DOC.
71
PRINCETON LECTURES 357
THE GENERAL
THEORY
get
from this
is
a
secular rotation
of
the
elliptic
orbit of
the
planet
in
the
same sense
as
the revolution of the
planet,
amounting
in
radians
per
revolution
to
(113)
247r3a2
(1
-
«*)e*r*
where
a
=
the
semi-major
axis
of
the
planetary
orbit in
centimetres.
e
=
the numerical
eccentricity.
c
=
3
.
10+10,
the
velocity
of
the
light in
vacuo.
T
=
the
period
of
revolution
in seconds.
This
expression
furnishes
the
explanation
of the motion
of the
perihelion
of
the
planet Mercury,
which
has
been
known
for
a
hundred
years (since
Leverrier),
and
for
which theoretical
astronomy
has
hitherto
been
unable
satisfactorily
to account.
There
is
no
difficulty
in
expressing
Maxwell’s
theory
of the
electromagnetic
field in
terms
of
the
general theory
of relativity;
this
is
done
by
application
of
the
tensor
formation
(81), (82)
and
(77),
Let
Ou
be
a
tensor
of
the
first
rank, to
be
interpreted
as an
electromagnetic 4-poten-
tial; then
as
electromagnetic
field
tensor
may
be
defined
by
the
relations,
(114) .
_
dh
_
df),
dx" ö*"
[124]
The second
of
Maxwell’s
systems
of
equations is
then defined
by
the
tensor equation, resulting
from
this,
(114a)
d/V
,
_
n
dx"
dx"
dx.
and the
first of Maxwell’s
systems
of
equations is
defined
by
the
tensor-density
relation
[97]