Freezing -Points and the Freezing -Point Methods. 471 



If tji<t g < t {%. e. if the temperature of the liquid be below 

 the convergence-temperature and the latter under the real 

 freezing-temperature), C/' (t — t fl ) is positive {i.e. the process 

 of ice-separation takes place and the liquid is warmed by the 

 freed latent heat of melting), C(t g —tji) is also positive (the 

 liquid is warmed by the arrangements of the experiment). 

 If tfl>t g and <t , 0," (to— tfl) is positive (the process of ice- 

 separation and warming of the liquid takes place), G(t g —tji) 

 is negative (i. e. the liquid is, on the other hand, at the same 

 time cooled by the arrangements of the experiment). If 



tji = t and > tff, we get -7- =0 (tg—t/i); that is to say, the liquid 



and the separated ice cannot be in equilibrium at zero, and 

 the liquid will be cooled by the arrangements of the experi- 

 ment. 



If tfl>t g >t , C," {t — tfl) is negative and C (tg—tfl) is also 

 negative. The meaning of this is as follows : — The liquid is 

 cooled by the arrangements of the experiment, but C/' (t — tfl) 

 no longer means a process of ice- separation, since the latter 

 can only warm and not- cool the liquid; and, indeed, the 

 highest limit for the process of ice-separation is t . (We 

 cannot use one equation for the processes of ice-separation 

 and of ice-melting, since it has been found that the constants 

 C," and K are different.) If equilibrium is attained at t', 

 we have 



I =o;>{to-t>) (t'-t m ) +Cfa-«')=o, . . ( B) 



dz 

 and 



t'—t 4- ( g ' ■ (V>'\ 



■ vy , t — t„„ 



in this t' must be >^ and <t . Because as C ; " (t — t')(t'—t 00 ) 



in the process of ice-separation is necessarily positive, C(tg — t) 



dt 

 must be negative ; i.e. in order that -y- can be =0, the process 



of warming the liquid must be compensated by the process of 

 cooling it. The real freezing-temperature when the convergence- 

 temperature is below the freezing-temperature will be obtained 

 therefore not at the real freezing -temperature t but at the 

 temperature t', which is more or less different from t 0; and the 

 obtained temperature t' ivill be betiveen the real temperature to 

 and the convergence-temperature t g . 



In order that the apparent freezing-temperature t' may 



be as near as possible to the real freezing-temperature t 0) 

 ft f f' 



rrn J, nrast also be kept, in this case, as small as possible ; 



