IMPARTED TO A VACUUM BY HOT CONDUCTORS. 
545 
temperature, whilst the numbers given on p. 544 show that the temperature coefficient 
of is of the same order of magnitude as the coefficient of linear expansion of the 
corresponding solid conductor. 
These facts render it probable that d) is a function of the size and distance apart of 
the molecules of which the conductor consists. If we consider ^ in the formula 
dJ = i as the distance apart of the centres of the molecules in the solid state, it 
will be j)roportional to the cube root of the atomic volume. We should therefore 
expect the work done by a corpuscle in passing through the surface layer of different 
metals to be approximately equal to a constant divided by the cube root of the 
atomic volume. Up to the present d) has been determined only for sodium, platinum 
and carbon, but fortunately these three elements furnish a considerable range of 
atomic volume. As a matter of fact, carbon has the smallest atomic volume of all 
elements, whilst that of sodium is only exceeded by the alkali metals of greater 
atomic weight. 
In the accompanying table values of the atomic volume and the inverse of its cul)e 
root are given in the first two columns. The third contains the surface discontinuity 
in the potential S^, which is proportional to d); whilst the numbers in the last 
column are the ratios of those in the second and third. In the case of carbon there 
is some doubt as to what the value of the atomic volume should be, since the density 
has different values for the different allotroplc forms. Thus for charcoal the density 
is 1’9, for graphite 2'2, and for diamond 3‘5. 
Element. 
At. vol. 
(At. vol.) 1 
S<^ [volts]. 
(At. vol.) 
Sodium. 
23 
•35 
2 ■45 
■14 
■ 12 
Platinum. 
9-3 
■476 
4^1 
Carbon charcoal. 
. I 
6-3 q 
■55 t 
■66 / 
6^1 
■09 1 
,, diamond 
- 
•; 
3-46 ; 
■11 / 
It will be seen that the numbers in the last column are not quite constant > l^ut 
they only change by about 40 per cent., whilst the atomic volume changes in the 
ratio of 6 to 1, and the atomic weight varies from 12 to 195. It seems therefore fair 
to conclude that the work done by a corpuscle in passing through the surface layer is, 
to a first approximation, inversely proportional to the cube root of the atomic volume 
of the element. 
§ 3. The Effect of Gas on the Current. 
The negative leak from a hot platinum wire surrounded by air at atmospheric 
pressure is always much smaller under a given voltage than at low pressures, when 
the wiie IS maintained at the same temperature in both cases. In one case, when 
the wire was giving a current of 3 X 10~® ampere at a pressure of ’05 millim., air 
VOL. CCI.—A. 4 A 
