170

DOC.

13 PROOF OF

AMPERE'S CURRENTS

Published

in

Deutsche

Physikalische

Gesellschaft.

Verhandlungen

17

(1915):

152-170.

Lec-

ture

held

on

19 February

1915.

Submitted

10

April 1915, published

30

April

1915.

[1]See, e.g.,

Harman

1982,

chap. 2,

for

an

overview of

nineteenth-century

theories of

mag-

netism. See also the editorial

note,

"Einstein

on

Ampere's

Molecular

Currents,"

pp.

145-149,

for

more

background

on

this

paper.

[2]See, e.g.,

Lorentz

1909 for

an

overview of electron

theory.

[3]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).

[4]See

the editorial

note,

"Einstein

on

Ampere's

Molecular

Currents,"

p.

146,

for

a

discus-

sion of Einstein's views

on zero-point

energy.

[5]E

is

the

charge

of the electron and

u its

mass.

[6]This

value

corresponds

to

a

value of

1.77

x

107

emu/g

for the

specific charge

of the elec-

tron,

in accordance with

recent experimental

results

(see, e.g.,

Neumann, G.

1914).

[7]"D" should be

"d."

[8]At

the

corresponding point

(p.

698) in

Einstein

and

De

Haas

1915c

(Doc.

14),

the

satu-

ration

magnetization per

cm3 is

put at

1000.

See also

pp.

164

and

169

of this

paper,

where the

values

1200

and

1260

are

used. The

density

of iron

is

7.8

g/cm3.

[9]"D"

should

be

"d."

[10]"Qä"

should

be

"Qä."

[11]See

Einstein and De Haas 1915c

(Doc.

14), pp.

699-700,

for

details

on

the

recording

of

the

oscillogram.

Walter

Rogowski

(1881-1947)

was a

permanent

member of the

Physikalisch-

Technische

Reichsanstalt,

where the

experiment

was

performed.

[12]"D"

should

be

"d."

[13]"w"

in in

the

upper

summation limit should

be

"oo."

[14]A

more

general

solution of

eq.

(8a),

also valid for

frequencies

other than the

resonance

frequency,

is

given

in

Einstein and

De

Haas 1915c

(Doc.

14),

pp.

701-702. See also

§6

below.

[15]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).

[16]Foucault

currents

are

the

eddy

currents

induced

in

a

conductor

moving

in

a

magnetic

field.

[17]In

Einstein and De

Haas 1915c

(Doc.

14), p.

704,

the value of

Q was

corrected

to

0.0065.

[18]See

the

previous note.

[19]Figure

6

shows the

torque

and the

angular displacement to

have the

same

phase,

which

is wrong,

as was

first

pointed out

by

Lorentz

in

a

telegram to

Einstein

(see

Einstein

to

H. A.

Lorentz, 28

April 1915,

in

which Einstein

acknowledges

the

error).

Einstein corrected the mis-

take

in

Einstein

1915d

(Doc.

16).

[20]See

Einstein

and De Haas 1915c

(Doc.

14), p.

701,

for

more

details

on

the derivation of

eq.

(16).

"J1"

in (16)

should

be "Js."

[21]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).

[22]In

Einstein and De Haas 1915c

(Doc.

14),

p.

710,

the number 0.128

was

corrected

to

0.124.

[23]At

the

corresponding point

(p.

710) in

Einstein and De Haas 1915c

(Doc.

14),

the value

of

the

saturation

magnetization per

cm3 is

put at 1300,

which results

in

slightly

different values

of

Js

and

Y.