DOC.

14

PROOF

OF

AMPERE'S

CURRENTS

189

Published

in

Koninklijke

Akademie

van

Wetenschappen te

Amsterdam. Section of Sciences.

Proceedings 18 (1915-1916):

696-711.

Original

Dutch version submitted

23

April 1915, pub-

lished

14 May

1915.

[1]This is

a

translation of Einstein and De Haas

1915b,

which

is in

Dutch.

Significant

dif-

ferences between the translation and the

original

version

are

annotated.

See

also Einstein and

De

Haas 1915a

(Doc.

13)

for

an

earlier

account

of the

same

work with

more

experimental

details, and

the editorial

note,

"Einstein

on

Ampere's

Molecular

Currents,"

pp.

145-149,

for

general background.

[2]See, e.g.,

Harman

1982,

chap. 2,

for

an

overview of

nineteenth-century

theories of

mag-

netism.

[3]See, e.g.,

Lorentz

1909 for

an

overview of electron

theory.

[4]Curie's

law,

found

empirically

in 1895

(Curie

1895),

states

that for

paramagnetic

sub-

stances

the

susceptibility

is

inversely proportional

to

the

temperature.

In 1905

Paul

Langevin

derived

a

formula for the

susceptibility

of

paramagnetic

substances that reduces

to

Curie's

law

for small

fields (see Langevin 1905).

His

theory

was

based

on

the

hypothesis

that each

atom

carries

a

permanent magnetic

moment,

due

to

intra-atomic electronic motion. Einstein dis-

cussed Curie's law and

Langevin's

theory in

his

course on

the kinetic

theory

of

heat

at

the Uni-

versity

of

Zurich,

summer

semester 1910 (see Vol.

3,

Doc.

4,

[pp.

38-39],

for Einstein's lecture

notes

on

this

topic).

[5]See

the editorial

note,

"Einstein

on

Ampere's

Molecular

Currents,"

p.

146,

for

a

discus-

sion of Einstein's views

on

zero-point energy.

[6]Richardson

1908. Richardson had

unsuccessfully

tried

to measure

the mechanical effect

of

a

sudden

magnetization

of

an

unmagnetized

iron

cylinder.

See

the editorial

note,

"Einstein

on

Ampere's

Molecular Currents,"

p.

149,

for other

contemporary experiments on Ampere's

currents.

[7]The

value of the numerical coefficient

in

eq. (5) corresponds to

a

value of

1.77

x

107

emu/g

for the

specific charge

of the

electron, in

accordance with

recent experimental

results

(see, e.g., Neumann,

G.

1914).

[8]At

the

corresponding point

(p. 155)

in

Einstein and De Haas 1915a

(Doc.

13),

the

satu-

ration

magnetization per

cm3 is

put at

1100. See

also

pp.

706 and 710 of this

paper,

where the

values

1200

and

1300

are

used.

The

density

of iron

is 7.8

g/cm3.

[9]"1/4x"

should be

"1/2tc,"

as

in

Einstein and De Haas 1915b.

[10]A more

detailed

description

of the

apparatus

is

given

in

Einstein and

De

Haas 1915a

(Doc. 13), §4.

[11]See

Weiss

1907,

1908 for Pierre Weiss's

theory

of

ferromagnetism.

Einstein discussed

Weiss's

theory

in

his

course

on

the kinetic

theory

of

heat

at

the

University

of

Zurich,

summer

semester 1910 (see

Vol.

3,

Doc.

4,

[pp.

41-43],

for Einstein's lecture

notes

on

this

topic).

[12]Foucault

currents

are

the

eddy currents

induced

in

a

conductor

moving

in

a

magnetic

field.

[13]The

number 0.0065

corrects

the values 0.0070 and 0.0069

given

in

Einstein and De Haas

1915a

(Doc.

13), pp.

162

and

164, respectively.

[14]In

the determination of the

charge

of the

circulating particles

as

presented

in

Einstein

and De Haas 1915a

(Doc.

13), pp.

165-166,

it

was

erroneously

assumed that the

torque

and

the

angular

displacement

have

the

same

phase.

The

error

was

first

pointed

out by

Lorentz

in

a

telegram

to

Einstein

(see

Einstein

to

H. A.

Lorentz,

28 April 1915, in

which Einstein acknowl-

edges

the

error).

Einstein corrected the mistake in Einstein 1915d

(Doc. 16).

[15]"v"

should be

"2v,"

as

in

Einstein

and

De Haas 1915b.

[16]In

a

letter

to

G. L. de Haas-Lorentz,

Einstein made the

stronger

statement

that the results

for small

displacements

seemed

to be

systematically

wrong (see

Einstein

to

Geertruida

de

Haas-Lorentz,

before

10 April 1915).

[17]The

number 0.124

corrects

the value 0.128

given

in Einstein and

De

Haas 1915a

(Doc.

13), p.

169.

[18]At

the

corresponding point

(p. 169)

in

Einstein and

De

Haas 1915a

(Doc.

13),

the

sat-

urization

magnetization per

cm3 is

put at

1260.

The

use

of

the

value

1300

here

leads

to

slightly

different results for

Is

and

X.