Freezing -Points and the Freezing -Point Methods. 469 



necessary : — the ice-bath must be arranged at temperatures 

 successively lower so that the convergence-temperature of 

 the solution falls below the convergence-temperature of 

 water by the amount of the freezing-point depression of the 

 given solution. 



I should like to draw attention to one point. It has been 

 said above that in dilute solutions t' — t" differs from t — td by 



— Sjl — ll t This difference between the real and apparent 



freezing-point depressions is only an ideal one. The absolute 

 values, t q — t', 0, and K / are of importance, not only because of 



the value of the correction -^- ~ — ~-^-, but also and chiefly 



&-1 ''O *00 



because of the variations of the obtained free zing -temperature. 



Since equilibrium has always to be established and brought 

 to the above theoretical condition (apparent freezing-tempe- 

 rature), the experimental error in the freezing-point method 

 may be considerably greater than can be concluded from the 



i Vj t a — tn 



value w f /- ■. 



When the convergence-temperature is above the freezing- 

 temperature it is easy to see why, calculating from a dilute 

 solution which does not form an ice-cap, we get van't Hojfs 

 constant, and why, calculating from water containing an ice-cap, 

 this constant is not obtained, but is so if the ice-cap be avoided*. 

 This is to be explained hy the fact that we can determine 

 freezing-point depressions only from the apparent freezing- 

 temperatures and not from the real ones, which in reality 

 we never get even in the presence of a well-closed ice- 

 cap. As in solutions which have a depression of O- 02 ice 

 does not settle on the mercury-bulb, the apparent freezing- 

 temperature is obtained ; therefore, in order to get correct 

 freezing-point depressions, we are obliged to prevent its 

 settling on the bulb in the case of pure water and the most 

 dilute solutions, which form an ice-cap, so as to get the 

 apparent freezing-temperature in these cases also. 



The ice-cap is interesting for us (working with the con- 

 vergence-temperature above the freezing-temperature), not 

 only because by avoiding it we have succeeded in confirming 

 van't Hoff's constant (in a second way) directly from water 

 and have been enabled to prove Arrhenius's generalization 

 experimentally, but it is to be regarded as an important proof 

 that we are justified in our conception of the equilibrium at the 



* See Phil. Mag. July 1895. 



