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310 PHYSICS: E. H. HALL ^ Proc. N. A. S. 
on a, and the transfer will have substituted for an ion of negative potential 
energy an ion of equal but opposite orientation, that is, an ion of positive 
potential energy of orientation, and the new ion will at once begin to 
swing in such a way as to resume the process that had come to an end on 
FIGURE 2 
the first ion. Other things being equal, the strength of the current will 
be proportional to the sine of the angle of orientation, a in figure 1, which 
through a wide range of field strength is (see Prop. (5)) practically pro- 
portional to this strength. Thus Ohm's law is satisfied, so far as the kind 
of conduction now under consideration, that is, the "associated-electron 
conductivity," which in my previous papers I have called ka. The 
"free electron conductivity," kf, is to be considered briefly later in this 
paper. 
The Temperature Relation 
14. It is misleading to speak of the conductivity of pure metals as being 
proportional to the reciprocal of the absolute temperature. If this re- 
lation held, the temperature coefficient of resistance would be 0.00367 
for all metals, whereas its mean value between 0° C. and 100° C. is greater 
than 0.00367 in most metals and is greater than 0.006 in some. Moreover, 
the purer the metal, the higher the value of this coefficient. Accordingly 
a theory of conduction that makes conductivity inversely proportional 
to T proves too much. It is probable that the observed rather loose 
relationship between conductivity and temperature is the outcome of 
opposing influences, the direct effect of rise of temperature being to in- 
crease resistance much more rapidly than the temperature increases, 
while increase in the number of ions with heating of the metal tends to 
reduce the resistance. This idea is elaborated in the following para- 
graphs. 
15. The necessary relative position of an ion and an atom, with a view 
to the passage of an electron from the atom to the ion, is indicated by 
figure 2, where the circle represents an atom, the imperfect circle an ion, 
p the point at which an electron must lodge in order to make an atom of the 
FIGURE 1 
