268
DOC.
281 NOVEMBER
1916
yesterday
at
the
colloquium,
Fokker
spoke
about the
problem
of
the
guv’s
at
infinity,[2]
prompted
by
the
second solution
by
Droste
to
the
gravitational
field
of
a
central
mass.[3]
I also have been
working
on
your
theory
in
the last
few
weeks,
and
I
found
that
Herglotz’s
mechanics of
deformable bodies
(Ann.
der
Phys.,
36, p.
493)[4]
can
easily
be
generalized
for
your theory.
For
rest deformations
eij,
Herglotz’s
expressions
(16') are
valid also in
the
general theory
of
relativity,
but the
Aij’s
are no
longer
defined
by
equations
(20)
but
by
the
more
general
[5]
(1)
The
function
$
=
fi(eij,
e)
.
\Z-A44
in
eq.
(45)[6]
thus
becomes
a
function of the
quantities
aij,
guv,
and
e,
$
=
$(aij,
guv,
e),
(2)
and because
the
aij's
and
guv's
occur
only
in connection with
Aij,
the relation
(3)
can
be
proven. Furthermore,
for each
g
function of
the
guv's:
(4)
hence
(5)
If this
equation is
divided
by
the
determinant
D.
=
|aij|,
Herglotz’s expression
(68)
for
the strain
components
is
obtained
on
the left-hand
side.[7]
Because
$
and
y-gD
are
scalars,
the
strain
tensor
-Eji
thus found
is
a
mixed volume
tensor,
and
(6)
where
3=-
$
-
=
volume scalar.
(7)