DOC.
3
47
where
E
is
given
directly, but
E0
has
to
be
determined
as a
function of
E
and
h
from
the condition
e-2h(E-E0)dp1...dqn =
N.
[40]
In this
way,
one
obtains
e
= ~y
-
\
+ 2/c
log-
e
dp^..
.dqn +
const.
In
the
expression
thus
obtained,
the arbitrary
constant
that has
to be added
to
the
quantity
E
does not
affect the result,
and
the third
term,
denoted
"const.," is
independent
of
V
and
T.
The
expression
for the
entropy
e
is
strange,
because it
depends
solely
on
E
and
T,
but
no
longer
reveals the special
form
of
E as
the
sum
of
potential
and
kinetic
energy.
This fact
suggests
that
our
results
are
more
general
than the mechanical
model
used,
the
more so as
the
expression
for
h
found
in
§3
shows
the
same
property.
[42]
[41]
§10.
Extension
of
the second
law
No
assumptions
had to be
made
about
the
nature
of
the forces that
corre-
spond
to
the
potential
Va,
not
even
that
such
forces
occur
in
nature.
Thus,
the mechanical
theory
of heat requires that
we
arrive
at correct results
if
we
apply
Carnot's
principle to
ideal
processes,
which
can
be
produced
from
the
observed
processes
by
introducing
arbitrarily
chosen Va's.
Of course,
the
results obtained
from
the theoretical
consideration
of
those
processes
have
a
real
meaning
only when
the
ideal auxiliary forces
Va
no
longer
appear
in
them.
[43]
Bern,
June 1902.
(Received
on
26
June
1902)
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