DOC. 268
JUNE
1911
189
taking
the derivative
with
respect
to
rv
& equating
with
zero,
one
obtains,
after
simple
calculation,
v20t2v
-
h2
-
+ 2arv
=
0
One
can
base the
following
approximation procedure
on
this
equation
Suppose
that
for
a,
t1...tn
one
has the
approximate
values
t
cl7
y
t
1.
t1..tn
.
Tn
Then
one
obtains
a
better
approximate
value
rv"
from
the
above
formula for
rv
by
setting
cl
y
t
1 ih2
*2
V2
{hl
+ A;
-
2aV}....(l)
From
this
one
obtains
a
better
value
for
a
(a") using
the
formula
_
"
1
a
-
-
/
{hl
^
A2
"V
a
\
V
/
Now
one
again
applies
formula
(1)
in
order
to
get
an even
better
approximation
rv"'
from
a"
and
r",
and then
formula
(2)
to
obtain
from this
a
better
approximation
for
a
(a"')
One
starts
the calculation
by
setting
as
the
first
approximation
A2
a
=
1
.(0)
_
h
_
hvV/
V
In
most cases,
the
approximation
that
follows next
a
(0)
=
n^
1
A
h2
+
A2
-
2aŪ7Ū
will suffice.
If
this
explanation is insufficient, I
will
gladly explain
the
thing
in
greater
detail.
With
small
particles
there
is
more
to
calculate,
but the result becomes
more
reliable.
This
method of calculation
fails for
very
small
particles,
where
a
horizontal
line
might
be
crossed
n^
several
times
But this
case
need
hardly
be
considered.
With cordial
greetings,
I
remain
your
A.
Einstein