DOC. 13 GENERALIZED THEORY OF RELATIVITY

343

[59]See

Bianchi

1896, chap. 2.

For

a

historical discussion

of Beltrami's work

on

differential

invariants

and

the earlier work

by

Lame

on

which it

is based,

see

Reich

1994,

sec.

2.

Einstein

used the various differential

invariants

in

his search for

a

possible gravitational tensor

in

his

research

notes on a

generalized theory

of

relativity (Doc. 10),

[p.

3],

and

[pp.

16-17].

[60]This

expression appears

on

[p.

11]

and

on [p. 13]

of Einstein's research

notes

on a

generalized theory

of

relativity

(Doc. 10).

[61]Bianchi

1896,

p.

47. In this

book the derivation

occurs

in the context

of

a

discussion of

differential invariants without reference

to vector

terminology.

See

also Ricci and Levi-Civita

1901,

p.

164.

[62]Kottler

1912,

p.

1679.

The

page

number "21"

given

in

Grossmann's footnote indicates

that

he

referred

to

an

offprint

of Kottler's

paper.

[63]Ricci

and Levi-Civita

1901,

p.

135.

[64]This

tensor appears

on

[p.

57]

of Einstein's research

notes

on a

generalized theory

of

relativity (Doc. 10).

[65]This

equation appears

with

a

slight

modification

on

[p.

57]

of Einstein's research

notes

on a

generalized theory

of

relativity (Doc. 10).

[66]Riemann

1892,

p.

270

[67]Christoffel

1869,

p.

54.

Christoffel

did not

refer

to it

as a

tensor.

[68]This

equation appears

on

[p.

27]

of Einstein's research

notes

on a

generalized theory

of

relativity

(Doc.

10).

[69]See

Bianchi

1896, chap. 2.

[70]See

Bianchi

1896, chap. 2.

[71]For

Einstein's

analysis

of

the

Riemann

tensor

as a

possible starting point

for construction

of

a

gravitational

tensor,

see

his

research

notes

on a

generalized theory

of

relativity

(Doc.

10),

[pp.

44ff.];

see

also Norton

1984, sec. 4,

for

a

historical discussion.

[72]On

[pp.

33ff.]

of Einstein's research

notes

on a

generalized theory

of

relativity (Doc. 10),

Einstein studied the

problem

of the weak field

limit

for

the Ricci tensor

(see

Norton

1984,

sec

4,

for

a

reconstruction of Einstein's

research).

For further

discussion,

see

the

editorial

notes,

"Einstein's Research Notes

on a

Generalized

Theory

of

Relativity,"

pp.

198-199,

and "Einstein

on

Gravitation

and

Relativity:

The Collaboration with Marcel

Grossmann,"

p.

296.