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SOURCES OF ION1ZATION 103

so that some of the particles will acquire-the energy due to
the full fall of potential. The expectation of a particle
passing without loss of charge and having the maximum
energy may not be so great as that for it to have been
without charge for part of its path when the energy it
will have acquired will be less; there will be thus a certain
energy, or velocity, of the particles for which the expectation
Is a maximum and at the point on the parabola corresponding
to this velocity the density of the photograph will be a
maximum. The density, however, will fall away gradually on
either side so that the parabola will not begin abruptly at
the velocity for which the expectation Is greatest, unless
that velocity is the maximum due to the fall through the
whole potential difference between anode and cathode. At
low pressures, however, the parabolas commence quite
abruptly and the variation in intensity does not show any
resemblance to that which would be represented by the
ordinate of a probability curve.

Wien compared the energy In the particles as calculated
from their electrostatic deflection by means of equation (2),
p. 21, with the potential difference between the anode and
cathode, the latter being calculated by the method of the
alternative spark gap. He came to the conclusion that the
energy of the particles was only about one-half of that which
they would acquire by falling through the potential difference
between the anode and cathode. This would be the case
if the free path of the particles when charged was equal to
that when it was uncharged, and each of them a small fraction
of the thickness of the dark space.

I tested the relation between the energy of the particles
and the potential fall by a different method, as the method of
the alternative spark gap is not under all conditions a
very satisfactory way of measuring potential differences. The



	SOURCES OF ION1ZATION 103 so that some of the particles will acquire-the energy due to the full fall of potential. The expectation of a particle passing without loss of charge and having the maximum energy may not be so great as that for it to have been without charge for part of its path when the energy it will have acquired will be less; there will be thus a certain energy, or velocity, of the particles for which the expectation Is a maximum and at the point on the parabola corresponding to this velocity the density of the photograph will be a maximum. The density, however, will fall away gradually on either side so that the parabola will not begin abruptly at the velocity for which the expectation Is greatest, unless that velocity is the maximum due to the fall through the whole potential difference between anode and cathode. At low pressures, however, the parabolas commence quite abruptly and the variation in intensity does not show any resemblance to that which would be represented by the ordinate of a probability curve. Wien compared the energy In the particles as calculated from their electrostatic deflection by means of equation (2), p. 21, with the potential difference between the anode and cathode, the latter being calculated by the method of the alternative spark gap. He came to the conclusion that the energy of the particles was only about one-half of that which they would acquire by falling through the potential difference between the anode and cathode. This would be the case if the free path of the particles when charged was equal to that when it was uncharged, and each of them a small fraction of the thickness of the dark space. I tested the relation between the energy of the particles and the potential fall by a different method, as the method of the alternative spark gap is not under all conditions a very satisfactory way of measuring potential differences. The