DOC.
495 MARCH
1918 519
in
place
of
the
jump
from
E1
to
E2,
I
take
a
boundary layer
in which
e1
varies
constantly
up
to
e2;
afterwards
I
simply
let
this
boundary
layer
become
infinitely
thin.
Then, however,
the
field
equations
must
apply
within
the
boundary
layer;
from
this
follows
the
existence of
the
differential
quotients,
from this
again
the
continuity
of
the
tangential
components,
etc.
Now,
this
reasoning
is
inadmissible here for
gravitation.
The
substitution
of
the
jump
with
a
boundary
layer
is
unfeasible. For
on one
side
is
a
tensor
field:
Gik
=
-kTik,
on
the other there
is
none:
GiK
=
0.
So qualitative
differences do
exist.
Provided,
the
TiK’s
changed continuously
from
0
to
infinite values.
But
this
is
not
the
case
for
the
mass
densities in Schwarzschild’s
example.
That
is
why
(you
have
probably
overlooked
this)
the
differential
quotient, according
to
the
normals of
1
.
1
gr =--5-
inside,
or gr
=--- outside,
1
~
R?
1
-
H
'
r
are
not constant
for
him
either!
Only
g4
is constant for
him,
because
he
assumes
T1(1)
=
p
to
be constant. There
is
a
priori
no compelling reason
for this
though,
otherwise
the
mass
density (in
my
depiction:
E/c2)
would
likewise
have
to
increase
continuously
a
priori
from
0 to
finite values. Then and
only
then
would
you
have
a
link
to
electrodynamics.
But
this would
apparently
not be
a significant move
for the
theory.[21]
As far
as
the
validity
of
your equations
in
the
boundary
surface
is
concerned
(incidentally, a
mathematical
argument,
not
a
physical
one),
the
Maxwellian
boundary
layer
is
eliminated. Therefore
we
have
an
abruptly
discontinuous
sur-
face
and
here, as
is
known,
the unilateral
partial
derivatives
then
occur
(hence,
in
the
above
example:
(d/dr)r=a+or(d/dr)r=a-0
by
which
the continued existence
of
the
equations seems
assured.
I
thus
believe
not to
have been
so
“entirely
inconsistent.”
Allow
me,
on
the
contrary,
to draw
your
attention
to
the
physical arguments
that
seem
to
speak
for
my
solution:[22]
First
of
all,
the
isolated
sphere’s
total
mass
becomes infinitesimal.
This,
as
is
generally known,
has
long
been
one
of
your own postulates,
which had not been
satisfied
until
then.[23]
Second,
the
Maxwellian
stability problem
of
the ether
(§28
of
my
paper)[24]
requires
that
gravitation
have
not just
an
attractive but
also
a
repulsive
effect.
This, however, plainly
determines
the
discontinuity
of
the
normal derivatives
dgiK/0n.