DOC.
561
JUNE
1918 583
are
established
up
to
relatively
infinitesimal
orders,
and these
quantities
form
a
four
vector.-
Now I
introduce
through
linear
transformation
a
second reference
system
K'.
Then
according
to
(2)
for
the
transformation[6]
J'
=
yi_
dxß
A
a
dxa
dx’e
ß
y
Üï^Axdxa
A
applies.
This
formula
applies
also
when
I choose
the
unprimed
system
in such
a
way
that
Ax1
=
Ax2
=
Ax3
=
0.[7]
In this
case,
it
takes
on
the
simpler
form[8]
ji
_
sy
dxß
(3)
Now, our proof
would be finished
if
this formula
were
proven
also for
the transition
from reference
system
K'
to
a
third
K".[9] This is
easily
done.
According
to
(3)
we
also have
pi
__
sy
dxß
On
the other
hand,
we
have
through
the
inversion
of
(3)
JB=Edx'TJ/dxB.
Hence,[10]
jii
_
^xß
v
_
dx'T
,
°-fTdxßdx"a
T_Z-9x"
T'
Thus
the
proof
is
complete.
With
all due
respect
and
greetings
from
yours truly,
A.
Einstein.
[5]Recipient’s
label: “world
strand.”
[6]Recipient’s
comment: “Instead of
this
it
ought
to be
possible
to
show
that
all
AaB's,
whose
a’s
differ from
4, are zero.
Yes!”
[7]Recipient’s
comment:
“E.
seems
to
compensate
the
first
error
with the
2nd.
(I
really
do not have
Ax1, Ax2, Ax3 freely
at
my disposal anymore;
they
are
given by
the
integration domain,
and
therefore
0
but
very
small relative to
Ax4.)”
[10]Recipient’s
comment:
“What about the
difference between
cogradient
and
con-
tragradient?”
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