182 
MR. ARTHUR SCHUSTER ON THE 
of 400 kilometres. # The height of meteors when they become luminous is as a 
rule over 100 kilometres, but there is one case on record in which a height of 
780 kilometres was found. We may therefore take 300 kilometres as an outside 
limit for e, giving the value of 1(U 13 as the lower limit for the conductivity. This 
no doubt is a high value, and there may be some hesitation in accepting it as a 
possible one. Mr. C. T. R. Wilson has, however, already drawn attention to the 
fact that at high altitudes we must, with the same ionising power, expect a much 
increased conductivity, for the ionic velocity due to unit difference of potential varies 
inversely with the pressure. If, further, as the experiments indicate, the ionising 
power and rate of recombination of ions both diminish directly as the pressure, it 
would follow that when the pressure is only the millionth part of an atmosphere the 
conductivity should be for the same ionisation a million times as great as at the surface 
of the earth. 
Researches on the conductivity of gases generally give relative measures, so that it 
is not always easy to infer its value in G.G.S. units, but I think the folio wing- 
examples will give an idea of the order of magnitude involved. 
The quantity of electricity in the form of ions of each kind under normal conditions 
at the surface of the earth is 0'33x 10~ 16 in electromagnetic measure. To obtain the 
conductivity the figures must be multiplied by the ionic velocity per unit fall of 
potential, the sum of the velocities of both kinds of ions being 3xl0 -8 . The con¬ 
ductivity of air at the surface of the earth is therefore under normal conditions HU 24 . 
Gerdien, in one of his balloon ascents, determined the conductivity at a height of 
6000 metres and found it to be 2x 10~ 24 , which, as far as it goes, confirms the con¬ 
clusion that the conductivity is inversely proportional to the density. At a height 
such that the pressure is one dyne per square centimetre, and assuming that the 
recombination of ions is not materially affected by the low temperature, we should 
thus get a conductivity of 10~ 18 , showing that, if the views discussed in this paper are 
correct, the ionising power at great altitudes must be considerably greater than that 
which acts on the air near the surface of the earth. 
In speaking of the ionising effects of Rontgen rays, Professor J. J. Thomson! 
states that even when the ionisation is exceptionally large the proportion of the 
number of free ions to the number of molecules of the gas is less than 1 to 10 12 . 
From this I calculate the conductivity to be about 10 -2 " at atmospheric pressure. 
Some experiments by Rhtherford fix the conductivity of air, subject to the action of 
radium having an activity 1000 times less than pure radium, to be Off x 10 -19 under 
normal conditions. These figures would give to the conductivity of air at a pressure 
equal to that of a millionth atmosphere a magnitude comparable with that required. 
We know of much more powerful ionisers than the Rontgen tube or even radium. 
An electric discharge itself is sufficient to ionise a gas, as I proved as far back as 
* ‘Rapports du Congres International de Physique,’ vol. III., p. 438 (1900). 
t ‘ Conductivity of Electricity through Gases,’ p. 256. 
