206
DOC.
4
KINETIC THEORY LECTURE NOTES
time? Let
nds
be the number of
points
in
the element
ds;
n
is
to
be
conceived
as
a
function of
s.
We
calculate
the
change
of
nds in
the
very
short
time
dt
Increase
in
n
=
vn
dt

v'n'dt
tPdsd,8s
vdt
n
but
now according
to
our assumption
this
number
must
remain
constant,
hence
v.n
independent
of
s
=
const
const.
n
=
v
nds
=
const
ds/v
=
const
.
x
But
up
to
a
constant
common
to all line
elements,
the
righthand side,
and thus also
the lefthand
side,
is nothing
else
but the
statistical
probability
of
the
element
ds.
Thus,
the
point density
n
is
proportional
to
the
probability
of the element
in
question.
Since
E
W
= 1
for the
whole orbit,
W
= nds,
if
ntotal
denotes the total number of the
points
distributed
over
the
curve.
n
tot