DOC.
4
KINETIC THEORY LECTURE NOTES
243
[14]In
Boltzmann
1896,
p. 18,
the
term
"Moleküle
hervorgehobener
Art" denotes those mole-
cules
whose
velocity components
are
inside
an
infinitesimal volume element around
a
certain
value.
Einstein
apparently refers to
those molecules whose
velocities
are
inside the solid
angle
dK.
[15]The lack of
dependence
of the heat
conductivity
(as
well
as
the
viscosity) on
the
density
was
experimentally
established
by
Stefan,
and
by
Kundt and
Warburg
(see Stefan
1872a, 1876,
and Kundt and
Warburg 1875a,
1875b).
The friction
coefficient
turned
out to be
slightly depen-
dent
on
the
pressure (see Warburg
and
Babo
1882).
[16]It
is
not
clear
what
source was
used
for the numerical values cited here.
They are compati-
ble,
though
not
identical,
with the values listed
in
Landolt
and
Börnstein
1905,
1912
(with
the
exception
of the
viscosity
coefficient
9?
for
oxygen,
which these tables
give as
2.060
x
10-4
at
room temperature).
[17]See
note
15.
[18]For
a
discussion of
this
point, see
Stefan
1872b
and
Boltzmann
1896,
p.
85.
[19]Einstein's
treatment
of diffusion
follows Boltzmann
1896,
§13.
Note that there
are
also
related formulas
in his
Scratch Notebook
(Appendix
A),
[pp. 24-25].
In the
following
calcula-
tion Einstein
temporarily changes
the notation
for
the
polar angle
from $
to
(p.
He
returns to
the former notation
on [pp.
9-10].
[20]For
the numerical calculation of
D
Einstein
uses
c
=
5x
104 cm/sec
(valid
for
nitrogen
or
oxygen
at
room temperature)
and
A
=
10-5
cm,
which
is
the value for
oxygen; see
[p.
8].
[21]Landolt
and
Börnstein
1905,
p.
375,
give
D
=
0.171
for the diffusion of
oxygen
into nitro-
gen
at 760
mm Hg
and
0°C. See
also
note
16.
[22]The
following
calculation
goes
back
to Loschmidt 1865
and
is
discussed
in Boltzmann
1896,
§12,
and
in
Meyer, O.
E.
1899, part
1, §69.
The determination of molecular dimensions
was
also the
subject
of Einstein's doctoral
thesis;
see
Vol.
2,
the editorial
note,
"Einstein's Disserta-
tion
on
the Determination of Molecular
Dimensions,"
pp.
170-182.
Although
in
this
case
"wahre Grösse der Moleküle"
refers to
the actual
size
of
molecules,
on
other occasions Ein-
stein
used
the
same
expression (or alternatively,
"Grösse der
Moleküle")
as a
synonym
for
Avogadro's
number,
just
as
he
used the word "Molekül"
to
denote
a
mole.
See,
e.g.,
Einstein
1904
(Vol. 2,
Doc.
5),
pp.
358-359,
Einstein
to
Jean
Perrin,
11
November
1909,
and Einstein
1979, pp. 38, 44.
[23]See
Perrin
1914a
for
a
survey
of methods for
determining Avogadro's
number,
including
a
list of the various numerical values obtained.
[24]The
square
brackets
are
in
the
original.
[25]There
is
a
minus
sign
missing
in
front
of
the
right-hand
sides
of the last
two
equations.
Some of the minus
signs
in
the
preceding equations
are
corrected from
plus signs. Perhaps
Einstein started the calculation
anew on
the next
page
because of
this
sign
problem.
See
also
[p. 53],
which
is
part
of
a
loose sheet inserted
at
the end of the
notebook,
for
a
related
calculation.
[26]See
Kundt and
Warburg 1875a, 1875b,
and
Smoluchowski 1898.
In Einstein
1922,
p.
823,
this
experimental
verification
is
given importance
because it
was
the
first
time
that
a new
effect
had
been
predicted
by
the kinetic
theory.
For further
details,
see
Brush
1976, §13.8.
[27]In the formulas
below,
cos
(p
should be
cos
9
and T should
read F.
[28]See
note 26.
[29]Knudsen's
investigations
on
the
properties
of rarefied
gases were
reported
in
a
number
of
articles,
published mainly
in
the
Annalen
der
Physik
between
1909
and
1911
(see, e.g.,
Knudsen
1909a, 1909b, 1910a, 1910b, 1910c,
1911).
A
comprehensive report
on
his work
was
given
at
the
1911
Solvay Congress (Knudsen 1912).
For Einstein's remarks
on
Knudsen's
lecture,
see
Doc.
25.
For
a
general
overview of Knudsen's
investigations, see
also
Knudsen 1934.
[30]In
the
expression
below
(which is
Poiseuille's
law), A
denotes the
pressure
difference
along
the
tube,
and
R is its
radius.
See
[p.
54],
which
is part
of
a
loose sheet inserted at the end of
the
notebook,
for
a
derivation. The factor
n/4
should
be
n/8.
"Querschnitt"
should
probably
be
"Weglänge."
[31]Einstein
assumes
that
the
mean
thermal
velocity
c
of the molecules has
a
nonvanishing