CONDUCTIVITIES OF METALS AND ALLOYS AT LOW TEMPERATURES. 443 
absorbed by the electrons in 1 gramme of a metal during an increase of temperature 
of 1° C. far exceed the observed specific heat of the metal. In this theory the electrons 
pass from one doublet, consisting of a positively and negatively charged atom, to 
another similar doublet, which have arranged themselves along the line of electric 
force, as in the old theory of electrolysis the molecules of the Grotthus chains were 
supposed to do. If cl is the distance apart of the charges of the doublet, and b is the 
distance between the doublets, Thomson shows that 1c/ Kt is 9b/Sa times the value 
found on the former theory. Since b/a may vary in value from metal to metal, and 
in the same metal at different temperatures, this theory may by a proper choice of the 
laws of variation be brought into unison with the observed facts. 
It is, however, open to doubt whether any theory which does not take into account 
the atomic differences of the various metals can give a satisfactory explanation of the 
whole facts. The nearness to each other of the curves for metals belonging to the 
same chemical group, Plate 31, suggests that atomic properties play their part in 
determining the behaviour of a metal to the flow of heat and electricity through it. 
Electronic theories have regarded the free electrons as the sole carriers of energy 
from molecule to molecule, and have therefore been unable to deal with the thermal 
conductivities of electrical insulators, in which there can be no free electrons. Now 
the thermal conductivities of some substances which insulate electrically are as large 
as those of the worse conducting metals, e.g ., the thermal conductivity of quartz along 
the axis is 0'029, while that of bismuth is only 0'016 to 0'019. It seems, therefore, 
that a theory of heat conduction which ascribes it to free electrons alone must be a 
very partial account of it. 
The fact pointed out on p. 427, that the variation of the thermal conductivities of 
the metals with temperature is of the same character as, though less marked than, the 
corresponding variations for electrical insulators, and that alloys vary in a manner 
similar to the only mixture (glass) of insulators yet investigated, both support this 
contention, that theories which depend solely on free electrons as carriers can hardly 
claim to be adequate expressions of the phenomena. 
This investigation was commenced in Manchester, where a liquid air plant was 
available. I have to thank Dr. E. C. C. Daily and the authorities of University 
College for kindly providing me with liquid air in London. 
I have also to thank the Committee administering the Government Grant for 
Scientific Investigations for a large proportion of the funds out of which the materials 
used in the investigation have been purchased. 
3 L 2 
PRESENTED 
8 AUG. 1308 
