XVI. 3] SPINNING ELECTRONS 223
to that of a rigid body. The final result found gives the energy as
T = me 2 + |(Aft)! 2 + Bco 2 2 + Ca> 3 2 ) + constant 16 : 1
In the first term m = m 0 /( 1 — /l 2 ) 172 where m 0 — \e 2 /ci and
p —v/c. The components of spin are (o x , co 2 , co 3 , and the
electrodynamic moments of inertia may, in general, be expressed
in the form
A=I(i+«i/3 2 +« 2 ^ 4 + • • )> B=C=I(i+c 1 jS 2 +c 2 iS 4 + . . ),
where I = \m a a 2 is the moment of inertia of the spinning electron
at rest.
It appears probable that the boundary conditions adjust
themselves so that the interior fields of the electron remain
unchanged at the velocity under consideration. This assumption
leads to the classical expressions for the force on an electron in
an electric or magnetic field.
The spinning or gyrostatic electron moving with uniform
velocity under no forces has a single precessional frequency v
given by
2nv=Q x (C—A)/C=Q 1 (c 1 —a 1 )p 2 (i+b 1 fi 2 +b 2 p i + . . .) 16:2
where Q x is the constant intrinsic spin of the electron.
Fitzgerald has shown that an oscillating magnet can radiate
electromagnetic waves, so that v may be regarded as the frequency
of the emitted radiation.
If we put
hQ x — nc 2 m 0 /(c x — a x ) . . . . 16 : 3
where (c x — a x ) is a numerical constant equal to 2/5 for the
simple model considered, we find to a first approximation :
hv — \m Q v 2 16 : 4
the well-known photo-electric equation.
Planck’s constant then appears as a quantity characteristic
of the spinning electron, and dependent on its intrinsic spin.
It is claimed that with similar hypotheses as to spinning
protons the series formula for line spectra can be deduced, and
the correct value for the Rydberg constant obtained. The photo
electric equation used in conjunction with a Maxwellian dis
tribution of electron velocities, also leads, with reasonable hypo
theses as to electron orbits in a space lattice, to Planck’s formula
for black-body radiation and the associated formulae for specific
heats.
Although objections may be raised against certain features of
the exposition, the attempt is interesting as indicating that there
are still possibilities in the construction of models which in
certain respects conform to the classical laws. There remains the
difficulty of accounting for an intrinsic spin which is to be the
same for all electrons.