138

REVIEW

OF LANGEVIN

Doc. 22

Review

of

P.

LANGEVIN,

"On

a

Fundamental Formula

of the Kinetic

Theory"

("Sur

une

formule fondamentale

de

la theorie

cinetique,"

Academie

des

Sciences (Paris).

Comptes

rendus

140 (1905): 35-38)

[Beiblätter

zu

den

Annalen

der

Physik 29 (1905):

640]

The

author

reports

that,

assuming

arbitrary

laws

of action

between

[1]

molecules

as

well

as

external forces

acting

upon

the

molecules,

he has

solved

[2]

exactly

the

problem

of

diffusion

of

two gases

by

the Maxwell-Kirchhoff

method,

[3]

requiring

only

a

graphic

integration. For

the

case

that the molecules

are

elastic

spheres

which

are

only

infinitesimally deformable,

and

that external

forces

do

not

act

on

the

molecules,

the author obtains for the diffusion

of

one

gas

(molecular

mass

m1)

in the other

gas

(molecular

mass

m)

[4] B

=

16

a2M

ihm

l

m+

m1

Here

D

denotes the diffusion

constant,

a

the

sum

of the radii

of

two

unlike molecules,

M

the

number

of

molecules

"m" per

unit

volume,

h

three-quarters of

the

reciprocal of

the

mean

value

of the

energy

of

the

translational

motion

of

one

molecule.

Boltzmann found

by

the Clausius

[5] approximation method

[6]

D

=

3ia2M\

ih(m+

)

The two

formulas differ

especially strongly

when

m

and

m1

are

very

different. It is further

reported

that

at constant

pressure

the diffusion

coefficient varies

as

T3/2 + 2/n

when two

unlike molecules

repel

each

other

with

a

force that

is inversely proportional to

the

n

+

1st

power

of

the

distance

between

the

centers

of the molecules.

The

author

has also

applied

the

theory to

changes

in

position of

electric

charges

in

gases. He

found

that