88 Dr. Meyer Wilderman on the Velocity of 



[It should be remarked that the values of K7 and K' . 10 

 have been calculated in the above tables for smaller intervals 

 (taken from the beginning to the end of the curve), since 

 only in this way can it be seen whether the curve follows the 

 same law over all its length. Naturally the experimental error 

 in the calculation of K is through this considerably greater.] 



Each of the curves changes its curvature, has a point of 



d 2 t 

 inflexion, i. e. where -j- 2 = the curve changes its sign from 



positive ^o negative; the curves approximate asymptotically 

 to the T oy + K axis (i. e. not to the T „ axis, but to one which 

 is parallel to it and is removed by K) as well as to the T 

 axis. The concave and the convex parts of the curve seem, as 

 far as one can judge, to be logarithmic; but the total curve 

 evidently cannot be a simple logarithmic one. Tables [. 

 and II. show that the following equation holds good for rhe 

 above curves: — 



log^-^ + ^-log^-^ + ^+log^-^) 



From this the differential equation (1) given above follows, 

 which means: the velocity of the reaction at the time t is 

 directly 'proportional to the remoteness of the heterogeneous 

 system front the point of equilibrium, T — T, and to the surface 

 of the solid (ice or salt) in contact with the liquid T— T oy (or 

 generally to the surface of contact of the reacting parts of the 

 heterogeneous system) + the co7istant K, tohiclt we shall call the 

 instability constant. 



If we integrate (1), we get 



K't = Yr\ log - — | + const. . 



t -t 0V + K\ to t -t ) 



(•2) 



At the beginning of the reaction, when t=0, T = T tw , we 

 have 



1 , K 



t n -t 00 + K 



= , : — — f^log h const., 



%. e. 



tt, 1 /i t — t 0V + ~K. i K \ 



K/t = -— T ^ I loo- log I 



t -t 0D + K\ ta t -t n t -tovJ' 



i. e. r is finite, the reaction can take place at any temperature, 

 Should there be no instability constant K in the equation, we 

 should have instead of (1) 



