676 

electrons coming from the hotter side of a cavity 
between two metal atoms will move more rapidly 
than when coming from the colder. There will 
therefore be a drift of energy towards the colder 
metal which bears to the slope of temperature such 
a relation that the heat conductivity of the metal 
is proportional to nd T. As the heat conductivity 
of a pure metal changes very little with change 
of temperature, this equation again implies that 
nd varies inversely as 4/T, and we have the same 
difficulty in understanding how this is brought 
about. On dividing the heat conductivity by T 
times the electrical conductivity the product mad 
disappears from the result, and we obtain a con- 
stant the value of which should be approximately 
2°3x 108 for all metals at all temperatures. At 
air temperatures the values found experimentally 
vary between 2 and 3 x 108, and at very low tem- 
peratures between 1°5 and 3x108. The agree- 
ment between the two results is undoubtedly good, 
but when the calculations are improved in accuracy 
by taking into account the variation of the speeds 
of the electrons about the mean value used by 
Drude, Lorentz finds the constant 1°5 x ro’, which 
is not in such close agreement with experiment. 
For alloys and conducting salts the experimental 
values are considerably higher than for pure 
metals, and Koenigsberger and others have put 
this down to the part played by the atoms them- 
selves in the conduction of heat. For quartz and 
other electrical insulators which are good con- 
ductors of heat there can be no question of the in- 
significance of the réle of the free electrons. 
Owing to the different values of the concen- 
tration n of electrons in different metals, there 
will be a flow of electrons through the surface of 
contact of two metals till the potential difference 
produced stops the flow. In an unequally heated 
metal the same process of compensation will 
occur. In the former case we get the Peltier and 
in the latter the Kelvin effect. The former agrees 
in order of magnitude with the values found by 
experiment, but as Sir J. J. Thomson has pointed 
out, it is difficult to reconcile the great decrease 
of electrical conductivity of a metal on melting 
with the small Peltier effect between solid and 
molten metal. The calculated Kelvin effect shows 
that the concentration n of the electrons must in 
all metals be nearly proportional to /T, a result 
which is not easily reconciled with that for ma 
deduced. from the electrical or thermal con- 
ductivity. 
Since a negative electron in motion in a mag- 
netic field is acted on by a force transverse to its 
path, the theory affords a simple explanation of 
the Hall effect, and gives the right sign and 
order of magnitude for the effect in bismuth at 
ordinary temperatures, but the wrong sign for 
the effect at low temperatures, and for the effects 
at ordinary temperatures in iron and antimony. 
In no field can the simple electron theory be 
said to have given a satisfactory quantitative 
account of the facts, and its elaboration in one 
region has in general led to greater difficulties in 
others. The kinetic energy of the electrons it 
NO. 2390, VOL. 95] 
NATURE 

[AUGUST 19, 1915 

postulates is so great that an increase of 1° C, in 
their mean temperature involves a supply of heat 
ten times the specific heat of the metal. After 
pointing this out Sir J. J. Thomson, in 1907, in his 
“Corpuscular Theory of Matter,” developed a 
new theory which may be called the doublet 
theory. According to this theory the atoms of a 
metal are grouped together in pairs, one of each 
pair positively, the other negatively charged. In 
ordinary circumstances the axes of these doublets 
point in all directions on the average equally. 
Under the action of an electric field the doublets 
tend to arrange themselves in lines, with the 
positive end of one near the negative of the next, 
and electrons may pass from the negative end of 
one doublet to the positive of the next, and so 
along the line of doublets. 
On the assumption that the axis of the doublets 
distribute themselves according to the gas law, 
that their centres are spaced on the average b 
apart while the charges of the same doublet are 
d apart, and p electrons are discharged from a 
doublet per second, the electrical conductivity of 
the medium works out proportional to nbdp/T 
where n is the number of doublets per c.c. and T 
the absolute temperature. The experimental facts 
show that nbdp is independent of temperature. 
In the same way the transport of kinetic energy 
by an electron leaving a doublet at a higher, and 
joining one at a lower temperature, leads to a 
heat conductivity proportional to nb*p, which the 
experimental facts show is independent of tem- 
perature. The quotient of the heat conductivity 
by T times the electrical conductivity on this 
theory comes 2°6b/dx 108, and as b/d must be 
greater than unity the agreement with the experi- 
mental value 2 to 3 x 108, is about as good as in 
the case of the simple theory. The presence of 
the b/d makes it possible to include in the theory 
those substances for which the quotient is high. 
At the junction of two metals the excess flow 
from one metal will cause a difference of potential 
and an electric field which will change the orienta- 
tion of the doublets until the flows are equalised. 
In an unequally heated metal the same method of 
compensation will come into play, and we have 
the Peltier and Kelvin effects. 
If the rotation of a doublet in an electric field 
does not take place about the middle point, the 
two charges of the doublet move with different 
speeds. If they are in a magnetic field its action 
on them will tend to incline the axis of the doublet 
to the plane containing the two fields, and there 
will be a flow of electrons at right angles to both 
fields. The direction of the flow will be deter- 
mined by that of the end of the doublet which 
moves most quickly. We thus have an explana- 
tion of the Hall effect, whether it be positive or 
negative. 
No numerical comparisons of theory with ex- 
periment appear to have been made in the case of 
| these thermo-electric and thermo-magnetic effects. 
In his addresses to the Institute of Metals on 
May 5, and to the Physical Society on June 25, 
Sir J. J. Thomson dealt with the modification of 


