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