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xii. 4] MAGNETIC TUBES IN ROTATION 165
potential energy is numerically double this amount. It may be
pointed out that in our present work we are virtually expressing
potential energy in terms of what, from the ordinary standpoint,
would be described as concealed kinetic energy.
4. Electrons regarded as Rotating Tubes
It is instructive to take some numerical examples of these
results.
Case I.— According to the principle of relativity the energy
corresponding to a mass m as judged by an observer relatively
at rest is wc 2 . Let us assume that in the case of a negative elec
tron this amount of energy may be identified with the energy
of rotation of a single magnetic tube. This corresponds to the
assumption made by Stark * who identified the equivalent energy
of an electron at rest, with one quantum of energy hv. Then
we have
hv — me 2 12 :10
Taking h = 6*558 x io -27 erg sec.
m = 9 x io -28 gm.
c — 3 x io 10 cm./sec.
this yields for v, the frequency of rotation, the value 1*24 x 10 20
sec -1 . That is, a single quantum tube rotating with this fre
quency would have an amount of inertia equal to that of a
negative electron.
The frequency in question may be expressed in a different
way by using the fundamental Rydberg frequency
Putting
_ 27r 2 me 4
h*K 2
27ie 2 _
JcK ~
12:11
12 :12
where a is a pure number, we may write
me 2
12:13
The form of this result suggests that the amount of the energy
me 2 associated with the mass of the electron may be regarded
as a quantum of energy, hv, provided v —
If we further assume that the maximum velocity of the
rotating tube does not exceed the velocity of light, the size of
our electron must be limited and we can form an estimate of its
* Stark, Phys. Zeitschr., voi. 8, p. 881, 1907.
