DOC.

8

ANALYSIS

OF

A

RESONATOR'S MOTION

281

Published

in Annalen

der

Physik

33 (1910):

1105-1115. Dated

Zurich, August

1910,

received 29

August 1910, published

20

December

1910.

[1]For

contributions

to

the derivation

of

the

Rayleigh-Jeans

law

of

black-body

radiation,

see

Rayleigh

1900,

1905a, 1905b,

Lorentz

1903,

Jeans

1905,

and Einstein 1905i(Vol.

2,

Doc.

14).

For

historical

accounts,

see

Klein,

M.

1962,

1977,

and Kuhn

1978,

pp.

143-152.

By

the time this

paper was written,

Lorentz's influential derivation

(first

presented

in

Lorentz

1908)

had

con-

vinced

many physicists

that this

law,

in

spite

of

its

failure

to account

for the

experimental

facts,

had

to

be

accepted

as a

necessary consequence

of

classical

physics.

For

a

historical discussion

of

the

acceptance

of this

law,

see

Kuhn

1978, pp.

188-210.

[2]See, e.g.,

Planck

1910a,

where

Planck claims that the

equipartition

theorem

is

not

applica-

ble

to

the

elementary

oscillators

(as

he

had

already suggested

in

Planck

1906,

p.

178).

Einstein

had criticized

a manuscript

version of

this

paper

(see

Doc.

3).

[3]At the time of

his collaboration

with

Hopf,

the methods

developed

in

their

joint papers

did

not

appear

to

the authors

to

contribute much

to

the solution of the

quantum problems

(see

Einstein

to

Jakob

Laub, 27

August 1910,

and

Ludwig

Hopf

to Einstein,

13

October

1911). See,

however, Klein,

M. 1964.

Einstein later used these methods

in

an

attempt

to

explore

the

issue

of

zero-point energy

(see

Einstein and Stern

1913

and for

a

commentary

from

a

modern

point

of

view,

see

Bergia,

Lugli,

and

Zamboni

1980).

[4]Einstein

had treated

a

similar

problem

in

Einstein

1909b

(Vol. 2,

Doc.

56),

§7,

where

he

analyzed

a

mirror

moving

in

a

radiation

field which

he

assumed

to be

characterized

by

Planck's

distribution

law.

[5]Abraham

1904, pp.

273ff.

[6]Planck

1906,

p.

113.

[7]The

second

y

in

the

right-hand

side

of

this equations

should

be

y.

[8]As

pointed

out in

Bergia,

Lugli,

and Zamboni

1979,

an

annotated

English

edition of the

present paper,

the

correct

equation,

which is used in

the

rest

of the

paper,

is

9y

=

(5

cos

w.

[9]Einstein's

notation for the external

or cross

product

of

two vectors follows

the

one

used

in

Abraham

1904.

For

a

brief overview of Einstein's

use

of

vector notation,

see

the editorial

note,

"Einstein's Lecture

Notes,"

pp.

3-10.

[10]Planck

1906, p. 114.

[11]The

"sin"

in

the

right-hand

side

of

this

equation

should

not be

squared.

[12]The

7i

in

the

right-hand side

of

this

equation

should

be

squared.

[13]See

Einstein and

Hopf 1910a

(Doc.

7).

[14]The

second "sin"

in

the

right-hand side

of

this equation

should

be

squared.

[15]Planck

1906,

pp. 122-123; in

these

pages,

Planck calculates the

sum

appearing

in

the first

of Einstein's

equations

by

transforming it

into

an

integral.

For

a

discussion of

the assumptions

underlying

this

derivation,

see Bergia, Lugli,

and Zamboni

1979,

fn. 28.

[16]Einstein

1905r

(Vol.

2,

Doc.

23), p.

914;

the

equations

given

here

are

first-order

approxi-

mations

in

v/c.

[17]See Einstein and

Hopf

1910a

(Doc.

7), p.

1099.

[18]The

left-hand

side

of

this

equation

should read:

dEz--dx.

ox

[19]In the

right-hand

side

of this

equation,

a

factor

1/2

is

missing;

the

sign

in

front of the

t

second

"cos" should

be positive;

and the

t

in

the

argument

of

this

"cos" should

be

t-T.

[20]In

this and the

following equation, t

should be

t

and the

v

in

the

right-hand

side

of

the latter

equation

should

be

n.

[21]The

"sin"

in

the second

equation

should

be

squared;

the

yn

should

be

yv;

the

v0

in

the

last

equation

should read

y0.

This derivation

follows

the

one

outlined

in

Planck

1906, pp.

122-123.

[22]Planck

1906,

p.

178.

[23]Einstein

1909b

(Vol.

2,

Doc.

56), §7.

For evidence of the

impact

that

Einstein's statistical

considerations had

on

Planck,

see

Einstein

to

Arnold

Sommerfeld,

July

1910:

"Planck has

come

up

with

no really convincing argument against my thoughts concerning energy

distribution