DOC.
153
MAY 1909
109
characterize
merely
a
property
of the
resonators.
As
you
see,
this
is
in
complete
agreement
with
your
view.
One
can
avoid the above
difficulty by ascribing
to
the
ether,
and not to
the
resonators,
the
property
that
energy can
be
taken
up
and
given
off
only
in
definite
quanta.
In the
case
of
this
assumption
as
well,
one can
start out
by
considering
"complexions,"[10]
as
Planck
does,
or one can
treat
the
problem
in
the
manner
indicated
by
Gibbs,
in which
case
one must,
of
course,
modify
the definition of the canonical
ensemble to
some
extent.
Suppose
that
a system
consists
of
a
part A,
whose state
is
determined
by
the
Lagrangian
coordinates
q
and the
corresponding
momenta
p,
and
of certain
structures
of whatever
kind
(let us
call
them
"elements")
G1, G2,
etc.,
which have
the
property
that
their
state
(insofar
as
it
is
considered)
is
determined
by
the
value
of the
energy,
and that
they
can
take
up
or
give
off
energy only
in
complete
finite
quanta.
Let the
value
of the
energy
quantum
be
e1
for
G1
e2
for
G2,
etc;
further,
let
E
be
the
energy
of
part
A,
s1
the
number of
energy
quanta possessed
by G1
s2
the
corresponding
number
for
G2,
etc.
The
total
energy
of the
system
is
then
E
+
s1e1
+
s2e2
+
...
Let
a
canonical ensemble
be
of
the kind in which the
number of the
systems
for which
the
p,
q
lie in
the
range dX and,
at
the
same
time,
the
numbers
s1, s2,
. . .
have
specific
definite
values,
is
given
by
E
+
S1Ģ1
+
s2e2
+
· · ·
Ce
6 dX.
To
have this
ensemble
serve
for the
determination of
the
state
in
a
real
system, one
must know,
first,
that
it
is stationary
(which,
of
course,
one
could
only
prove
if
one
could
form
a
definite idea about
the
way
the
energy
is
transferred
from
A to
G1, G2
. . .
and
vice
versa),
and,
second,
that
the
great
majority
of
the
systems belonging
to
the ensemble
are
identical
in
their
observable
properties.
We shall
assume
both of these
things.
We
now
calculate
some mean
values and
assume (as a
result of the
assumptions
made)
that
they
hold for
the
real
system.
If
the
part A
contains
a
gas
molecule
(coordinates
x, y, z),
then
the
factor
dxdydz
occurs
in
dX,
and the
part
1/2
m(x2
+
y2
+ z2)
in
E, and
one
obtains for
the
mean
value
of
the
kinetic
energy
of
the
molecule in
the familiar
way
3-0.
2
On
the other
hand,
for
the
mean
energy
of the element
G1
one
obtains
Ģ|
2el
3ß1
^
~~e~
~~Đ~
e1e
ö
+
2e1e
w
+,
3e1e
0
+
...
e1
B{
2fi1
3
Ģ1
1
A (K) (H) (m)
fi)
4
1
+ e
u
+ e
u
+ e
u+...
e
u
-
1