170
DOCS.
176,
177 DECEMBER 1915-JANUARY
1916
in which
B/r3
is
a (dimensionless) number,
thus
requires
that
ß
be
equal, apart
from
a
numerical
factor,
to
(km/r)3.[3]
I
am very
satisfied with
the
theory.
It
is not
self-evident
that
it
already yields
Newton’s
approximation;
it
is
all the
more
gratifying
that
it also
provides
the
perihelion
motion and line
shift,
although
it
is not
yet sufficiently
secure.[4] Now
the
question
of
light
deflection
is of
most
importance.
With
my
best
regards
and wishes for
the
New
Year, yours,
Einstein.
177. To Hendrik A. Lorentz
[Berlin,] 1
January 1916
Highly
esteemed
Colleague,
Your
enticing
invitations
make
it hard
for
me
to
stay
put here.[1] I
can
visualize
a
visit in
your midst,
can
depict
for
myself
the
very
interesting
conversations,
can
imagine
that
for
a
few
days
I
was
allowed
to
walk
around without
a
muzzle,
so
to
speak,
and
can see
myself
sitting
in Ehrenfest’s
cozy
little
home.[2]
But
I
must
forgo
all
this
because
I
cannot
easily get away
for
a
number of
reasons.
With
all of
your permissions, however,
I
am going
to extend
the date
set for
me
to
a
time when I
really
can
travel;
I
shall
certainly
not
postpone
it
for
longer
than
is
necessary.
Trying
times awaited
me
last
fall
as
the
inaccuracy
of
the
older
gravitational
field
equations
gradually
dawned
on me.
I
had
already
discovered earlier
that
Mercury’s perihelion
motion had
come
out
too
small. In
addition, I
found
that
the
equations
were
not
covariant for
substitutions
corresponding
to
a
uniform
rotation
of
the
(new)
reference
system. Finally,
I found
that the
consideration
I
made
last
year
on
the
determination of
Lagrange’s
H
function
for
the
gravitational
field
was
thoroughly
illusory,
in
that
it could
easily
be modified such
that
no
restricting
conditions
had
to
be
attached
to H,
thus
making
it
possible
to choose it
completely
freely.[3]
In
this
way
I
came
to
the
conviction
that
introducing adapted
systems
was on
the
wrong
track
and
that
a more
broad-reaching covariance,
preferably
a
general
covariance,
must
be
required.
Now
general
covariance has
been
achieved, whereby
nothing
is
changed
in
the
subsequent specialization
of
the
frame of
reference.[4]
I
had considered
the
current
equations
in
essence already
3 years
ago
together
with
Grossmann,
who had
brought
my
attention
to
the
Riemann
tensor.
But
because
I
had
not
recognized
the
formal
importance
of
the