619 
As wea priori do not even know the form of the relation (2c), 
the following course is, however, to be preferred. A value is chosen 
for the velocity v'). When further v is considered as given, the 
temperature can be determined from (1), (2a), and (26), hence also 
the temperature 6 at the boundary. By causing the solidification to 
take place under different circumstances, different values of v can 
be obtained, and for each of these values the corresponding tempe- 
rature 9 can be calculated, and in this way the relation between 
v and 6 can be found. To check the theory, the temperature 6 may 
be determined experimentally, but this is not necessary in order to 
find the relation given by (2c) for a definite substance. 
§ 2. Theory of the solidification in a cylindrical tube. 
One of the simplest phenomena of solidification, which has also 
been studied most fully experimentally, is the crystallisation of a 
supercooled liquid in a cylindrical tube. 
Let the solid substance be in one part (A) of a straight tube, the 
supercooled liquid in the other part (B). The whole is surrounded 
by a space of constant temperature, which must also prevail in A 
and B within the tube at infinite distance from the boundary surface. 
This temperature must, of course, lie under the melting-point of the ° 
substance used, because else no solidification takes place *). 
The solidification now proceeds as follows. Heat is liberated at 
the boundary surface of the phases (heat of melting). It flows off 
on both sides through the solid substance and the liquid, and finally 
passes through the wall of the tube to the sphere of constant tem- 
perature. In every vertical section of the tube the temperature is 
highest in the axis of the cylinder and decreases towards the outside. 
This is also the case at the boundary surface of the phases. Hence 
the normal velocity at this surface cannot be the same every where, 
but must increase or decrease from within outward as the velocity 
of solidification v increases or decreases with diminishing temperature. 
Both cases may occur. The velocity v is, of course, zero at the 
melting-point, then increases with decreasing temperature, after which 
it begins to diminish again, as experience teaches, approaching asy mp- 
totically to zero at sufficiently low temperature. 
Let us suppose the temperature of the surrounding space to be 
1 The velocity v can be determined in a simple way experimentally, and can, 
therefore, conveniently be used as basis for the calculation. 
9) A process of melting, analogous to the process of solidification treated here, 
is impossible, because a liquid cam exist under its melting-point, but a solid 
substance cannot exist above its melting point. 
