We see that except in the case of the lowest temperature, that of
liquid air, where there is a great drop in the velocity, the
velocities of the ions are proportional to the absolute temperature.
On the hypothesis of an ion of constant size we should, from the
kinetic theory of gases, expect the velocity to be proportional to the
square root of the absolute temperature, if the charge on the ion did
not affect the number of collisions between the ion and the molecules
of the gas through which it is moving. If the collisions were brought
about by the electrical attraction between the ions and the molecules,
the velocity would be proportional to the absolute temperature. H. A.
Wilson (_Phil. Trans._ 192, p. 499), in his experiments on the
conduction of flames and hot gases into which salts had been put,
found that the velocity of the positive ions in flames at a
temperature of 2000° C. containing the salts of the alkali metals was
62 cm./sec. under an electric force of one volt per centimetre, while
the velocity of the positive ions in a stream of hot air at 1000° C.
containing the same salts was only 7 cm./sec. under the same force.
The great effect of temperature is also shown in some experiments of
McClelland (_Phil. Mag._ [5], 46, p. 29) on the velocities of the ions
in gases drawn from Bunsen flames and arcs; he found that these
depended upon the distance the gas had travelled from the flame. Thus,
the velocity of the ions at a distance of 5.5 cm. from the Bunsen
flame when the temperature was 230° C. was .23 cm./sec. for a volt per
centimetre; at a distance of 10 cm. from the flame when the
temperature was 160° C. the velocity was .21 cm./sec; while at a
distance of 14.5 cm. from the flame when the temperature was 105° C.
the velocity was only .04 cm./sec. If the temperature of the gas at
this distance from the flame was raised by external means, the
velocity of the ions increased.
We can derive some information as to the constitution of the ions by
calculating the velocity with which a molecule of the gas would move
in the electric field if it carried the same charge as the ion. From
the theory of the diffusion of gases, as developed by Maxwell, we know
that if the particles of a gas A are surrounded by a gas B, then, if
the partial pressure of A is small, the velocity u with which its
particles will move when acted upon by a force Xe is given by the
equation
Xe
u = ------- D,
(p1/N1)
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