117 



in other words the conductivity of tlie super-conducting mercury 

 might practically be considered Infinite. 



§ 12. Failure of the relations of Wiedemainn and Franz and of 

 LoRENZ uuth super-conductors, a. If tlie conclusion concerning the 

 non giving otf of heat to the glass by a mercury thread below 

 4°.19 K. which we discussed in § 11, were applicable, we should 

 arrive at a different view concerning the potential phenomena, from 

 that arrived at above. If the mercury has an appreciable real 

 micro-residual-resistance, so that heat is developed throughout the 

 thread, and if we need not take any account of apparent micro- 

 residual-resistances, the distribution of tem])erature in the part of the 

 wire that is below the vanishing point, is govei-ned by the ordinary 

 formula for the rise of temperature of a wire conveying a current 

 without external conduction of heat. 



Let us keep as near as possible to the well known ordinary case 

 in order to show the nature of the phenomena that are to be 

 expected in the case in point, and for the sake of simplicity, as it 

 is principally a question of order of magnitude, let us assume that 

 below the vanishing point the ratio of the electric conductivity /; to that 

 of heat I, is given by the same formula as holds approximately above 

 the vanishing point, with the difference that the constant has a diffe- 

 rent value 10'' times smaller, so that while above the vanishing point ; 

 A 

 — z=aT with a = 0,023.10-6 (watt, ohm, degree-'), 



below the vanishing point 



I 



— — a!T with a' — a.lO-\ 



We arrive at the low value which we ascribe to a' amongst 

 other things in consequence of the fact that X remains of the same 

 order of magnitude below the vanishing point as above it, as appears 

 when on the supposition that all the heat in the experiments is 

 developed in the middle of the thread and only flows away at the 

 extremities, we deduce an upper limit for the heat conductivity ^). 



1) This conclusion is confirmed by preliminary determinations of the lieat- 

 conductivity of mercury above and below the vanishing point made by me and 

 Mr. G. Holst. We conclude from these that this constant does not undergo any 

 considerable change at the vanishing point, and the same is true for the specific 

 heat, which we have also investigated, however important this point may be for 

 the electric conduction. 



[Our preliminary yet very uncertain values are: for the conductivity between 

 40.5— 60.5 K., k = 0,25 cal. cm. sec, between 39.8— 4o.2 K., k = 0.46 cal. cm, 

 sec, for the specific heat between 4o.2— 6'^.5 K., Cp ==0.0014 and between 

 3 —4° K., Cp = 0.00053 (Added in translation)]. 



