617 
The question which should be posed when one wishes to examine 
the course of the process of solidification, is the following: 
Given a supercooled liquid, in which there are one or more pieces 
of the solid substance. At a definite moment the temperature is 
given as function of the place. Required to determine for every 
successive moment the temperature as function of the place and the 
velocity with which the boundary surface of the two phases moves 
in consequence of the solidification. 
When the general principles and methods that may serve to solve 
this problem, are known, all the cases that present themselves can 
in principle be treated by the aid of them. This treatment only 
requires the surmounting of mathematical difficulties. The theory 
must be developed for a particular case and compared with the 
experiments. As is the case in every phenomenological theory, certain 
constants or functions which are characteristic of the substance, 
remain undetermined a priori here too. Comparison of theory and 
observations makes us acquainted with these constants or functions. 
When the above mentioned questions are answered, it should be 
borne in mind that in a substance in which the temperature differs 
from point to point, conduction of heat takes place. The conduction 
should not be considered as accessory, for without transport of heat 
solidification cannot take place. 
In a substance moving with a velocity V the temperature @ satisfies 
a generalized differential equation of the conduction of heat 
00 : 
(Bra A Ed ae ate) A ag eae oe let) 
This equation contains the quantities c, @, and 2, (resp. specific 
heat, density, and conductivity of heat), which refer to the phase 
for which (1) holds. An equation of the shape of (1) exists for the 
solid as well as for the liquid phase. In these equations there occur 
constants which are characteristic only of one of the phases separately, 
and not for the heterogeneous reaction between the two phases. 
As in every problem of conduction of heat there are here too, by 
the side of the differential equation, boundary conditions which the 
temperature 6 must satisfy, viz.: 
1. At the boundary plane of two media the temperature is 
continuous. This refers both to the boundary surface of the solid 
and the liquid phase and to the surfaces along which each of the 
phases touches the wall of the vessel in which they are contained. 
2. At a boundary surface the normal component of the current 
of heat is continuous, when no generation of heat takes place at 
