DOC.

32

181

latter

theory.

We

will

then have

to apply

these laws

to

the

following

special

cases:

1.

a

is the x-coordinate of

the center

of gravity of

a

spherically

shaped

particle

suspended

in

a homogeneous

liquid

(which

is

not subject to

gravitation).

2.

a

is the

angle

of rotation that determines the position

of

a

spherical

particle

suspended

in

a

liquid and

capable

of

rotating

about

a

diameter.

§1.

On a case

of

thermodynamic

equilibrium

In

an

environment

of absolute

temperature

T

let there

be

a

physical

system

in thermal interaction with this

environment and

in

a

state

of thermal

equilibrium.

This

system,

which hence

also

possesses

the absolute

temperature

T,

shall

be completely

determined

by

the

state

variables

P1...Pn

according

to

the molecular

theory

of heat.1 In the

special

cases

to be considered,

we

can

choose

for the

state

variables

P1...Pn

the coordinates

and velocity

components

of all

atoms constituting

the

system

under

consideration.

The

probability that

at

a

randomly

chosen

instant of time all

state

variables

P1...Pn

will

lie

in the n-fold

infinitesimally

small

region

(dp1....dpn)

is

given

by

the

equation2

(1)

dw = Ce

dp1...dp~,

where

C

denotes

a

constant,

R

the universal

constant

of the

gas

equation,

N

the

number

of

true

molecules

per

gram-molecule,

and

E

the

energy.

Suppose

that

a

is

an

observable

parameter

of the

system

and

that

to

each

system

of values

P1...Pn

there

corresponds

a

definite value

a.

We

denote

by

Ada

the

probability that

at

a

randomly

chosen

instant the value of

the

parameter

a

will lie

between

a

and

a

+

da.

We

then

have

1Cf. Ann.

d.

Phys.

17 (1905):

549.

2Loc.

cit.,

§§3

and 4.

[7]

[8]