627 
ANDES AOD am Bee 2 8 (30) 
lil 
When finally the constants A,“ are expressed in A,“ by the aid 
of (27), then follows from (30) : 
= AO alk (p, Od, + p, 2) = Be TN, 
=i 
The equations (31) are infinite in number and contain infinitely 
many unknowns A,”. As we have not used orthogonal normal 
functions, we do not find the coefficients A, expressed explicitly, 
but as solutions of a system of linear equations. Practically this is, 
however, not a very serious drawback. For the quantities aj. are 
small for &=J/; hence they differ only little from one if & = l. 
In the first of the equations (31) all the terms but one can be left 
out in the first member in first approximation. The value of A, 
thus found is substituted in the second equation, in which all the 
terms following the second, are left out. Thus an approximated 
value of A,®) is obtained from this equation. Proceeding in the 
same way, an approximation is found for all the values 4,0. Now 
_the calculation is repeated, but no terms are left out. The terms 
which were neglected in first approximation, are now replaced by 
the value which they appeared to have in first approximation. By 
this method of successive approximation, which quickly converges, 
the values of the coefficients A,” are found. The values of the 
constants A,“ (or 4,%) are then found from (27). 
The temperature 6, in the solid substance and 6, in the liquid 
is found by substitution of the values found of A,” and A, in 
(18) and (19); the problem we had proposed to ourselves, has, 
therefore, been solved. 
The above-developed theory becomes of importance when it leads 
to a clearer understanding of the result and the interpretation of 
observations. Experiments on solidification in a tube and their rela- 
tion to the theory will be found in a subsequent communication. 
Institute for Theoretical Physics. 
Utrecht, June 1920. 
