472 Dr. M. Wildermann on Real and Apparent 



the conditions are the same as when the convergence-tempera- 

 ture is above the freezing-temperature. 



For the freezing-point depressions we have : — 



t'^o+^r/f^r (Water), 



V_^ I -f- l ov 



C t ' ' —t" 

 tr f = to'+ p-„ ?,_' / (Solution), 



and 



t t -to t + Lc/ / t >_ tov q u „ r- t jS ^ ) 



Since it has been found that Cy/'in dilute solution can be put 

 equal to C/', and conducting the overcooling so that t' —t ov — 

 t" —too or to — tov = to' — t v', we have therefore also in this case 



f cF-L ?=£ J 



o t a -tj 



or 



t'-t" = t -tj + 



^ °0 l OV 



and we get for the freezing-point method, in this case, the 

 same conclusions for dilute and concentrated solutions as 

 before. 



We have a further convenience here that we are able to 

 determine the freezing-point of water and of the most dilute 

 solutions with great simplicity and certainty without the 

 necessity of avoiding the ice-cap : — As the apparent freezing- 

 temperature in this case is below the real, and the ice can 

 only melt above the real freezing-temperature, the separated 

 ice can obtain the temperature of the liquid by conduction, 

 and in reality does so. (See "ice-caps," "net-work of ice," 

 " well-closed ice-caps/' &c. in the paper " On the Determina- 

 tion of the Freezing-point in Dilute Solutions to '4° depres- 

 sion," which will soon be published.) It is hardly necessary 

 to add that the equilibrium, when the convergence-temperature 

 is below the freezing-point, is also a dynamic one, and that 

 overcooling by the arrangements of the experiment, as well 

 as the separation of ice, continues to take place at equilibrium. 



The principles laid down in this paper are of a general 

 nature, i. e. they give the leading points for the arrangements 

 of the equilibrium of the heterogeneous system for all solvents 

 or solutions and for all temperatures, ivhether we determine the 

 freezing-point of water, of a metal, or of a liquefied gas. 



It is clear that there is no reason whatever to think that 

 one method is better than the other because a *001° instead 



