232

DOC. 10

RESEARCH NOTES

[64]Einstein's

nomenclature

is

nonstandard. The

terms

"Punktvektor"

(point vector)

and

"Ebenenvektor"

(plane

vector)

are

not

used

in the

vector analysis

of

Föppl 1894,

Abraham

1901, Abraham/Föppl 1904,

Minkowski

1908, Sommerfeld 1910a,

1910b,

or

Laue

1911a. An

interpretation

consistent

with the

examples

listed,

with

the

exception

of

[eq.

89],

is

that

"Punktvektor"

designates

a

contravariant

vector

and "Ebenenvektor"

a

covariant

vector; "."

then

designates

a

contravariant index and

"-" a

covariant

index,

so

that

a

"••- tensor"

has

two

contravariant

and

one

covariant index. The

same

prefixes

are

applied to tensors

as

well:

see, e.g.,

[p.

33],

where

the

fully

covariant fourth-rank Riemann

curvature tensor

is

called

"Ebenentensor" (surface tensor) and its

fully

contravariant second-rank contraction

is

"Punkttensor" (point tensor).

[p. 26]

[65]

I

a

r

gmvYaßaxaaxßy

d2y

'JIV

^

-*x

2

^

dxm

y«ß

a*aaxß

[eq. 90]

aß(iv UA|i

V

Dritte

Ableitungen treten

nicht

auf,

wenn

^

dy

UV

=

0 ist.

[66]

n

[65][Eq.

90]

arises from

the

substitution of

YaßYuv,

aß

for the

stress-energy tensor

Guv

in

the

energy-momentum

conservation

law

as

given

in

Einstein and Grossmann

1913 (Doc.

13),

p.

10, equation

(10)

for

the

case -g

=

1.

This substitution

suggests

that Einstein

was

consid-

ering

the

gravitational

field

equation

YaßY^v

aß

=

K®^V'

from which

it

would follow that

[eq. 90]

equals

zero.

[66]Einstein

expands

[eq.

90]

under the

assumption

y^v

^

=

0,

which

ensures

that

no

third-

derivative

terms

in the

metric arise.

mv

1

dg

(IV

\

Y«ßax"axn

d\v

+

..X

v

s.

dxß

2

dxm

J a~"ß

(ivaß

,

^a^ß

a

(X«XvYuv) =

0

IV

V

Xy

=

0

dx

a

f

äYaß

a

3Yaß^

mv

g

Y

dxa

mv

dxa

{

rJxp

dxß

,

V ß

/

3Yaß

dr

dxa