462 Dr. M. Wilderrnann on Real and Apparent 



dt 



dz 



the equation %=C{T A -t g ) +K/ = that 



and putting this value t A in the equation (I.) we get 



i. <?. we can with Prof. Nernst bring the velocity of cooling of 

 the liquid into connexion with the convergence-temperature t g . 

 Since K' is positive, C(T A — ^) must be negative; i. e. the 

 convergence- temperature is always above the temperature of 

 the air-bath. 



3. As regards the process of ice-melting'. Prof. Nernst makes 

 the assumption, on the basis of Boguski's investigations, 

 that the velocity of ice-melting is to be expressed, as above 



quoted, by the equation — = K(^ — t). Since the conclu- 

 sions obtained greatly depend upon the form of the equation, 

 the latter must be first ascertained. Neither Boguski nor 

 Spring, who later investigated the same subject, could succeed 

 in getting a- simple expression for the velocity of the processes 

 with which they dealt, because of the unfavourable and very 

 difficult experimental conditions. But besides this, as men- 

 tioned above, their reactions do not belong to those under 

 consideration here (processes before perfectequilibrium). I 

 should like, however, to give another explanation why the above 

 equation must nevertheless represent the velocity of ice-melting. 

 We investigate the velocity of ice-melting by measuring the 

 velocity of the cooling of the liquid by the melting ice. Now 

 this may be regarded as a phenomenon which is regulated by 

 Newton's law of conduction. The convergence-temperature 

 is that at which cooling of the liquid no longer takes place; 

 i. e. the freezing-temperature at which ice and liquid are in 

 equilibrium, and the ice plays the role of the heat-absorbing 

 medium. Should the ice not dissolve, its surface remaining 

 constant, Newton's equation dt = ~K(t —t)dz would express 

 the process of ice-melting, where t is the freezing-temperature, 

 and t is the temperature of the liquid at the time z. Since the 

 melting of the ice takes place through its surface, the con- 

 duction is directly proportional to the surface of ice in contact 

 with the liquid; i. e. K is directly proportional to the quantity 

 of ice present in the liquid at the time z. It is obvious that 

 the surface of the ice is a function of the temperature of the 

 liquid, since the latter is conditioned by the amount of melted 



