DOC. 17

PROBLEM OF GRAVITATION

503

[43]The

reference

is possibly to

the "hole

argument,"

first

published

in

Einstein 1914d

(Doc.

26);

see

the

editorial

note,

"Einstein

on

Gravitation

and Relativity:

The

Collaboration with

Marcel

Grossmann,"

pp.

297-298,

for

a

historical

account.

[44]This

argument

in

favor of

a

restriction of

general

covariance

is

also mentioned

in

Einstein

1914g (Doc. 16), p.

289,

Einstein 1914e

(Doc.

25),

p.

178,

and

Einstein

to

H. A. Lorentz, 16

August

1913

(Vol. 5,

Doc.

470). See

Einstein

to

Paul

Ehrenfest,

before

7

November

1913

(Vol.

5,

Doc. 481),

and Einstein

to Paul Ehrenfest,

second half of November

1913

(Vol. 5,

Doc.

484),

for

a

discussion of the

geometrical implications

of this restriction. See Norton

1984,

sec.

5,

and

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Collaboration

with

Marcel

Grossmann,"

p.

297,

for historical discussions.

[45]This

section summarizes Einstein and Grossmann

1913

(Doc. 13), part

1,

§5.

[46]For

a

discussion of the conditions under which Einstein's

approach

leads

to

a

unique

solution,

see

Norton

1984, sec.

4.

[47]"YtP"

should

be

"YtP"; "Yßv"

in

the second

term

on

the right-hand side

should

be

"Yaß".

[48]A

summation with

respect

to

u

is

implied

in

these

two

equations.

[49]This

form of the

field

equations, expressed

in terms

of mixed

tensor densities,

was

to

become

the

standard form of the

equations

first

published

in

Einstein and Grossmann

1913

(Doc. 13), p. 17; see

Einstein

1914g

(Doc. 16), p. 289,

Einstein 1914d

(Doc. 26),

p.

261,

and

Einstein and Grossmann

1914b,

p.

217.

[50]The first

summation should

be

with

respect

to

ß, t,

and

p;

"dav"

in

the second

term

on

the

right-hand

side should be

"8av."

[51]In

Einstein and Grossmann

1913

(Doc. 13), p.

17,

Einstein

emphasized

the fact that the

two tensors

enter

the

field

equations

on

the

same footing,

without,

however, relating this

fact

to

the

equality

of inertial

and gravitational

mass as

he

does

here.

[52]A

similar

equation

is

found

on [p.

1]

of

Einstein

and Besso's

manuscript on

the motion

of

the

perihelion

of

Mercury (Doc. 14).

Part of the material

presented

in

this and the

following

section

is

used for the calculations

in this manuscript;

see

the editorial

note,

"The Einstein-

Besso

Manuscript on

the

Motion of

the

Perihelion

of

Mercury,"

pp.

344-359,

for

a

discussion.

[53]For

a

historical discussion of the role of the Newtonian limit

in

Einstein's

early

devel-

opment

of

a

generalized theory

of

relativity, see

Norton

1984, sec.

3.

[54]This

equation

is also

found

in

Einstein

and

Besso's

manuscript

on

the

motion

of

the

perihelion

of

Mercury (Doc.

14),

in

particular

on

[p. 1],

[p. 13],

and

[p. 52].

[55]See

Nordström

1913b,

§5.

[56]"x" in

the numerator

of

the

last

quotient

should

be

"x."

[57]See, e.g.,

Mach

1908,

chap.

2, sec. 6,

for Mach's

critique

of Newton's

concept

of inertia.

For

a

comparative study

of Mach's

and

Einstein's criticisms of

classical mechanics,

see

Barbour

1992. See

also Einstein

to

Ernst

Mach, 25

June

1913

(Vol. 5,

Doc. 448),

where Einstein calls

his results

on

the

relativity

of

inertia

a

vindication of Mach's studies

on

the

foundations of

mechanics.

[58]See

Hofmann

1904.

[59]A similar

equation appears

on [p.

20]

of Einstein

and

Besso's

manuscript

on

the motion

of

the

perihelion

of

Mercury (Doc. 14).

[60]"rotg"

on

the

right-hand

side

should

be "rotg."

[61]"y"

should

be "y."

[62]There

should be

a

minus

sign on

the

right-hand side

of

the second

equation.

[63]See

Einstein and Besso's

manuscript

on

the

motion of

the

perihelion

of

Mercury

(Doc.

14),

[pp.

36-37],

for calculations related

to this

effect. The effect

is

mentioned

in

Einstein

to

Ernst

Mach, 25

June

1913

(Vol. 5,

Doc.

448),

and Einstein

to H. A. Lorentz,

14 August

1913

(Vol. 5,

Doc. 467).

[64]See

Mach

1908,

chap.

2, sec.

6.5.

[65]Einstein

refers

to

the solar

eclipse

of

21 August 1914; see

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Collaboration with Marcel

Grossmann,"

p.

295,

for further

discussion

and

references.