CONDUCTIVITIES OF METALS AND ALLOYS AT LOW TEMPERATURES. 439 
which, however, was very free from impurity. All the alloys show a decrease of the 
product as the temperature decreases. 
A comparison of this table with the table of thermal conductivities given on p. 42G 
will show that there is some similarity between the two. 
Section II I.—-Comparison of Thermal and Electrical Conductivities. 
In 1882 L. Lorenz 4 ' showed by measuring both the thermal and electrical con¬ 
ductivities of bars of a number of different metals, that the quotient of the thermal 
by the electrical conductivity was not constant, as Wiedemann and Franz! had * 
supposed, but increased with the temperature, so as to be nearly proportional to the 
absolute temperature, a result which he had anticipated! on theoretical grounds. His 
results did. not attract much attention till the publication of Riecke’s electron theory 
of conduction in 1898§ and the confirmation of Lorenz’s theory for pure metals 
between the temperatures 18° C. and 100° C. by Jager and Diesselhorst, in 1899,|| 
by a method which gives the quotient of the two conductivities directly. 
Next year Drude’s electron theory appeared,11 and more recently H. A. Lorentz 
has published one A* 
According to these theories the electricity and energy are supposed to be carried 
entirely by free electrons which move to and fro and come into collision with the 
molecules of the metal and with each other, and are assumed to have on the average the 
same kinetic energy of translation as the molecules of a gas at the same temperature. 
In the first two theories both positive and negative electrons are movable, in the 
third the negative only. 
On the former theories if we limit ourselves to two kinds of electrons carrying 
charges e v and e 2 where e 2 =— O = —e, and if %, n 2 are the numbers per cubic centi¬ 
metre, ?q, u 2 their velocities at a temperature t, l x , l 2 their mean free paths, we have the 
thermal conductivity 
k = \a (n 1 u l l 1 + n 2 u 2 l 2 ), 
and the electrical conductivity 
k = (at )- 1 {n x u x l x e?+n 2 uU?\ 
where a is the mean kinetic energy of translation of a gas molecule at absolute 
temperature 1°. 
* L. Lorenz, ‘Ann. cler Phys.,’ 13, p. 422 (1882). 
t G. Wiedemann and R. Franz, ‘ Ann. der Phys.,’ 89, p. 497 (1853). 
| L. Lorenz, ‘ Ann. der Phys.,’ 147, p. 429 (1872). 
§ E. Riecke, ‘Ann. der Phys.,’ 66, p. 353 and 545 (1898). 
|| W. Jager and II. Diesselhorst, ‘Sitz.-Ber. Akad. Wiss. Berlin,’ 38, p. 719 (1899); and ‘ Abhand. 
der Phys.-Tecli. Reichsanstalt,’ 3, p. 282 (1900). 
P. Drure, ‘Ann. der Phys.,’ 1, p. 566, 3, p. 369 (1900). 
** H. A. Lorentz, ‘ Proc. Amsterdam,’ 7, p. 438, Ac. (1905). 
