170
DOC.
13 PROOF OF
AMPERE'S CURRENTS
Published
in
Deutsche
Physikalische
Gesellschaft.
Verhandlungen
17
(1915):
152-170.
Lec-
ture
held
on
19 February
1915.
Submitted
10
April 1915, published
30
April
1915.
[1]See, e.g.,
Harman
1982,
chap. 2,
for
an
overview of
nineteenth-century
theories of
mag-
netism. See also the editorial
note,
"Einstein
on
Ampere's
Molecular
Currents,"
pp.
145-149,
for
more
background
on
this
paper.
[2]See, e.g.,
Lorentz
1909 for
an
overview of electron
theory.
[3]Curie's
law,
found
empirically
in 1895 (Curie
1895),
states
that for
paramagnetic
sub-
stances
the
susceptibility
is
inversely proportional to
the
temperature.
In 1905
Paul
Langevin
derived
a
formula
for the
susceptibility
of
paramagnetic
substances that reduces
to
Curie's law
for small
fields (see Langevin 1905).
His
theory was
based
on
the
hypothesis
that each
atom
carries
a
permanent magnetic
moment, due
to
intra-atomic electronic motion. Einstein dis-
cussed Curie's
law
and
Langevin's theory
in
his
course on
the kinetic
theory
of heat
at
the Uni-
versity
of
Zurich,
summer semester
1910
(see
Vol.
3,
Doc.
4, [pp.
38-39],
for Einstein's lecture
notes
on
this
topic).
[4]See
the editorial
note,
"Einstein
on
Ampere's
Molecular
Currents,"
p.
146,
for
a
discus-
sion of Einstein's views
on zero-point
energy.
[5]E
is
the
charge
of the electron and
u its
mass.
[6]This
value
corresponds
to
a
value of
1.77
x
107
emu/g
for the
specific charge
of the elec-
tron,
in accordance with
recent experimental
results
(see, e.g.,
Neumann, G.
1914).
[7]"D" should be
"d."
[8]At
the
corresponding point
(p.
698) in
Einstein
and
De
Haas
1915c
(Doc.
14),
the
satu-
ration
magnetization per
cm3 is
put at
1000.
See also
pp.
164
and
169
of this
paper,
where the
values
1200
and
1260
are
used. The
density
of iron
is
7.8
g/cm3.
[9]"D"
should
be
"d."
[10]"Qä"
should
be
"Qä."
[11]See
Einstein and De Haas 1915c
(Doc.
14), pp.
699-700,
for
details
on
the
recording
of
the
oscillogram.
Walter
Rogowski
(1881-1947)
was a
permanent
member of the
Physikalisch-
Technische
Reichsanstalt,
where the
experiment
was
performed.
[12]"D"
should
be
"d."
[13]"w"
in in
the
upper
summation limit should
be
"oo."
[14]A
more
general
solution of
eq.
(8a),
also valid for
frequencies
other than the
resonance
frequency,
is
given
in
Einstein and
De
Haas 1915c
(Doc.
14),
pp.
701-702. See also
§6
below.
[15]See Weiss
1907,
1908 for Pierre Weiss's
theory
of
ferromagnetism.
Einstein discussed
Weiss's
theory
in
his
course on
the
kinetic
theory
of heat
at
the
University
of
Zurich,
summer
semester
1910 (see Vol.
3,
Doc.
4,
[pp.
41-43],
for Einstein's lecture
notes
on
this
topic).
[16]Foucault
currents
are
the
eddy
currents
induced
in
a
conductor
moving
in
a
magnetic
field.
[17]In
Einstein and De
Haas 1915c
(Doc.
14), p.
704,
the value of
Q was
corrected
to
0.0065.
[18]See
the
previous note.
[19]Figure
6
shows the
torque
and the
angular displacement to
have the
same
phase,
which
is wrong,
as was
first
pointed out
by
Lorentz
in
a
telegram to
Einstein
(see
Einstein
to
H. A.
Lorentz, 28
April 1915,
in
which Einstein
acknowledges
the
error).
Einstein corrected the mis-
take
in
Einstein
1915d
(Doc.
16).
[20]See
Einstein
and De Haas 1915c
(Doc.
14), p.
701,
for
more
details
on
the derivation of
eq.
(16).
"J1"
in (16)
should
be "Js."
[21]In
a
letter
to
G. L.
de
Haas-Lorentz,
Einstein made the
stronger
statement
that the results
for small
displacements
seemed
to be
systematically
wrong (see
Einstein
to
Geertruida de
Haas-Lorentz,
before
10 April 1915).
[22]In
Einstein and De Haas 1915c
(Doc.
14),
p.
710,
the number 0.128
was
corrected
to
0.124.
[23]At
the
corresponding point
(p.
710) in
Einstein and De Haas 1915c
(Doc.
14),
the value
of
the
saturation
magnetization per
cm3 is
put at 1300,
which results
in
slightly
different values
of
Js
and
Y.