252 



Dr. M. Wildermann. 



[Feb. 6, 



equation dt/dz = ~K(t — t), in which K is directly proportional to the 

 surface of the separated ice, t is the freezing temperature of the 

 liquid, and t is the temperature of the liquid at the time z. The 

 velocity of ice separation has been found to "be expressed by the equa- 

 tion dt/dz = c"(t —t), in which t is the freezing temperature of the 

 given liquid, t the temperature of the liquid at the time z. If the 

 convergence temperature is above the freezing temperature the general 

 equation will therefore be: dt/dz = K(f — process of ice melt. 

 + c(t g — tj/) arrang. exper. 

 Equilibrium takes place when dt/dz = c(t g — t') +K(£ — = and 



t' = t +Ut g -t'), i.e., the mercury thread comes to equilibrium, not at 



the real freezing temperature t , but at the temperature t' {apparent freezing 

 temperature), ivhich is more or less different from t (Nernst), and t' 

 will be between t and t g . In order that t' may be as nearly equal to t 



as possible, — (t g — t') must be kept as small as possible, and for 



this it is necessary for a successful freezing point determination that 

 (a) c be kept very small (the quantity of liquid used for the experi- 

 ment must be as large as possible, an air bath preferred to a liquid 

 bath), (b) K be as great as possible (the overcooling of the liquid 

 before ice separation must be sufficiently great, the ice must be sepa- 

 rated into fine needles, and not allowed to form conglomerate masses ; 

 subsidiary to this are good stirring arrangements, the proper choice 

 of the beaker, &c), (c) t g — t' or t g — 1 be kept very small, i.e., 

 the convergence temperature must be as near as possible to the 

 freezing temperature (the temperatures of the air bath and ice bath 

 most suitable to the given temperature of the room must be experi- 

 mentally found). For the frpezing point depressions we get t' — t" = 



to-t ' + 



:(tff—t t )—~(t g '—t")"J, in which t'~ t" is the apparent 



c 

 K 



freezing point depression as obtained from the apparent freezing 

 points, and t — 1 ' is the real freezing point depression as obtained 

 from the real freezing points. As in dilute solutions it has been 

 found that c can be put = e', K = K', we have t' — t" = t — 1 ' 



+ ^[(t g —t g ') — (t ! — t")~\. In order that the apparent freezing point 



depression may be, as far as possible, equal to the real, ^\_(tg— t g ) 



is. 



— (t' — t")'] must be kept as small as possible. In dilute solutions 

 t' — t" may be neglected, t g — t g being of importance; but in concen- 

 trated solutions t' — t" becomes of more importance. So we get for the 

 freezing point method in dilute solutions the rule : the same conver- 

 gence temperature, the same temperature of the ice bath, at the same 

 temperature of the room, the same regular stirring in all concentra- 



