Freezing-Points and the Freezing-Point Methods. 467 



different values are obtained at the same value of t g —t i 

 We now know why it must be so. As the liquid has the 

 temperature t', we always obtain the apparent freezing- 

 temperature if the ice-cap is removed, and, if the mercury-bulb 

 is covered by ice ; the latter cools the thermometer according 

 to the amount of surface covered and tends to bring it 

 to t , and in the presence of an ice-cap the freezing-tem- 

 perature must therefore be obtained between t and t' . 



I pass now to the consideration of the question which is of 

 most importance to us, the freezing -'point depressions when 

 the convergence-temperature is above the freezing-tem- 

 perature. 



We have 



t'^t +~-^- (Water), 



t" =t ' + ^ 7 -H—fr (Solution) 



-TV; to t QV 



and 



\J t a 1 \J tn t 



where t' — t" is the apparent freezing-point depression as 

 obtained from the apparent freezing-temperatures, and 

 tl — to' is the real freezing-point depression as obtained from 

 the real freezing-points. In order that t' — t" may be as 

 equal as possible to t — t o r , the expression 



\J tg t \J tg t 



X / — t K ' t ' —i ' 



•*-*./ l l 0V / ° °v 



must be brought as nearly as possible to zero. This becomes 

 more easy when 0=0' and K ; = K/, t — t ov =to' — t /. 



(a) and C : The velocity of overcooling of water and of 

 very dilute aqueous solutions must be regarded as pretty 

 much the same. 



(b) K, and K/ : From the paper " On the Velocity of 

 Reaction before Perfect Equilibrium takes place " it will be 

 seen that, going over from more dilute to more concentrated 

 solutions, the velocity of ice-melting probably decreases but 

 very slowly, so that we can in dilute solutions assume the 

 same value for K. Then the amount of overcooling under 

 the t 0} i.e. t —t ov and t ' — t J, must be in all dilute and in 

 more concentrated solutions as nearly as possible the same *. 

 Because of this, all the methods in which the freezing-point is 



* Since in dt=K(t — t)dz, K is directly proportional to the total 

 surface of the ice. 



