1407 
any perceptible potential difference at the extremities of the thread 
being necessary. It appears therefore that the thread has no resi- 
stance, and for the residual resistance which it might possess, a 
higher limit can be given determined by the smallest potential 
difference which could be established in the experiments (here 
0.03. 106 V)and the “thresbold value” of the current. At a lower 
temperature the threshold value becomes higher and thus the highest 
limit for the possible residual resistance can be pushed further back. 
As soon as the current density rises above the “threshold value”, 
a potential difference appears which increases more rapidly than the 
current; this seemed at first to be about proportional to the square 
of the excess value of the current above the initial value, but as 
a matter of fact at smaller excess values it increases less and at 
greater excess values much more rapidly. 
It appears that the phenomena at least for the greater part are 
due to a heating of the conductor. It has still to be settled whether 
this heating is connected with peculiarities in the movement of elec- 
tricity through mereury, which for a moment I thought most pro- 
bable in connection with various theoretical suppositions (comp. $ 4), 
when this metal has assumed its exceedingly large conductivity at 
low helium temperatures; or whether it can be explained by the 
ordinary notions of resistance and rise of temperature of a conduc- 
tor carrying a current, perhaps with the introduction of extra nume- 
rical values for the quantities that influence the problem. A further 
investigation of this with mercury in the most cbvious directions, 
such as cooling the resistance itself with helium, presents such diffi- 
culties that I have not pursued if, as it would not be possible to prepare 
the necessary mercury resistances by the comparatively simple process 
of freezing mercury in capillary tubes. When I found (Dec. 1912) 
that, as I shall explain in a following Comm., (see VIII of this series 
Comm. N°. 132d) tin and lead show properties similar to those of 
mercury, the investigations were continued with these two metals. 
Thus the experiments with mercury which are described below may 
be regarded as a first complete series. 
Various circumstances combined to make even the investigation of 
the mercury inclosed in capillary tubes difficult. A day of experi- 
ments with liquid helium requires a great deal of preparation, and 
when the experiments treated of here were made, before the latest 
improvements in the helium circulation were introduced, there were 
only a few hours available for the actual experiments. To be able 
to make accurate measurements with the liquid helium then, it is 
necessary to draw up a programme beforehand and to follow it 
