506
DOC.
487
MARCH
1918
This
now
is
exactly
the
expression
for
the
hydrostatic pressure
which,
in
ac-
cordance
with
classical
theory, governs
the
interior
of
the
sphere,
and
ƒ
-3p
•
dv
is
at the
same
time
no more
than
the
potential
we
attribute
to
the
sphere itself
as
a
consequence
of
the
gravitation.
This
agreement,
it
seems
to
me,
is
an
important
argument
for the
practicality
of
my
proposal.[18]
For
the
energy components
chosen
by me,
we
naturally
have
the
equations
which
you
write
thus
in
(22)
of
your
paper:[19]
dxu
-
¿¡TV
=
o.
To
this
Runge
has remarked in
a
lecture[20]
he
gave on
8
March before
our
Society
of
Sci.
that in
each individual
case
the
form
you
desire,
dxv
=
0,
can
be
produced
by specifying
the coordinate
system,
which
is just
barely accept-
able,
so
that the
sums
guvEuv
are
eliminated!
A true
philosopher’s
stone.
(Both
communications,
mine and
Runge’s,
are
just
being
prepared
for
publication.[21]
In
the
meantime,
I
also
followed
up on your cosmological
ideas of
1917,[22]
in
that
I
allow
Xa
of
Schwarzschild’s
paper
=
n|2,
in which
case
Schwarzschild’s fluid
sphere
fills
the entire
“elliptic”
space![23]
Thus
I
come very
close
to
your spec-
ifications,
only
that the
numerical factors
are
not correct
yet.
Of
course-now
written in Schwarzschild’s first designation-p
=
-p0;
the
world in
the
region
of
constant
curvature becomes
kp0/3,
from which R
=
/3/kp0
results,
whereas
you
find
/2/kp0. The
Kuv's
become
-kp0
•
guv,
hence
your
A
=
kp0,
whereas
you
have
kp0/2
.
What
could be
the
cause
of these
differences?)[24]
Now I
am
eager
to know
what
you
will
say
to this
long
letter.
I
only
want
to
add
that,
meanwhile, my
general
lectures
on
quadratic
differential
formulas have
also been
typed.[25]
But
only
in
ca.
2
weeks
can
I send
you
a
copy
(which
I
would
then
request you pass
on
to Sommerfeld
again).[26]
Very
truly
yours,
Klein.