60 



BRIDGMAN. 



The formula is readily derived by the thermodynamic potential. 

 We first deri\e again l)y this method the ordinary expression for the 

 temperature depression, since it is very easily done, and may perhaps 

 make matters a little clearer. Let us suppose that pure (1) and (2) 

 are in equilibrium at p, t on the transition line. (See Fig. 2.) 



Figure 2. Showing the displacement of pressure and temperature pro- 

 duced by impurities. 



»■ 



Then we know that at this point the thermodynamic potentials are 

 equal, or Zi = Z2. Let us now subject the phase (2) to a tempera- 

 ture increment (At) only, but the phase (1) to a simultaneous tempera- 

 ture increment (At) and pressure increment {^p'). We demand 

 that At and Ap' be so chosen that (1) and (2) are in equilibrium under 

 the new conditions, that is, AZj = AZo. We have in general 



Qt Jp ' \dp 

 = — i^ At + V Ap 



Now if A;;' is chosen as the negative of the "osmotic pressure" of 

 impure (1), it is obvious that impure (1) at p, t + At will be in equili- 

 brium with pure (1) at p -\- Ap', t + At, and that hence the impure 

 (1) will be in equilibrium with pure (2), where now pressure and 

 temperature are the same on both impure (1) and pure (2), as they 

 actually are. We have, therefore, 



— S]_ At + Vi Ap' = — So At 



ViAp' TVi 



At= — = - ^^Ap 



si — So AH 



where Ap (= — A^^') is the osmotic pressure of the impurity. This 

 is the formula derived in the previous paper, except for sign. Ap is 



