J Gibbs shows that, for a component the quantity of which is 

 small, the value of the potential is given by an expression such as 



A log (Cm/v), or A log (m/v) + B , 



where m/v is of course the volume concentration of the compo- 

 nent in question and A,C (or B) are functions of the pressure, 

 temperature, and the ratios of the quantities of the other 

 components. For a dilute solution regarded as "ideal" this 

 result becomes 



M = Mo + -RHog c , 



where c is the concentration of the solute and /io is a function of 

 pressure and temperature. This is proved in standard texts of 

 physical chemistry. For non-ideal and concentrated solutions, 

 the relation is given by 



fi = Ho + Rt log a , 



where a is the "activity," whose value in any case can be 

 determined by well-known methods described in the standard 

 works. As the concentration diminishes the activity approaches 

 the concentration in value. On this account an approximate 

 form of Gibbs' equation is frequently used for a binary mixture, 

 where the dividing surface is so placed that the surface con- 

 centration of one constituent (the solvent) is made zero. It is 



c da , . 



since b^x is put equal to Rt bc/c if temperature and pressure do 

 not vary. Now in Thomson's derivation of his result he uses 

 the methods of general dynamics. The reader may be aware 

 that in that science a system is specified by the coordinates and 



