464 Dr. M. Wildermann on Real and Apparent 



not in its purpose, identical with Newton's equation. A full 

 account of the reactions of ice-melting and ice-separation and 

 the experimental proof of the above equations will be given 

 in the paper " On the Velocity of Reaction before Perfect 

 Equilibrium takes place." (See Report Brit. Assoc. Liverpool, 

 1896.) 



Let us now bring into connexion those processes which 

 take place simultaneously before and after equilibrium : — 



A. When the Convergence-Temperature is above the 

 Freezing-Temperature. 



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



The general equation is -j- = 'K. t {t — tjj){t o — t ol ^ {ice-melt- 

 ing process) +C(t g — tfi) {experimental arrangements). Since 

 t — t ov is always positive, we have: — 



If tji>t g , t g is also > t (/. e. if the temperature of the 

 liquid is above the convergence-temperature) ; C(tg—tfl) is 

 then negative (the liquid is cooled by the arrangements of the 

 experiments); and K,(£ — tji) is also negative (i. e. the liquid 

 becomes cooler while the ice is melting) . 



If tji > t and < tg (i. e. if the temperature of the liquid is 

 below the convergence-temperature and above the freezing- 

 temperature), then G(tg — tji) is positive (the liquid is warmed 

 by the arrangements of the experiment), K(£ — fy) is nega- 

 tive (the ice-melting process takes place and the liquid cools 

 down) . If t fl < t < tg (i. e. if the liquid is below the freezing- 

 temperature) , C(t g — tji), as well as K(f — tfl), is positive; the 

 meaning of it is: — the liquid is warmed by the arrangements 

 of the experiment ; but K(k> — tfl) does not mean that the 

 ice-melting process is taking place, since through the latter 

 the liquid can only be cooled, not warmed ; and indeed the 

 lowest limit, where the process of ice-melting no longer 

 comes into consideration, is t . If tfl=t and < t g , then 



— =G{t g —tft), and C(tg—tji) is positive; i. e. the liquid and 



ice cannot be in equilibrium at the temperature t , and the 

 liquid must become warmer. If equilibrium takes place at 

 the temperature i', we have 



^£=C(tg-t') + K(t o -t')(t o -t ov )=0, ... (A) 



and ,=,.+ £&=£>, (A') 



•*-*-/ *o too 



and t', as can be seen, must be > than t and < t g , for since 



