MAGNETIC TUBES
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identical closed trajectories in a molecular magnetic field, the
number of lines of force cut by the radii vectores at each revolu
tion is one and the same universal constant.” In other words,
all the electron-resonators are transversed by a like tube of
magnetic force. The product of the induction flux and the
charge is equal to Planck’s constant. Bernoulli’s treatment is
perhaps not altogether satisfactory since he makes the assump
tion—which must be wide of the mark—“ that the molecular
magnetic field may be regarded as uniform.”
We consider first the number of magnetic tubes threading
through a circular orbit in which a point charge e is travelling
with large velocity. Such a charge making v revolutions per
second may be regarded as equivalent to a current i = ev. Let
L denote the self-inductance of the equivalent current circuit,
then the electrokinetic energy is given by
T = |L« 2 10 :1
But by definition the product Li is the number of magnetic
tubes threading through the circuit, i.e.
Li = N TO 10 : 2
Substituting this value in the expression for T we get
T = IN,/*' ..... 10 : 3
Now according to the quantum theory the steady motion of the
system must be such that the kinetic energy obeys the relation
2 $Tdt — nh 10 : 4
where n is an integer and the integration is to be extended over
a complete period of the motion. Although the quantum theory
has been expressed by different investigators in many different
ways, in this simple case where the energy can be expressed by
one single term, all forms of the quantum theory lead to the
same condition. This fact has been pointed out by W. Wilson.
We now make a further assumption, namely, that as all mass
may be regarded as electromagnetic mass the kinetic energy of
the moving charge may be identified as electrokinetic energy,
that is, we assume that the value for T given in equation (3)
may be employed in equation (4). Substituting the value for T
given in (3) we get
$>N m evdt — nh 10 : 5
If in this motion Maxwellian principles are suspended there is
no radiation, and the kinetic energy may be assumed constant.
Consequently N m is constant, for both e and v are constant.
Since (pvdt = 1, we find