DOC.

4

49

i(p1...pn)

=

const.,

which does not

contain the time

explicitly.

However,

for

a

system

of

equations

that represents the

changes

of

a

physical

system

closed

to

the

outside,

we

must

assume

that

at

least

one

such equation

exists,

namely

the

energy

equation

E(p1...pn)

=

const.

[4]

At

the

same

time,

we

assume

that

no

further

integral

of this kind that is

independent

of the

above

equation

is

present.

§2.

On

the stationary

distribution

of state of

infinitely

many

isolated

physical

systems

of almost

equal energies

Experience

shows

that after

a

certain time

an

isolated

system

assumes

a

state

in

which

no

perceptible quantity of the

system undergoes

any

further

changes

with time;

we

call

this

state

the stationary

state. Hence

it

will

obviously be

necessary

for the functions

/i

to

fulfill

a

certain condition

so

that

equations

(1)

may

represent

such

a

physical

system.

If

we now assume

that

a

perceptible quantity

is

always

represented

by

a

time

average

of

a

certain function of the

state

variables

p1...pn, and

that

these

state

variables

p1...pn keep

on

assuming

the

same

systems of

values

with

always

the

same

unchanging

frequency,

then it necessarily follows

from

this

condition, which

we

shall elevate

to

a

postulate, that the

averages

of

all

functions

of the

quantities

p1...pn

must be constant; hence,

in

accordance with the

above,

all

perceptible quantities

must

also

be

constant.

We

will

specify

this

postulate precisely. Starting at

an

arbitrary

point

of time

and

throughout

time

T,

we

consider

a

physical

system

that is

represented

by

equations

(1)

and has the

energy

E.

If

we imagine

having

chosen

some

arbitrary

region

T

of the

state

variables

p1...pn, then

at

a

given

instant of time

T

the values of the

variables

p1...pn

will lie

within

the

chosen

region T

or

outside

it;

hence,

during

a

fraction

of

the

time

T,

which

we

shall call

T,

they

will lie in the

chosen

region T. Our

condition then reads

as

follows: If

p1...pn are

state

variables of

a