533 



It follows from the third of these that ^^= =r « wliere « is constant. 



vt 



On account of the constancy of a the fourth equation can also be 

 satisfied. Eliminating (he constants A, B we find for a: 







Hc-H, 



c;',3. 



(11) 



■<'VS)] 



The expression 



"«g^s) 



4 



l-ö(^K|ï, 



increases from to oo as « increases from to oo. We can deduce 

 from this that whatever the values of //,, //,, Re ma}' be (provided 

 He is between i/j and i/,) there is always one and only one value 

 of a which satisfies (IJ). An increase in | //, — H^\ leads to an 

 increase in u. An increase in | //c — ^i| gives a decrease in «. Since 

 (i, is very large we are concerned with 





V'= 



whence by (11) 



y—Hc — H^ 



V Jr=:r 



R.-Rc. 



2 A 2 



(12) 



o IT 



If /ƒ J = and if — ~-j — ^ is \ n i. e. if the externally applied 



field is 2.77 Ec both sides of (12) are unily and hence 



aV^, . 



is the 



value of X that makes xe^"^ (.r) = 1. 



Tliis value is about 0.77. Since jij is roughly 1 for tin the con- 

 stant « is of the order of magnitude of 1.6 and the law of pene- 

 tration of tiie boundary is Xc^\-^^^ t. 



It may be shown that the field is unchanged in the bulk of the 

 supra-condnctor and that only a surface current is induced. From 



