486 DOC. 47 THE RELATIVITY
PRINCIPLE
identical to that
of
the last
paragraph on p.
911
of
Einstein
1905r
(Doc. 23).
[32]
See the
corresponding paragraph on
aber-
ration in
Einstein 1905r
(Doc. 23),
p.
912,
and
note 29 to that
paper.
[33]
Laue
1907.
[34]
In
a
reprint
copy
in the Holton collection
of Einstein's
reprints
(see
the
Acknowledg-
ments,
p.
xxxiv),
Einstein
changed
this formula
to:
V'
G'
=
'w'
dV'
1
+
V
da)'
The
plus sign
in the denominator
should be
a
minus
sign.
[35]
Einstein here combined the treatment of
what,
in
Einstein
1905r
(Doc. 23),
he called the
Maxwell-Hertz
equations
for
empty space
(see
ibid.,
§
6)
and the Maxwell-Hertz
equations
with convection
currents (see
ibid.,
§
9).
This
section also includes
some
material treated in
§
7 and
§
8
of
the 1905
paper.
[36]
See Einstein 1905r
(Doc. 23),
pp.
908-
909,
for
the
proof.
[37]
The discussion in the
following
two
para-
graphs corresponds
to
that in Einstein
1905r
(Doc.
23),
last
portion
of
§
6,
pp.
909-910.
[38]
The
following paragraph proves an
asser-
tion in Einstein
1905r
(Doc.
23),
final
paragraph
of
§
9, p.
917.
[39]
In
the
equation
for
4,
"w"
should be
"w".
[40]
The
"w'"
should be
"w'."
[41]
This section
presents a
modified treatment
of
the material in
§
10
of
Einstein 1905r
(Doc.
23), largely
based
on
the
work of
Planck
(see
Planck
1906a).
[42]
In the first
denominator,
"x'"
should be
"x0."
In the second
denominator,
the
paren-
thesis should be raised
to
the third
power.
[43]
This form
of
the the
equations
of
motion
and the
corresponding
definition
of
the relativ-
istic
force
differ from those
given
in Einstein
1905r
(Doc. 23),
§
10.
Einstein followed Planck
here
(see
Planck
1906a).
[44]
The "x,
y,
z"
should be "x,
y,
z."
[45]
In
a reprint
of
this
paper
(see
note
34),
Einstein indicated that the
square
bracket after
"2"
should be
deleted,
and
a square
bracket
placed
after
"-ZM)."
An
open parenthesis
should also be inserted before
"YN."
See also
Einstein
1908b
(Doc. 49).
[46]
Einstein here followed Planck in the defi-
nition
of
the relativistic
momentum
of
a particle
(see
Planck
1906a).
[47]
In this
expression
for the relativistic La-
grangian,
as
in
the rest
of
this
paragraph,
Ein-
stein
followed
Planck's
treatment
(see
Planck
1906a).
[48]
In the final
term,
"x"
should be
"x."
[49]
Einstein did not introduce the
concepts
of
longitudinal
and transverse
mass,
which he had
used in earlier discussions
of
this
topic.
See Ein-
stein
1905r
(Doc. 23),
pp.
918-921, and Ein-
stein
1906g (Doc. 36).
[50]
The
c2
inside the brackets should be
placed
outside.
[51]
Starke
1903, e.g.,
indicates that it
was
dif-
ficult to exceed
discharge potentials
of
38,000
volts,
corresponding
to velocities
of
1.17
x 1010
cm/sec
for
cathode
rays.
[52]
Kaufmann
1906a. This
paper
cites Kauf-
mann's earlier
papers on
his
experiments, start-
ing
with
Kaufmann
1901.
[53]
The
drawing
of Kaufmann's
apparatus on
p.
438 is
reproduced
from
Kaufmann
1906a,
p.
496.
[54]
The
figure on p.
439 is based
on fig.
11,
table
IV
of
Kaufmann
1906a.
[55]
That
is,
the
curve was
calculated
on
the
as-
sumption
that the deviations
are negligibly
small
compared
to the dimensions
of
the
apparatus
(see
Kaufmann
1906a,
p. 524).
[56]
This is the value calculated
by
Kaufmann
(see Kaufmann
1906a,
p. 551).
[57]
Planck
1906b,
1907b.
[58]
See
Laub
1910 for
a contemporary
review
of
experiments by
Kaufmann and others
on
the
dependence
of
electron
mass on
velocity.
For
a
discussion
of
these
experiments, see
the editorial
note,
"Einstein
on
the
Theory
of
Relativity,"
pp.
270-272.
[59]
Abraham
1902a.
[60]
Bucherer
1904. See also
Langevin
1905c.
[61]
Einstein had
previously
discussed this
topic
in Einstein 1905v
(Doc. 27)
and Einstein
1906e
(Doc. 35).
His treatment here is similar to
that in
Einstein
1907h
(Doc.
45),
§
1
and
§
2.
[62]
The
"E"
on
the
right-hand
side
of
this
equation
should be "E0."
[63]
The
quotation
is
from
Planck
1907a,
§
18,
p.
568.
Planck's
text
has
"1
gr
Atom"
where
Einstein's
text has
"ein Grammatom."
[64]
Precht
1906.
[65]
In
Planck's
text (see note 63),
the refer-
ence
is
to
eq.
(48)
on p.
564
of Planck
1907a,
which differs from
Einstein's
eq.
(17).
Planck
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