8. "Relativity
and Gravitation.
Reply
to
a
Comment
by
M.
Abraham"
[Einstein
1912h]
Received
4
July
1912
Published
13 August
1912
In: Annalen der
Physik
38
(1912):
1059-1064.
DOC.
7
GRAVITATIONAL INDUCTION
179
Published
in
Vierteljahrsschrift
für gerichtliche Medizin
und
öffentliches
Sanitätswesen 44
(1912):
37-40. Published
July
1912.
[1]See
Einstein's lecture
notes
on
mechanics
(Vol. 3,
Doc.
1),
[p. 20],
for
a
derivation of
the
force exerted
by a mass
shell
on a
point mass;
see
also Einstein's "Scratch Notebook"
(Vol.
3, Appendix
A), [pp.
63-65],
for calculations which
are
probably
related
to this
problem.
[2]"c2"
should
be
"c2."
[3]See Einstein 1905s
(Vol.
2,
Doc.
24).
[4]See Einstein 1912c
(Doc. 3),
which
appeared
23
May
1912.
[5]The
"x"
in
"Rx" should
be
a
subscript.
The
same
equation
also
appears
in
Einstein's
"Scratch Notebook"
(Vol.
3, Appendix A),
[p.
38].
Both there
and in
Einstein 1912c
(Doc. 3)
Einstein
uses
"S"
instead of
"R."
[6]The
integration gives
O0
-
Q =
(1/2)
(C20 -
c2),
which
corresponds
to
the relation between
4
and
c as
derived
in
Abraham 1912a. The relation
given
here
is the
same as
the
one
derived
in
Einstein 1911h
(Vol. 3,
Doc.
23).
The
question
of how the
gravitational potential depends
on
the
velocity
of
light
had been
a
topic
of debate between Einstein
and
Abraham. Abraham
claimed that Einstein's
expression
for
this dependence is only
an
approximation
for small
O/c. For further
discussion,
see
the editorial
note,
"Einstein
on
Gravitation
and
Relativity:
The
Static
Field,"
pp.
124-127.
[7]See Mach
1908.
Einstein later extended the
analysis presented
in this
paper
to
the
problem
of
a
rotating
shell
(see
Einstein
to
Ernst
Mach,
25
June
1913
[Vol. 5,
Doc. 448],
Einstein
to
H. A.
Lorentz, 14 August
1913
[Vol. 5,
Doc.
467],
Einstein
and Besso's
manuscript
on
the
motion of
the
perihelion
of
Mercury
(Doc. 14), [pp.
36-38],
and
Einstein 1913c
[Doc. 17], §9).
For further discussion of
the
role of Mach's
critique
of Newton's
dynamics
for the
development
of
general relativity,
see
the editorial
notes,
"Einstein
on
Gravitation and
Relativity:
The Static
Field,"
p.
127,
and "Einstein's Research Notes
on a
Generalized
Theory
of
Relativity,"
pp.
194-195.
[8]"(3b)"
should
be
"(3a)."
