224
DOC.
228
JUNE
1916
228.
From
Théophile
de
Donder[1]
[Brussels,]
27
June
1916
Sir and
highly
esteemed
Colleague, (Einstein)
I just
noted
with
pleasure
that
your
system
of
10
diff.
eqs.
for
the
gravita-
tional
field
is
equivalent
to
the
sys.
of
11
diff.
eqs.
that
I
had
found,
as
a
result
of
Hamilton’s
principle
extended to
the
generalized
Maxwell-Lorentz
electromag-
netic
field.
The
same
method also
provided
me
simultaneously
with
the
gravitational
tensor
tAß
(A,
u =
1...4) in its full
generality.
These results
were
summarized in
a
note
appearing, I
believe,
on
the 27th
of
May
in
the
Verslag[en]
of
the
Acad. of
Amsterdam.[2]
The
develop[ment]
of
this
note,
which
I
have
the
honor of
offering
to
you respectfully
with
the
enclosed,
will
furnish
chapter
VII of
a
report
that
will be
appearing
soon,
I
hope,
in the Archives
du
Musée
Teyler.[3]
I
compared
this tensor
tAu
to
your
functions[4]
tuA
in
the
particular
case
where
(-g)1/2
=
1. Well,
the
result of
my
calculations is
that there
is
no identity;
it
is
in
this
regard
that
I
turned
to
your
insights.
The
method
adopted,
the
generality
of
the
result,
and
the
simple
covariance
of
tAu
nevertheless instill in
me
great
confidence in
the
values
I
attributed
to
tAu.
I
have also calculated
your
function
t11
and
my
function
t11,
setting
out from
the
quadratic
formula
related
to
your
admirable
application
to
the
mo[tion]
of
Mercury
around the
Sun.[5] I
find
your
t11
=
R-2,[6]
and
my
t11
=
0.
It
likewise
appears
that
your
t33
#
0,
while
my t33
=
0.
All
my tAu's are zero
in the
problem
considered
except
for
t22
which
is
equivalent
to
-R-2.
The
result
of
this
is
that
everywhere
and
always (except
at
the
origin)
the
KA's are zero
(A
=
1...4).[7]
I
am
also
sending you
a
note
that
appeared
on
6 July
1914
in
the
Comptes
Rendus.[8]
You
will
see
that
at
that
time
I
already
had
the
method for calculat-
ing
Tij;
some
calculation
errors
led
me
to
inexact
values for this
tensor;
since
September
1914 I
have
been in
possession
of
the
exact values for
Tij.
You will
notice
that
my
method
also
applies
to
systems
in which
DI*
#
0,
systems
that
you
have
already
considered.[9]
Please,
Sir
and
highly
-
Colle[ague],
allow
me
to
assure
you
of
my
greatest
respect.
Previous Page Next Page