DOC.
8
ANALYSIS
OF
A
RESONATOR'S MOTION
281
Published
in Annalen
der
Physik
33 (1910):
1105-1115. Dated
Zurich, August
1910,
received 29
August 1910, published
20
December
1910.
[1]For
contributions
to
the derivation
of
the
Rayleigh-Jeans
law
of
black-body
radiation,
see
Rayleigh
1900,
1905a, 1905b,
Lorentz
1903,
Jeans
1905,
and Einstein 1905i(Vol.
2,
Doc.
14).
For
historical
accounts,
see
Klein,
M.
1962,
1977,
and Kuhn
1978,
pp.
143-152.
By
the time this
paper was written,
Lorentz's influential derivation
(first
presented
in
Lorentz
1908)
had
con-
vinced
many physicists
that this
law,
in
spite
of
its
failure
to account
for the
experimental
facts,
had
to
be
accepted
as a
necessary consequence
of
classical
physics.
For
a
historical discussion
of
the
acceptance
of this
law,
see
Kuhn
1978, pp.
188-210.
[2]See, e.g.,
Planck
1910a,
where
Planck claims that the
equipartition
theorem
is
not
applica-
ble
to
the
elementary
oscillators
(as
he
had
already suggested
in
Planck
1906,
p.
178).
Einstein
had criticized
a manuscript
version of
this
paper
(see
Doc.
3).
[3]At the time of
his collaboration
with
Hopf,
the methods
developed
in
their
joint papers
did
not
appear
to
the authors
to
contribute much
to
the solution of the
quantum problems
(see
Einstein
to
Jakob
Laub, 27
August 1910,
and
Ludwig
Hopf
to Einstein,
13
October
1911). See,
however, Klein,
M. 1964.
Einstein later used these methods
in
an
attempt
to
explore
the
issue
of
zero-point energy
(see
Einstein and Stern
1913
and for
a
commentary
from
a
modern
point
of
view,
see
Bergia,
Lugli,
and
Zamboni
1980).
[4]Einstein
had treated
a
similar
problem
in
Einstein
1909b
(Vol. 2,
Doc.
56),
§7,
where
he
analyzed
a
mirror
moving
in
a
radiation
field which
he
assumed
to be
characterized
by
Planck's
distribution
law.
[5]Abraham
1904, pp.
273ff.
[6]Planck
1906,
p.
113.
[7]The
second
y
in
the
right-hand
side
of
this equations
should
be
y.
[8]As
pointed
out in
Bergia,
Lugli,
and Zamboni
1979,
an
annotated
English
edition of the
present paper,
the
correct
equation,
which is used in
the
rest
of the
paper,
is
9y
=
(5
cos
w.
[9]Einstein's
notation for the external
or cross
product
of
two vectors follows
the
one
used
in
Abraham
1904.
For
a
brief overview of Einstein's
use
of
vector notation,
see
the editorial
note,
"Einstein's Lecture
Notes,"
pp.
3-10.
[10]Planck
1906, p. 114.
[11]The
"sin"
in
the
right-hand
side
of
this
equation
should
not be
squared.
[12]The
7i
in
the
right-hand side
of
this
equation
should
be
squared.
[13]See
Einstein and
Hopf 1910a
(Doc.
7).
[14]The
second "sin"
in
the
right-hand side
of
this equation
should
be
squared.
[15]Planck
1906,
pp. 122-123; in
these
pages,
Planck calculates the
sum
appearing
in
the first
of Einstein's
equations
by
transforming it
into
an
integral.
For
a
discussion of
the assumptions
underlying
this
derivation,
see Bergia, Lugli,
and Zamboni
1979,
fn. 28.
[16]Einstein
1905r
(Vol.
2,
Doc.
23), p.
914;
the
equations
given
here
are
first-order
approxi-
mations
in
v/c.
[17]See Einstein and
Hopf
1910a
(Doc.
7), p.
1099.
[18]The
left-hand
side
of
this
equation
should read:
dEz--dx.
ox
[19]In the
right-hand
side
of this
equation,
a
factor
1/2
is
missing;
the
sign
in
front of the
t
second
"cos" should
be positive;
and the
t
in
the
argument
of
this
"cos" should
be
t-T.
[20]In
this and the
following equation, t
should be
t
and the
v
in
the
right-hand
side
of
the latter
equation
should
be
n.
[21]The
"sin"
in
the second
equation
should
be
squared;
the
yn
should
be
yv;
the
v0
in
the
last
equation
should read
y0.
This derivation
follows
the
one
outlined
in
Planck
1906, pp.
122-123.
[22]Planck
1906,
p.
178.
[23]Einstein
1909b
(Vol.
2,
Doc.
56), §7.
For evidence of the
impact
that
Einstein's statistical
considerations had
on
Planck,
see
Einstein
to
Arnold
Sommerfeld,
July
1910:
"Planck has
come
up
with
no really convincing argument against my thoughts concerning energy
distribution