5 8 6 A P P E N D I X B
1. On the Moment of Momentum in a Magnetized Body
by W. J. de Haas.
§1. Theoretical, by Prof. Einstein.
The formula
can be deduced without making special hypotheses concerning the motions of the electrons
in the atom or the molecule.
If a molecule situated at the origin of coordinates has the magnetic moment m, the com
ponents of the magnetic force h at a point sufficiently distant will be given by
(1)
On the other hand we can calculate the magnetic force caused by intramolecular currents.
If V is the vectorpotential we have
(2)
We have to consider the mean values of V and h taken for a long lapse of time. Introducing
the retarded potentials we have, if i is the current,
(3)
(dS element of volume) Integrating over an electron having a charge e and a velocity v, and
confining ourselves to terms proportional to v, we find
Now, let an electron have a stationary motion in a small space surrounding the origin O. Its
coordinates being small in comparison with r, we may write
(4)
so that the mean values of the components of the vector potential become
, etc.
Here the mean value vanishes. Further, if the vector f is the moment of the velocity of
the electron with respect to the origin,
[p. 1]
moment of momentum
magnetic moment
  2
mc
eelectrost.
 2
m
eelectromag.
= =
x1, x2,
x3
h1
1
2
2
∂x1
∂ 1
r
 
è ø
æ ö
2
∂x2
2
∂x1
∂ 1
r
 
è ø
æ ö
3
∂x3
2
∂x1
∂ 1
r
 
è ø
æ ö
, etc. + + =
h1
∂x2
∂V3
x3 ∂
∂V2
etc. , – =
V
1
c
ò

i] [
r
dS
=
V = [ ]
e
c

v
r

[p. 2]
ξ1, ξ2, ξ3
1
r
 
1
r0

1
r
 
∂
∂ξa
 ξa
a
å
+
1
r0

1
r
 
∂
∂xa
  ξa
a
å
– = =
V1
e
c

1
r0

∂
1
r
 
∂xaø
÷
è
ç
æ ö
0
ξa
a
å
– ξ1
·
=
ξ
·
ξ2 ξ1
·
1
2
  f3 – = ξ3 ξ1
·
1
2
  f2 =