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.
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