DOC.
3
THEORY
OF THERMAL EQUILIBRIUM 75
sion
of
the
problems posed by
these theorems.
[21]
In his next
paper,
Einstein
attempted a
generalization
of
the
concept
of
a
"mecha
nisches System"
(see
Einstein 1903
[Doc. 4],
§
1).
[22]
Boltzmann 1898a. In
§
33 Boltzmann de
fined "Momentoiden," and in
§
33 and
§
34 he
proved
the
equipartition
theorem for
a
microca
nonical
ensemble, or,
in
Boltzmann's
terminol
ogy,
an
"Ergode"
(see
note
6).
In
§
42 he
proved
the
equipartition
theorem
by a
method
quite
similar to
Einstein's, but
only
for
a
real
ensemble
of
canonically
distributed
systems
whose interactions
are
assumed to
be
negligible;
nowhere did he
prove
it for
a canonically
distrib
uted virtual ensemble.
[23]
The
exponents
of
e
in both
numerator
and
denominator should be

h[2V
+
a1r12
+
a2r22
+
...
+
anrn2].
Cf. Boltzmann
1898a,
§
42,
p.
124.
[24]
Here and in the next
line,
L
should
be L,
the
mean
kinetic
energy
of
the
system
as a
whole.
[25]
K
=
k/2,
where
k is
now
called Boltz
mann's
constant.
[26]
A minus
sign
should be added to the
right–
hand side
of
the
equation.
[27] By
"Gleichungen
(1)" Einstein
evidently
meant Lagrange's
equations as given
above
on
this
page.
[28]
The
denominator of the
expression
in
curly
brackets should be
dp'v.
[29]
On the
righthand
side,
dpv
should be
dp'v.
[30]
On the lefthand side
of
the first
equation,
pv
should be
p'v.
On the lefthand side
of
the
second
equation,
the
denominator of
the first
term should be
dpv.
[31]
On the
righthand
side,
the denominator
of
the first
term
should be
dpv.
[32]
L should be
L;
see
note
24.
[33]
The dL in this
equation
is
reinterpreted as
8L below;
see
note 39.
[34]
This
assumption regarding
dt
anticipates
Einstein's
explicit
identification
of
time and
en
semble
averages
in Einstein 1903
(Doc. 4),
§
2.
[35]
The
integral
should be
/
dp1
. . .
dqn.
[36]
The
subscripts
on
the lefthand side should
be
v
rather than
n.
From
here
to
the end of
§
8,
every V
or
V
should be V*
or
V*, respectively.
[37]
In the second
integral, 8(L)
should be
just
L.
[38]
From here to the end
of
§
8,
every
occur
rence
of
L
should be L.
[39]
Einstein tacitly
assumed
that
dL in
eq.
(1)
is to
be
replaced by
8L,
in
accord
with
his earlier
remark that differentials
corresponding
to dt
are
to be
replaced by corresponding
ensemble
aver
ages
derived from
a
variation in the
state
distri
bution,
here
8h,
bV*.
[40]
The
exponent on
the lefthand side
of
the
equation
should be

2h(E +
E0).
[41]
The E/T should be E/T. In Einstein 1905k
(Doc. 16),
p.
551,
and in all
subsequent
cita
tions
of
this
equation,
Einstein
was
careful to
write
E
(or
some equivalent)
for the
average en
ergy,
whereas in all
previous
citations he
ne
glected
to do
so.
Einstein's
expression
for the
entropy
is
essentially
identical
to
that
derived
in
Boltzmann
1871b,
pp.
725728.
[42]
Just
such
a generalization
is
attempted
in
Einstein's
next
paper on
the foundations of sta
tistical
physics,
where
no assumption
is
made
about the distinction
between
potential
and
ki
netic
energy
in
defining a physical system (see
Einstein 1903
[Doc.
4],
§ 1).
The avoidance
of
a
distinction between kinetic and
potential en
ergy is
characteristic of Heinrich
Hertz's
pro
gram
in mechanics
(see Hertz,
H.
1894,
pp.
25
27).
Einstein
is
reported
to
have studied
at
least
the
opening portion
of
Hertz,
H. 1894
as a
stu
dent
(see
the
transcript
of
the
radio
talk
by
Jo
seph
Sauter
in
Flückiger 1974,
p. 154).
[43]
In
effect,
Einstein here claimed
to
have
given a justification
for his
hypothetical
exten
sion
of
the second
law,
stated in Einstein 1902a
(Doc. 2),
p.
799.