DOC.
4
KINETIC
THEORY
LECTURE NOTES
245
[52]The
equality
is in fact
only
a
proportionality.
The surface
area
of
an
l-dimensional
hyper-
sphere
is
given
by Rl-l2nl/2Y(l/2).
[53]The
last
term
of this
equation
should
be
- -.
[54]For
the
following discussion,
see
chap.
14
("Diskussion thermodynamischer Analogien")
of
Gibbs 1905.
[55]"mikrokanonische
Gesamtheit" should
be
"kanonische
Gesamtheit.".
[56]The
preceding
sentence
is
interlineated
in
the
original.
[57]At
this
point
in
the
text
Einstein indicates
a
note he
has
appended
at
the foot of
this
page:
"Wir
sagen, dann,
dass sich
beide
Systeme
berühren."
[58]The
words
"(unendlich lange)"
are
interlineated
in
the
original.
[59]The
preceding seven
words
are
interlineated in the
original.
"aus dessen" should be "auf
dessen." In the
equation
below,
the
numerator is corrected
from
n.
[60]The
preceding
four words
are
interlineated
in
the
original.
[61]The
evaluation of I is
in fact
an
evaluation of
4I2.
The result of
the
following integration
should therefore
be
jn
instead of
2sn.
[62]See
note
14.
[63]The
word
"mittl[ere]"
is
interlineated
in
the
original.
The derivation of
this
theorem here
and
the
following
derivation
of
Avogadro's
law
satisfy
the earlier
given
statement
[pp.
2,
3]
that
these theorems should
be
derived from
purely
molecular-theoretical
considerations,
i.e.,
inde-
pendently
of
the
phenomenological
ideal
gas equation;
see
also
note 4.
[64]See
[pp.
45-46].
[65]The square
brackets
are
in
the
original.
[66]The
problem
of the
specific
heat of
polyatomic
molecules
is
taken
up again
on
[p.
38].
[67]This notation
is
the
same
as
the
one
used
by
Boltzmann
1898,
§25,
and
as
that
used
in
Einstein
1902b
(Vol. 2,
Doc.
3);
in Gibbs
1902, 1905,
the
coordinates
are
denoted
by
q
and their
associated
momenta
by p,
which conforms
to
modern notation.
See
also
notes 49
and
72.
[68]The
problem
of
magnetism is
also treated
on
[pp. 39-44].
For
references
concerning
Langevin
and
Weiss, see
notes 76
and 84-87.
[69]The
square
brackets
are
in
the
original.
[70]A
similar model had been
employed
earlier
by
Einstein
in
Einstein
1907a
(Vol.
2,
Doc.
38)
to
calculate
specific
heats of
solids.
[71]The
square
brackets
are
in
the
original.
[72]In Gibbs
1905,
p.
31,
a
similar notation
is
introduced.
There, however,
+
does
not
denote
an
additional
energy
term
but
is
determined
by
the normalization
condition;
see
also notes
49
and
67.
[73]See
the discussions of
molecules in
a
magnetic
field,
Brownian motion under the influence
of
gravity,
and Brownian motion of
rotating particles
on
[pp. 38-40], [pp. 40-41],
and
[p. 44],
respectively.
[74]For
experimental
data
on
the
specific
heat
of
diatomic
molecules,
see,
e.g.,
Meyer, O.
E.
1899, part
1,
§55.
The
question
of
how
many degrees
of
freedom
of
a
diatomic molecule contrib-
ute to the
specific
heat
had been
a
subject
of debate
in
kinetic
gas
theory; see,
e.g.,
Brush
1976,
§10.8.
[75]Curie's law
(which
states
that the
magnetic susceptibility
is
inversely
proportional
to
the
temperature)
was
first
published
in
Curie
1895.
[76]Langevin's
formula
=
Cosha
1/a,
where
a
MH/O,
which
reduces
to
Curie's
law
for
small
a (see
also
[p.
41]),
was
first
derived
in
Langevin
1905.
Langevin
also
gave
a report
of
his
theory
at
the
1911
Solvay Congress
(Langevin 1912).
[77]Weiss's
theory
of
ferromagnetism is
taken
up again
on
[p. 41].
[78]These
topics
are
treated
in
more
detail
on [pp.
41-43].
[79]For
general
information and
a
survey
of Einstein's work
on
Brownian
motion,
see
Vol.
2,
Previous Page Next Page