DOC.
47 THE RELATIVITY
PRINCIPLE 487
defines the
mass
M
of
a body as
the limit
of
its
momentum divided
by
its
velocity as
the veloc-
ity approaches zero
(see
ibid.,
p.
564).
Applied
to
black-body
radiation, this
gives
M
=
(E0
+
pV0)/c2,
which
is
Planck's
eq. (48).
[66]
See
Cockcroft
and
Walton 1932 for the
first
reported
verification
of
the
mass-energy re-
lationship
in
a
nuclear reaction.
[67]
See
Planck
1907a,
§
18,
pp.
568-569, for
a
discussion
of
the
relationship
of
inertial and
gravitational mass.
[68]
See Eötvös 1890 for
a report
of
the most
accurate tests
of
this
proportionality
then avail-
able.
[69]
The
"Xa" should
be
"X'a."
[70]
The
"e2"
should
be
"c2."
[71]
The
following
discussion
is based
on
Ein-
stein 1907h
(Doc.
45),
§
1.
[72]
Einstein
1907h
(Doc. 45);
the reference
should be
to
§
1.
[73]
The
"q"
on
the
left-hand side
of
this
equa-
tion should be
"G."
[74]
Planck derived results
equivalent
to the
following
two
equations
from
a
variational
prin-
ciple
in
Planck
1907a,
§ 11
and
§
12.
[75]
Planck derived transformation
equations
for volume and
pressure by
different methods in
Planck
1907a,
§
5
and
§
6.
[76]
The
u
should be omitted from this
equa-
tion.
[77]
See
Mosengeil
1907 for
a
discussion
of
this
system
not
involving
the
theory
of
relativity.
Planck
1907a,
§
1,
summarizes
Mosengeil's
re-
sults;
§
15
shows how
to
obtain them with the
help
of
the relativistic transformation laws.
[78] The
"E0"
should be "E0/c2."
[79]
The
"c2"
should be "V0."
[80]
In
a
reprint
copy
(see note 34),
Einstein
crossed out the factor
"4/3"
in this
equation.
See also
Einstein
1908b
(Doc. 49).
[81]
Einstein
1907h
(Doc. 45).
[82]
In
a
reprint
copy
(see note 34),
Einstein
corrected the term "-
q
dQ" to
"-
q
dG."
[83]
Planck
1907a. The
quotation
is
from
p.
552. Planck used S
as
a symbol
for the
entropy
throughout
his text.
[84]
Planck's
text
(see
note 81)
has
"dasje-
nige"
where
Einstein's
quotation
has
"das."
[85]
Planck's
text
(see
note
81)
has
"Bezugs-
system"
following
"ungestrichene."
[86]
Planck's
text
(see
note 81)
has
"S'1S1,"
where
Einstein's
quotation
has
"n'1n1."
[87]
The "T"
in this
equation
should be
"T0."
[88]
Planck
gave a
different derivation
of
this
result in
Planck
1907a,
§
6. Einstein returned to
the
question
of
the transformation law for
tem-
perature
many years
later,
and arrived
at
a
dif-
ferent result:
-
T/T0
=
Vl
-
v2/c2
(see
Einstein
to
Max
von
Laue,
27
January
1952).
[89]
Planck
1907a.
[90]
In
a
reprint
copy
(see note 34),
Einstein
corrected
the coefficient
of
dz to
Fz,
and the
coefficient
of
T to
dn.
See also Einstein 1908b
(Doc. 49).
[91]
In
a reprint copy (see
note
34),
Einstein
corrected
the term
"x dG"
to
"x
dGx."
See also
Einstein 1908b
(Doc. 49).
[92]
See
Planck
1907a,
§
2. The definition
of
the kinetic
potential
H
is
given on p.
549,
and its
relationship
to the
energy
E
on p.
550.
[93]
See
Einstein
1908b
(Doc. 49),
p.
99, for
a
clarification
of
the
meaning
of
constant acceler-
ation.
[94]
This
paragraph
contains
Einstein's
first
formulation
of
what he later termed the
equiva-
lence
principle
(see
Einstein
1912b,
p.
365).
[95]
In
a reprint copy
(see
note
34),
Einstein
crossed
out
"nutzbar"
and
wrote
"ersetzbar."
See also
Einstein
1908b
(Doc. 49).
[96]
See
p.
413
of
the text
above,
and note
6.
The first
equation on p.
457
corresponds
to Lo-
rentz's
original
definition
of
the local time
("Ortszeit").
[97]
In
a reprint copy (see
note
34),
Einstein
corrected
"gleichen" to "gleicher."
[98]
The reference
to
eq.
(29)
should
be to
eq.
(12).
[99]
See
Einstein
1908b
(Doc. 49), p. 99,
for
a
comment
on
this
equation.
[100]
Einstein
evidently
calculated the
gravita-
tional
potential
at the surface
of
the
sun
and
di-
vided it
by c2.
This is
Einstein's
first
prediction
of
what
came
to
be known
as
the
gravitational
red shift
of
spectral
lines.
His next
paper
on
gravitation
contains
a
discussion
of
this effect
that differs
from the
one given
here
(see
Einstein
1911g,
p.
905).
[101]
In
a reprint copy (see
note
34),
Einstein
corrected
"d/dt" on
the
right-hand
side
of
this
equation to
"d/da"
See also
Einstein
1908b
(Doc. 49),
p.
99.
[102]
In
a
reprint
copy
(see
note
34),
Einstein
added
"u"
following
the
closing parenthesis
in