108 DOC.
5
GENERAL MOLECULAR
THEORY OF HEAT
of
a
distribution
of
microstates
over a hypersur-
face
of
constant
energy.
[14]
It
is
not clear
just
what Einstein
meant
by
the
term
"kinetische Atomtheorie"
("kinetic
theory
of
atoms").
The term
suggests a
kinetic
theory,
like the kinetic
theory
of
gases,
but
ap-
plicable
to
any system
with
an
atomistic
struc-
ture,
that
is,
possessing
a
finite
number
of
de-
grees
of freedom. See the editorial
note,
"Einstein
on
the Foundations
of
Statistical
Physics,"
note
59.
[15]
See Boltzmann 1898a,
§
42.
What
was
"geläufig" ("customary")
was
Boltzmann's
proof
of
the
equipartition
theorem
(see
Einstein
1902b
[Doc. 3],
note
22);
Boltzmann did
not
go
on
to
estimate the value
of
K
(or,
equivalently,
the Boltzmann
constant,
k-see
Einstein 1902b
[Doc.
3], note 25),
as
Einstein did below.
[16]
Einstein 1903
(Doc. 4).
The
incompressi-
bility
condition,
E(d(pv/dpdv) =
0, is
not stated
explicitly
in
the cited
paper;
this
is
Einstein's
first
mention
of
it
in
print.
See Einstein 1903
(Doc.
4), note
7.
[17]
The first
exponent
in
both the
numerator
and the denominator
on
this
line
should be
-O(x1
...
xn)/2KT0; a
minus
sign
should be
added to the
exponent
inside the
integrals
in both
the
numerator
and the denominator
on
this line
and the
next.
The factor
preceding
the left-hand
side
of
the next line should be 3/2.
[18]
Boltzmann 1898a.
[19]
This
is
the
same
value
of
R given
in
Planck
1901b,
p.
564,
which
is
probably
Einstein's
source (see
note 5).
[20]
Nowhere in
Meyer,
O. E.
1877, 1895,
or
1899 does
one
find the value
of
N
given
here.
However,
exactly
this value
is
given
in
Planck
1901b,
p.
566,
where Planck cited
Meyer,
O. E.
1899,
p.
337.
At
the
time
of
this
paper,
there
was
considerable
uncertainty regarding
the
value
of
Avogadro's number,
N. For
a
discus-
sion
of
the
problems
involved in its determina-
tion, see
the editorial
note,
"Einstein's
Disser-
tation
on
the Determination
of
Molecular
Dimensions,"
pp.
179-182.
[21]
Einstein's
value for
K
yields a
value of
1.30
x 10-16,
for Boltzmann's
constant. Planck
calculated
the value 1.346
x 10-16
with the
help
of
his
formula for the
energy spectrum
of
black–
body
radiation
(see,
e.g.,
Planck
1901b,
p.
565).
The
agreement
between the two values
is
surprising,
given
the
uncertainty
in the value
of
N
(see note 20).
[22]
In this and in three
of
the
following
four
equations,
wE should be
w(E).
[23]
In the bracketed
expression,
E2
should
be
E2.
[24]
The first term
on
the
right-hand
side
should be
E2.
[25]
The first term
on
the left-hand side should
be
E2.
[26]
The term
on
the
right-hand
side should be
E2.
[27]
See
Stefan
1879 and Boltzmann 1884.
[28]
Einstein's
value for
c
is
the
same as
that
given
in
Planck
1901a,
p.
562, which, in turn,
cites Kurlbaum
1898, p.
759. For
K,
Einstein
used the value 6.5
x 10-17
calculated above
on p.
359.
[29]
The
equation xmT
=
constant, a special
case
of Wien's
displacement
law
(see
Wien
1893),
had been derived earlier
by
Einstein's
ETH
physics professor,
H. F.
Weber,
from his
semi-empirical
radiation law
(see Weber,
H. F.
1888;
for the
early history
of
the
displacement
law,
see
Kangro 1976,
chap.
3).
The value of
the
constant
used here
appears
to
be the
average
of
the value
(0.294) given
in Lummer
and
Pringsheim 1899,
p.
218,
and the value
(0.292)
given
in
Paschen
1901b,
p.
657. See
Paschen
1901b for
a summary
of
the
controversy over
the
value
of
this
constant.
[30]
In
a
letter
to
Conrad Habicht
of
15
April
1904,
Einstein
wrote
about
this result:
"I
have
now
found
in the
simplest way
the relation be-
tween
the
magnitude
of
the
elementary quanta
of
matter
and the
wave lengths
of radiation"
("Die
Beziehung
zwischen der Größe der Elementar-
quanta
der Materie und den
Strahlungswellen-
längen
habe ich
nun
in höchst
simpler
Weise
ge-
funden").