618 
the surface. If this ¢s the case, the normal components of the current 
of heat in the two substances at the two sides of the surface together 
lead off a quantity of heat equal to the generation of heat taking 
place at this surface. 
The boundary conditions 1 and 2, however, together with the equation 
(1) are not yet sufficient to determine the condition for every succes- 
sive moment. For one thing, the velocity with which the boundary 
surface of the solid phase moves is not known, hence it is not 
known either at a definite moment, at what surface the conditions 
1 and 2 are valid. The velocity of the boundary surface of the 
phases is directed from solid to liquid during the solidification. This 
velocity can only depend on the condition of the substance at this 
surface, hence on the nature of the substance and the temperature 
there. As third limit condition we get, therefore, the relation that 
must exist between the linear velocity of crystallisation (or solidi- 
fication) and the temperature at the boundary. 
When the value of a quantity in the solid phase is denoted by 
the index 1, and in the liquid phase by the index 2, and when pv 
is the normal at the boundary surface solid-liquid, we have at this 
boundary surface the conditions: 
Bd) rna 
‚ % „dine 2b 
a gaa text +. o> a 0 le 
r=fO%) oi. 2-2 2 
When vo, is the mass solidifying per unit of time and per unit 
of surface, ve,Q represents the difference of the normal-component 
of the current of heat on the two sides of the boundary surface, 
when Q represents the melting heat at the temperature @ prevailing — 
at this surface. 
The differential equation (1) with the boundary conditions (2) now 
determines the course of the process of solidification. (1) and (2) can, 
however, not be solved, when the function f, which is characteristic 
of the substance, is not known. It might be tried to make different 
suppositions about the relation between @ and wv, e.g. that @ is equal 
to the temperature of melting. Every supposition leads to a definite 
value of the temperature as function of place and time. Hach of 
these results might be compared with the observation, and in this 
way it might be found what relation there exists between 0 and v. 
1) A horizontal line indicates the value at the limit. 
2) Of course inversely 6 = ¢ (+). 
