Gu4 REPORT — 1895. 



wbicli these processes tate place, and to find the common equation for all of 

 them. 



1. On the Velocity of Solidification of Over-cooled Liquids, of Solutions, and of 



Liquid Mixtures. — From the experiments of Moore, made in Ostwalds laboratory,' 



dv 

 the author shows that the equation -^ =c{t^^—t) is to be applied for the velocity 



of solidification, where t is the actually existing- temperatui'e of the over-cooled 

 liquid, ^0 the temperature, where the solid and liquid solution are in equilibrium, 

 since beginning with the greater differences (instead of as has been done by Moore, 



with the smaller) tn — t, it is easy to show that -" — '- = > '- ~ — "1 ' . 



t^-t,, {d.v_:clz)i„ 



2. On the Velocity of Crystalhsafio7i of Over-cooled Liquids and Solutions. — 

 The same equation -- = c(tf^ — t) is found to be applied for the velocity of crystal- 

 lisation. Now, since the separation of the solid solvent is accompanied by evolu- 

 tion of heat (latent heat of melting), and the increase of the temperature of the 

 liquid is directly proportional to the quantity of separated ice, we can, instead of 



the above equation, put - = c'(^(j — t), where c' is directly proportional to the latent 



heat of melting, and inversely proportional to the specific heat of the liquid. Very 

 careful measurements have been carried out. The liquid was at first over-cooled 

 to below its freezing-point ; the distance from the freezing-point was then measured 

 on the '01° thermometer, and the time noted by my assistant to J second. 



3. On the Velocity of Meltivg of Solid Solvents in the Warmer Liquids and 



Solutions. — For the process of melting, Newton's equation ' = c{tQ— t) for conduc- 

 tion is to be used ; the convergence temperature is here that at which ice and liquid 

 are in equilibrium, i.e., the freezing-point ; the ice plays here the part of the cooling- 

 medium, abstracting heat from the liquid. Since now the velocity of reaction 

 takes place through the ice-surface, tlie velocity of reaction at a given time s will 

 be also directly proportional to the surface of the ice present in the liquid at the 



times. Our equation can therefore get the form --=e'(^o- O*-^? where O is in 



proportion to the surface of the ice. The liquid or solution to be investigated is 

 at first over-cooled 1° or 1°'2 below its freezing-temperature; the ice is then 

 crystallised. After the separation of the ice we allow the ice to rise in the beaker 

 to the upper part of the liquid, warm the liquid to about 0°-3 or 0°-4 above tlie 

 freezing-point ; the liquid is then stirred, the temperature rises at first, and after 

 reaching its luaximum falls. The time is measured to J second. 



We have therefore investigated two classes of reactions before perfect equili- 

 brium takes place. The first is where the temperature of both parts of the hetero- 

 geneous system is below or above the temperature of equilibrium (solidification, 



crystallisation). For this class we have to apply the equation 1 =c(ff^—t) or 



_ =c'(fo — <), which in its form, but not in its purport, is identical with Newton's 

 dz 



equation for conduction. Tlie second class is where one of the parts of the hetero- 

 geneous system is at the temperature of equilibrium and the other is above or 

 below tbat of equilibrium (melting process in liquids). The velocity of these pro- 

 cesses is regulated by Newton's law for conduction. 



As we know, we have two kinds of equilibrium, j9er/ec< and imperfect equili- 

 brium. While in the case of perfect equilibrium (for example, ice and water) at 

 a constant pressure, the smallest change of temperature is sufiicient to cause one 

 of the parts of the heterogeneous system to disappear, in the case of imperfect 

 equilibrium (for example, acid + alcohol, ether -h water) a small change of tempera- 

 ture produces only a small change in the state of equilibrium, while the relation 



' ZeitscTir. phys. Chem., vol. xii. p. 545. 



