DOC. 4
KINETIC THEORY LECTURE NOTES
205
Application
of
Probabilistic
Analysis
to
Processes
of
Motion.[106]
1)
Point
moving
with constant
velocity
along
a
closed
curve
Two
elements
chosen,
ds1
&
ds2,
where
ds1 =
ds2.
We
say:
it
is
equally
probable
that
we
will find
the
point
in
ds1
&
ds2
2)
The
same case
considered,
but
v
=
p(A).
Now it
is
no longer
equally
probable
that
we
will find
the
point
in
ds1
as
in
ds2.
What
is
meant
by
this?
In order
to traverse
ds1,
it
requires
the
time
ds1
-,
and to traverse
ds2,
it
requires
the
v1
ds2
ds1
ds2
ds1
ds2
time
-
It
turns out
that
- -
We
will
consider
-
&
- as a
relative
measure
v2
V1 V2
V1
V2
for the
probability
of
finding
the
point
on ds1.
We
divide in
the
following way
dsx
ds2
V
Vv2
1
T, T2
I
1 1
1
\
T
=
duration of
one
orbit
Probability
for
region
ds1
= T
"
ds2=h2
T
Thus,
by
the
probability
associated with
the
region
ds
we
understand the fraction of
time
during
which
a point
is
found
in
ds1,
divided
by
the
time
of
a
whole orbit.
W
=
length
of
time
the condition
applies
total
time.
This
definition
can
also
be understood
in
another
way.
We
imagine
that
very many
(00
many)[107]
points
are
traversing
our curve
in
the
same
direction and
according
to
the
same
law.
Can
they
be distributed
in such
a way
that
every
region
ds
always
contains the
same
number of
points,
i.e.,
that for
a specific
region
this
number
does
not
change
with