DOC.

40

231

direction

of

motion had

changed

drastically,

and

in

a

completely

irregular

manner,

already

in

the extraordinarily short time d.

It is therefore

impossible-at

least for ultramicroscopic

particles-to

determine v2

by

observation.

3.

If

we

limit ourselves

to

the

investigation

of the paths,

or-to

be

more

precise-of

the

changes

of

position,

in times

r

that

are

substantially

greater

than

$,

we

will

have

according

to

the

molecular

theory

of heat

[9]

T7

_

rz

W

1

T'

3S7

'

where

yx

denotes the

change

of the

particle's

x-coordinate

occurring during

r.

As

the

mean

velocity

in the time interval

r

we can

define the

quantity

where

we

put

for brevity

*2

w

fr

RT

1

-w

But

this

mean

velocity increases

as r

decreases;

as

long

as r

is

large

compared

with

d,

the

velocity does not

approach any

limiting value with

decreasing

r.

Since

an

observer

operating

with

certain

means

of observation in

a cer-

tain

manner can never

perceive paths

traveled in arbitrarily short

times,

a

certain

mean

velocity

will

always

appear

to

him

as

instantaneous

velocity.

But

it is clear that

no

objective

property

of the

motion investigated

corresponds

to

the

velocity

so

obtained,

at

least if the

theory corresponds

to

the facts.

Bern, January 1907.

(Received

on

22 January)

[10]

[11]