252 DOC.

10

RESEARCH NOTES

[111]Einstein

convinces himself that

g44

is

the

only nonconstant

metrical coefficient

in

a

static

field,

an

assumption clearly

stated

in

Einstein and

Grossmann

1913 (Doc.

13),

p.

7. He

asserts

that the

space-time components

g14, g24,

etc.,

vanish. From the fact that the accelera-

tion of fall of

all

bodies

is

the

same

it follows that the

force

[eq.

161]

on a mass

and

its

energy

[eq. 162]

must

be

proportional.

Unless

all

space-space components

of the metric

are

constant,

however,

the ratio between force

and

energy

will

vary

according to

the

velocity

of the

mass.

Einstein's

statement

that

"g11,

g22

etc.

vanish"

actually

refers

to

the derivatives of these

quantities.

This

simplified

form

of

the

static metric

is incompatible

with the harmonic coordi-

nate condition,

which

no

longer appears in

the notebook.

[112][Eq.

164]

corresponds

to

the

x-x

component

of the

gravitational field

stress tensor

of

Einstein 1912d

(Doc. 4),

p.

456.

Equation

(5)

on p.

456 of this

paper

is

reexpressed

as

[eq.

140]

in

terms

of the coefficients of the

corresponding

metric

[eq.

163]

by means

of the

substitutions

c

=

J-G,

g44

=

c2,

y44

=

1/c2.

[p. 43]

dY X'

^iv

dx'

=

0

(IV

=

1

a

XIlvi3x.

{^lioc^vßYaß}

®

=

5^a1k7i

'a

+

XVvi

dPliaPvß

dX:

^

5Pvß

^P\x a

verschwindet,

wenn

dp

*

|1(X

=

ZYa;-^-

+

IyaßV

5/7vß

Funkt. Det.

=

1.

dx:

=E6(raiPma)-

P

H,,

a

'K,

+

^aß^(iaPv$ ^x

** dx:

0

^

^vß

^ai~dx~

+y*-VPvunvi-fo~

dxf^i(xiP^a