DOC.

4

KINETIC

THEORY

LECTURE NOTES

245

[52]The

equality

is in fact

only

a

proportionality.

The surface

area

of

an

l-dimensional

hyper-

sphere

is

given

by Rl-l2nl/2Y(l/2).

[53]The

last

term

of this

equation

should

be

- -.

[54]For

the

following discussion,

see

chap.

14

("Diskussion thermodynamischer Analogien")

of

Gibbs 1905.

[55]"mikrokanonische

Gesamtheit" should

be

"kanonische

Gesamtheit.".

[56]The

preceding

sentence

is

interlineated

in

the

original.

[57]At

this

point

in

the

text

Einstein indicates

a

note he

has

appended

at

the foot of

this

page:

"Wir

sagen, dann,

dass sich

beide

Systeme

berühren."

[58]The

words

"(unendlich lange)"

are

interlineated

in

the

original.

[59]The

preceding seven

words

are

interlineated in the

original.

"aus dessen" should be "auf

dessen." In the

equation

below,

the

numerator is corrected

from

n.

[60]The

preceding

four words

are

interlineated

in

the

original.

[61]The

evaluation of I is

in fact

an

evaluation of

4I2.

The result of

the

following integration

should therefore

be

jn

instead of

2sn.

[62]See

note

14.

[63]The

word

"mittl[ere]"

is

interlineated

in

the

original.

The derivation of

this

theorem here

and

the

following

derivation

of

Avogadro's

law

satisfy

the earlier

given

statement

[pp.

2,

3]

that

these theorems should

be

derived from

purely

molecular-theoretical

considerations,

i.e.,

inde-

pendently

of

the

phenomenological

ideal

gas equation;

see

also

note 4.

[64]See

[pp.

45-46].

[65]The square

brackets

are

in

the

original.

[66]The

problem

of the

specific

heat of

polyatomic

molecules

is

taken

up again

on

[p.

38].

[67]This notation

is

the

same

as

the

one

used

by

Boltzmann

1898,

§25,

and

as

that

used

in

Einstein

1902b

(Vol. 2,

Doc.

3);

in Gibbs

1902, 1905,

the

coordinates

are

denoted

by

q

and their

associated

momenta

by p,

which conforms

to

modern notation.

See

also

notes 49

and

72.

[68]The

problem

of

magnetism is

also treated

on

[pp. 39-44].

For

references

concerning

Langevin

and

Weiss, see

notes 76

and 84-87.

[69]The

square

brackets

are

in

the

original.

[70]A

similar model had been

employed

earlier

by

Einstein

in

Einstein

1907a

(Vol.

2,

Doc.

38)

to

calculate

specific

heats of

solids.

[71]The

square

brackets

are

in

the

original.

[72]In Gibbs

1905,

p.

31,

a

similar notation

is

introduced.

There, however,

+

does

not

denote

an

additional

energy

term

but

is

determined

by

the normalization

condition;

see

also notes

49

and

67.

[73]See

the discussions of

molecules in

a

magnetic

field,

Brownian motion under the influence

of

gravity,

and Brownian motion of

rotating particles

on

[pp. 38-40], [pp. 40-41],

and

[p. 44],

respectively.

[74]For

experimental

data

on

the

specific

heat

of

diatomic

molecules,

see,

e.g.,

Meyer, O.

E.

1899, part

1,

§55.

The

question

of

how

many degrees

of

freedom

of

a

diatomic molecule contrib-

ute to the

specific

heat

had been

a

subject

of debate

in

kinetic

gas

theory; see,

e.g.,

Brush

1976,

§10.8.

[75]Curie's law

(which

states

that the

magnetic susceptibility

is

inversely

proportional

to

the

temperature)

was

first

published

in

Curie

1895.

[76]Langevin's

formula

=

Cosha

1/a,

where

a

MH/O,

which

reduces

to

Curie's

law

for

small

a (see

also

[p.

41]),

was

first

derived

in

Langevin

1905.

Langevin

also

gave

a report

of

his

theory

at

the

1911

Solvay Congress

(Langevin 1912).

[77]Weiss's

theory

of

ferromagnetism is

taken

up again

on

[p. 41].

[78]These

topics

are

treated

in

more

detail

on [pp.

41-43].

[79]For

general

information and

a

survey

of Einstein's work

on

Brownian

motion,

see

Vol.

2,