38
THEORY OF THERMAL
EQUILIBRIUM
where
the
p's
and
dp's
have
the
same
values
as
in
d[w(E1)],
but
L
lies
between
the limits
E2
-
V
and
E2
-
V
+ dE.
Thus,
according
to
the
proposition
just
proved,
d[w(E2)] d[w(E1)]
.
Consequently,
I
d[w(E2)]
I
d[w(E1)]
,
where
S
has
to
be
extended
over
all
corresponding regions
of the
p's.
However,
I
d[w(E1)]
=
w(E1)
,
if the
summation
sign
extends
over
all
p's,
so
that
V
i
E1
.
Further,
we
have
[19]
I
d[w(E2)]
w(E2)
,
since the
region
of the
p's,
which
is determined
by
the
equation
nh/=E2
includes all
of
the
region
defined
by
the
equation
v
i
E1
§5.
On
the temperature
equilibrium
We now
choose
a
system S
of
a
specific constitution
and
call it
a
thermometer.
Let
it interact
mechanically
with the
system S
whose
energy
is
relatively infinitely
large.
If the
state of
the entire
system
is
stationary,
the
state of
the
thermometer
will
be
defined
by
the
equation
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Extracted Text (may have errors)


38
THEORY OF THERMAL
EQUILIBRIUM
where
the
p's
and
dp's
have
the
same
values
as
in
d[w(E1)],
but
L
lies
between
the limits
E2
-
V
and
E2
-
V
+ dE.
Thus,
according
to
the
proposition
just
proved,
d[w(E2)] d[w(E1)]
.
Consequently,
I
d[w(E2)]
I
d[w(E1)]
,
where
S
has
to
be
extended
over
all
corresponding regions
of the
p's.
However,
I
d[w(E1)]
=
w(E1)
,
if the
summation
sign
extends
over
all
p's,
so
that
V
i
E1
.
Further,
we
have
[19]
I
d[w(E2)]
w(E2)
,
since the
region
of the
p's,
which
is determined
by
the
equation
nh/=E2
includes all
of
the
region
defined
by
the
equation
v
i
E1
§5.
On
the temperature
equilibrium
We now
choose
a
system S
of
a
specific constitution
and
call it
a
thermometer.
Let
it interact
mechanically
with the
system S
whose
energy
is
relatively infinitely
large.
If the
state of
the entire
system
is
stationary,
the
state of
the
thermometer
will
be
defined
by
the
equation

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