622 
Den DrK) OE 
dE) de, resp. BE Tides) 
When (5) is substituted in the equations (3) and (4), and when 
in these equations the following form is written: 
4! Q, 
MSV Stee S= 
0, 
it is found that: 
1-8 00 
li . «2 
“= =a, han tral =) (6) 
dot MU ded IUD ADE ze 
AT A, es a 
Besides there are still the limit conditions (2a) and. (26), which 
are in this case: 
(Ods Odon * oo 
(sy sigs 00, iyi ee 
The liquid having a ate Mere v at the boundary surface, 
it is not self-evident that (26) may be applied unmodified. A closer 
examination, however, teaches that this is, indeed, the case, and 
that therefore (80) is correct ’). 
Besides the relations (6), (7), and (8) the temperatures must satisfy 
other conditions which hold at infinite distance and on the wall of 
the tube. The tube being in surroundings of constant temperature, 
this temperature in both phases must exist at infinite distance from 
the boundary surface, where the influence of the generated heat of 
melting is not felt. The zero-point of the temperature being arbitrary, 
the temperature of the surroundings is chosen for it, and thus the 
following conditions are obtained : 
(Omen = 9 3 (Ode 2°) oe 
It is less simple to take the influence of the wall of the tube 
into account. When one wants to solve the problem accurately, also 
a differential equation must be drawn up for the temperature in 
the wall of the tube, and this temperature must be brougbt in connec- 
tion with the temperature of the solid and the liquid substance in the 
tube by means of boundary conditions corresponding to (2a) and (20). 
At the outer surface of the wall the temperature must be zero, i.e 
equal to that of the surrounding space. 
To put this train of reasoning into practice, though not impossible 
in principle, would lead to very elaborate calculations. In the cases 
1) Compare also W. HERGESELL, Ann. de Phys. u. Chem. 15, 1882, p. 19. 
