119 



hold value on the temperature, because it is determined by the 

 temperature function, which we liave arbitrarily assumed as constant. 

 a' while we have seen that in the train of reasoning followed it 

 might have very different values at different temperatures, from 

 a' = 10—5(2 to a'^rlO-'r;,. And it is very questionable if, when 

 the necessary data are known for working out the sketch talking 

 note 1 into consideration, the potential phenomena would corre- 

 spond quantitatively to those observed. For the supposition with 

 regard to the absence of external conduction of heat, upon which 

 the theory in this § is based, might be untrue. (Cf. § 16 (f of VIII). 



It would be of great importance^) to cool by immediate contf^ct 

 the thread over its whole surface with liquid helium ; if the poten- 

 tial phenomena are to be ascribed to a real micro-residual resistance 

 of the mercury, then the throshokl value of the current density 

 could probably be raised considerably higher than was now possible. 

 This is too difficult with mercury. Thus for further experiments the 

 use of tin and lead (see § 1) was indicated, these metals being more 

 easily manipulated than solid mercury, and with them the conditions 

 of the external conduction of heat being more easily regulated^). 

 We shall treat of these investigations in future papers. 



I?. We ma}^ here add a few remarks concerning the supercon- 

 ducting condition. 



The experiments described above leave no doubt that for mer- 

 cury below 4°. 19 K. there is no question of an approximate validity 

 even as regards the order of magnitude of the relations established 

 by Wiedemann and Franz and by Lorenz. The failure of this 

 relation between I, k and T indicates a difference between the 

 super-conducting and the ordinary conducting state which may be 

 regarded as a characteristic difference of both. 



Both according to § 11 and to § J2«, we come to a conductivity 

 of mercury which is say 10^" times as great, or even more, than 

 that at the ordinary temperature. If we assume that the numl^er of 

 free electrons per unit of volume at the transition from the ordinary 

 to the super-conducting condition undergoes no important change, 

 and then calculate according to the ordinary electron theory from 

 the conductivity the free path of the electrons, we arrive at values 

 which are comparable to the lengths of the mercury threads used in 



') Less, when the particular circumstances mentioned in note 1 should exist. 



2) The purity of both can probably not be made so high as that of mercury 

 so that disturbances from a trace of additive admixture resistance in the super- 

 conductive state do not seem impossible. 



