532 



inatheinaticallj to Stefan's problem of the propagation of the frost ') 

 thougli for one case a slight extension of his mathematical method 

 will be necessary. 



Case 1. The material is siipraconducting to start with, the field 

 inside and outside is homogeneous and equal to //, <^ i/c- Suddenly 

 the field outside is increased to a value H, > He- 



We begiu counting time from the instant of the sudden change. 

 After the lapse of a time t the non-supraconductive state will have 

 advanced a certain distance .i\. into the metal. A moving plane 

 separates the regions having the two values of a. The low value <j, 

 is on the right of this bounding plane while tiie high valne (T, is 

 on the left. Corresponding to the two values of here are two values 

 of /i on the right and left ((3,, /ï, respectively). On both sides of the 

 surface of separation i;? = //c. Also E must be continuous at the 

 boundary. Letting 



&(x)z=—= fe-"' du 

 y Jr J 







we know from the work of Stefan that it is possible to satisfy 

 all the conditions of the problem by letting H on the left and on 

 the right of the boundary have respectively the expressions: 



H, = A, + B,eC^lX''A (9) 



H. = A. + B.„(jlX^) (10, 



In fact these satisfy (3^1) and by a proper choice of the constants 

 A^, jBi, A„ B, the initial and boundary conditions can also be satisfied. 

 The equations are 



h;=a, h;=a, + b. 



1) Webeb Riemann, Differentialgleichungen der Mathematischen Physik, Vieweü 

 und SoHN, 1919. Vol. II, pp. 117-121. 



J. Stefan, Wiener Monatshefte fur Malhematik and Physik, I. Jahrgang, p. 1, 

 1890. 



Sitzungsberichle der Wiener Akadeniie. Vol. 98, Div. Ila, p. 473, 1890. 



