118 



With the assumption indicated the maximum temperature T„mx of 

 a thread, the extremities of which are at the temperature 2\, with 

 a potential difference of E volts at the extremities is determined by 



-' max — -t- b — -T', -C/ . 



4a 



From this formula can be seen at once that the well known 

 property of good conductors, that comparatively small potential 

 differences, when external heat conduction is excluded, produce 

 considerable heating, which may even lead to melting, becomes 

 enormously more prominent in the su})8rconducting condition. 



In fact we find that at the smallest potential difference E of 

 0.5 microvolts, which is only a little above that which at 2°. 45 K. 

 is first observed, such comparativel}- great heating can take place, 

 that even at the lowest values of Ti, T^ax rises to 4°. 20 K. At 

 higher bath temperatures of course smaller potential differences 

 are sufficient to reach the vanishing point, or at the same poten- 

 tial difference a' can be placed lower, at 4°. 18 K. for instance 

 a! = a. 10-5 . 



With the rough estimation of a' given, and assuming that the 

 mercury thread where its temperature has fallen below the vanishing 

 point gives off no heat to the glass '), we can, therefore, without 

 the assumption of heating caused by local disturbances, predict 

 j)henoniena such as threshold value of the current density and the 

 differences of potential, that appear at gi-eater current densities. 



At current strengths below the threshold value, the thread will 

 all along be in the condition of superconduction, Avithout external 

 heat conduction, at current densities above the threshold value this 

 only exists for portions below the vanishing point temperature ; 

 for the portion of the thread that is above the vanishing point, 

 the regime of ordinary conduction with loss of heat at the sur- 

 face comes in its place '^). In this way there can, however, be no 

 question of the deduction of the law of dependence of the thres- 



1) This calls our attention to the question of the distribution of temperature 

 along a thread through which a current passes without external conduction of 

 heat for different laws of dependence of A, A; and T. Laws might be imagined, 

 which would cause the rise of temperature to run through the values from 

 to T"'ox — Tb practically whhin a very small length of the thread, in which case 

 the heating by a microresidual resistance could not be distinguished from a 

 heating caused by a local disturbance. For the present, however, we adhere to 

 the simpler supposition that the thread gives off no heat to the glass. 



-) The divergence of the lines for 0,4 and 0,004 amp. in fig. 7 may also indicate 

 ^he transition from the one regime to the other. 



