DOC. 2 COVARIANCE PROPERTIES
15
/1
0
____
I
1?afl
would be
a
scalar under
arbitrary
transformations.
However,
as
is known from the
theory
of differential
invariants,7
this
quantity
does not coincide with the
only
[p.
225]
differential invariant
of
second
order, viz.,
Vim
{ik,km}.
imk
This
new
theory
of
gravitation gains
convincing
power by
the
far-reaching
covariance
of
the
gravitational equations,
even
if
the
foregoing
deliberations
may
not
provide complete transparency
of
adapted
coordinate
systems
and admissible
transformations. We believe to have shown that the covariance
of
the
equations
is the
optimum
imaginable,
since the conditions
Ba
=
0,
by
which
we
restricted the
coordinate
systems, are a
direct
consequence
of
the
gravitational equations.
Additional
notes
by
translator
{1}
"8yu'"
on
the left-hand side has been corrected to
"Sv'uv."
{2}
The
parenthesis
")"
was missing
after
dyuv
/dxß.
[19]
7See
§4
of
part
II
of
the "Outline."
Previous Page Next Page