470 Dr. M. Wildermann on Real and Apparent 



apparent freezing-temperature as a dynamic one, where the 

 processes which took place before equilibrium continue. From 

 the above equation for the velocity of melting or separation 

 of solid solvends, 



j r 0;'{t-t)(t-t ov ) or ( ^ = K{t-t){t -t 0V ), 



clt 

 it follows that when /' becomes equal to t , y becomes =0 



and no further reaction takes place. At the real freezing- 

 temperature the equilibrium is therefore a static one ; but as 

 the reaction of ice- melting or ice-separation never takes place 

 alone, we never reach the real freezing-temperature, and the 

 dynamic, not the static, in reality takes place in nature. (See 

 Hep. Brit. Assoc, Liverpool, 1896.) 



From this conception of equilibrium at the apparent 

 freezing - temperature, it follows for the freezing - point 

 method : — Since at the freezing-temperature the liquid 

 continues to be warmed by the arrangements of the expe- 

 riment and, correspondingly, the ice continues to melt, the 

 warming of the liquid must be kept as small as possible ; 

 i. e. C and t g — t must be, also for this reason, correspondingly 

 small (the conditions are given above). This is especially 

 necessary in the case of solutions in which the melting of the 

 ice is accompanied by change of concentration and therefore 

 of the freezing- temperature. From the data, given below, it 

 will be seen that the velocity of warming or cooling the liquid 

 by the arrangements of the experiment, if t g — £' = o, 4 or 

 = — o- 4 (in our method), is less than about o, 0012 per 

 minute ; during the time of 15 minutes, which a freezing- 

 point determination requires, the quantity of melted or 

 separated ice corresponds therefore to o, 018, and the solution 

 becomes after 15 minutes of the experiment less dilute 

 or more concentrated by about '025 per cent. This is in 

 complete accordance with the direct experimental proof of the 

 same question (see footnote to the paper of P. B. Lewis, 

 Zeitschr.f. phys. Chem. vol. xv.). 



B. When the Convergence-Temperature is below the 

 Freezing-Temperature. 



Here we have to deal with the process of ice-separation. 



The general equation is -y- = V / "(t — tf) (tfl—t ov ) (separation 



of ice) + C(t g —tfl) (arrangements of experiment) . Since tfl — t ov 

 is always positive, we have : — 



