[p.
4]
454 DOC.
19
LECTURE ON FLUCTUATIONS
W
= w0e{d2s/dE2*c2/2K)
de fIg
e2e~e2'2a2 de
_
J
xV*2
dx
_
^
(
.
i i/
i
c2,2'2de
$e
x2dx
£2
=
k
J
+
P
hvVdv
3 3
d2S
f
k
dE2
(3)
-
/
o
\
c^ f~\p2
e2
=
(
1
+
-p.1
hvpVdv
=
hvpVdv
+
(8nhv3}
Vdv
nj2hv
v2
E)
=
J+eü£VT»
?y
stimmt.
Undulationsth.
[7] Temperaturschwankung
eines
Korpers
im
Strahlungsraum.
Brown'sche
Be-
wegung
eines monochromatischen
Spiegels:
AD.
[2 081].
The
notes
are on
three
sheets,
numbered
"1,"
"(2),"
and
"(3)"
in Einstein's hand.
The
first
sheet contains
text
on
both
sides.
They
are
presented
here
as [p.
1]
and
[p. 2].
The
recto
of the second sheet
is
[p.
3];
its
verso
is
blank. The
recto
of the third sheet
is [p. 4].
The
verso
of the third sheet contains unrelated calculations
(concerning
the
integral
of
lg
sin
x),
partly
in
an
unknown hand. These calculations
are
omitted here.
[1]The
document
is
dated
on
the
assumption
that the
notes
were
written for Einstein's
first
lecture
in Leiden,
on
10 February 1911
(see
Einstein
to H.
A.
Lorentz,
15 February
1911)
to
a
student
association
(see
Einstein
to
Heike
Kamerlingh
Onnes,
31
December
1910).
Although
Einstein
in
later
years gave many
lectures
in Leiden,
the
topic
and the
way it
is
treated
in these
notes
suggest
that
they
were
written for the
1911
lecture.
[2]The words "Entwurf ... Leiden"
at
the head of the document
are
in
an
unknown hand.
[3]The
first part of Einstein's
notes
probably
refers to
an
argument
such
as
the
one
given
in
Einstein
et
al. 1914
(Doc. 27),
pp.
355-357.
[4]The left-hand
part
of the
notes
on
[p.
1]
sketches
a
derivation of
Einstein's Brownian
motion
formula
essentially
similar
to
the
elementary argument
given
in Einstein
1908c
(Vol. 2,
Doc.
50)
but
using,
instead of the diffusion
coefficient,
the
probability
distribution for
a sus-
pended particle's position
derived
on
the
upper
part
of this
page.
The
notes
on
the
right-hand
side
of
the
page,
on
the other
hand,
introduce
a
probability
distribution for the
displacement
of
the
particle, apparently following
the
line
of
reasoning
in
§4
of
Einstein 1905k
(Vol.
2,
Doc.
16).
[5]The correct
formula
is
A2-r =kT-3nt]P
(see
Einstein
1908c
[Vol. 2,
Doc.
50],
p. 238),
where
A2
actually
stands for the
mean
square
of
the displacement
of
the suspended particle in
the time
r,
P for
the
particle's radius,
rj
for the
viscosity
of the
medium,
k
for
Boltzmann's
constant,
and
T for
the
temperature.
An
erroneous
factor
2
was
introduced into the
first
line
of
Einstein's
calculation.
[6]The following
calculations relate
to
Einstein's formula for the
energy
fluctuations of
black–
body radiation;
in
fact,
they provide
the
steps
omitted in
the
derivation of
this
formula
as
presented in
Einstein
1909b
(Vol. 2,
Doc.
56),
pp.
188-189. Einstein
starts
from Planck's
expres–