600 silsbee: conduction at low temperatures 



layer is shunted by the superconducting core, the whole current 

 will tend to flow in this core. This, however, would make the 

 field at the edge of the core even greater than that in the former 

 outer layer, since by equation (2) the field varies inversely as the 

 external radius. 



The system is therefore unstable and the current will shift 

 suddenly to a new distribution. This distribution will depend 

 on the exact form of the relation connecting resistivity with mag- 

 netic field; and if this relation were known, the current distribu- 

 tion might be computed from the usual electromagnetic equations. 



If it be assumed that the resistivity increases discontinuously 

 by a large factor, k, at a definite field intensity H c , then for a 

 current very slightly in excess of the critical value there will be 



a superconducting core of radius — , in which the current density 



will be k times the average value; and therefore - of the total 



k 



current will flow in this core. Outside of the core the material 

 will be in a field equal to or greater than H c and will by hypothe- 

 sis have an increased and uniform resistivity. Since the core 

 is so small that in spite of the great current density existing 

 there it carries only a small part of the total current, the resist- 

 ance of the wire as a whole is nearly k times the superconducting 

 value. For the materials studied k is of the order of 10 7 , so that 

 the effect of the core is negligible. 



For any other relation between resistivity and field there 

 would be a corresponding current distribution. In general the 

 abruptness of the increase of resistance with current would be 

 similar to that of the increase of resistivity with field. 



Owing to the great experimental difficulties of working at these 

 extreme temperatures the data available for an experimental 

 verification of this theory are rather scanty. Table 1 contains in 

 condensed form the observed values of threshold current for 

 various wires at different temperatures, as published by the 

 Leiden laboratory. Since the threshold values depend con- 

 siderably on temperature, a comparison is possible only when ob- 



