210

BROWNIAN MOTION

invented

ultramicroscope[28]

made it

possible

to resolve

many

colloidal solutions into

their

constituents.[29] The

ultramicroscope

not

only

demonstrated the

physical reality

of

colloi-

dal

particles,

but showed that

irregular

motion

is

one

of

their

outstanding

characteris-

tics.[30]

Although

the

ultramicroscope

brought

closer the

"distant

reality" ("realite loin-

taine")[31]

of

molecules,

one

of

their fundamental

properties,

their velocities,

remained

inaccessible to measurement. The inconsistencies that result from

presumed

velocity

measurements,

such

as

Exner's, had hinted

at this

problem;

but it

was

explicitly

discussed

for the

first time in the

theoretical studies

of

Brownian motion

that Einstein and Smolu-

chowski

independently published

between 1905 and

1907.[32]

Both introduced

the

mean

square

displacement

of

the

suspended particles as

the

primary

observable

quantity

in

Brownian

motion.[33]

Einstein

argued

that

dissipative

forces

change

the direction and

mag-

nitude

of

the

velocity

of

a suspended particle on

such

a

short time scale that it cannot be

measured.[34] This

argument

demonstrates the fundamental role

of

dissipation

in

Einstein's

analysis

of

Brownian motion.

In

summary,

the

study

of

previous explanations

of

Brownian motion shows

that

three

elements

of Einstein's

approach are

characteristic

of

his decisive

progress: (1)

he

based

his

analysis on

the osmotic

pressure

rather than

on

the

equipartition

theorem;

(2)

he iden-

tified the

mean square displacements

of

suspended particles

rather than

their

velocities

as

suitable observable

quantities;

and

(3)

he

simultaneously applied

the

molecular

theory

of

heat and the

macroscopic theory

of

dissipation

to

the

same

phenomenon,

rather

than

re-

stricting

each

of

these

conceptual

tools to

a single

scale,

molecular

or

macroscopic.

IV

In his first paper

on

Brownian

motion,

Einstein 1905k

(Doc. 16),

Einstein

proved:

that,

on

the

assumption

of

the molecular

theory

of

heat,

bodies

of

the

order of

magnitude

of

1/1000

mm suspended

in

liquids

must

already carry

out

an

observ-

able random

movement,

which

is

generated by

thermal motion.

daß

unter

Voraussetzung

der molekularen

Theorie

der Wärme in

Flüssigkeiten

suspendierte Körper von

der

Größenordnung

1/1000

mm

bereits eine wahr–

[28]

The

ultramicroscope, developed by

Sie-

dentopf

and

Zsigmondy,

is based

on a new

illu-

mination

technique

that makes it

possible

to ob-

serve

the diffraction discs

of

otherwise invisible

objects;

it increased the limit

of

visibility

to

ap-

proximately

5

x 10-3 micron. For

a contempo-

rary

discussion

of

ultramicroscopes,

see

Cotton

and

Mouton

1906, chap.

3.

[29]

See

Siedentopf

and

Zsigmondy

1903.

[30]

Siedentopf

and

Zsigmondy

1903. The

identification

of

this

irregular

motion with

Brownian motion

was questioned (see,

e.g.,

Ostwald

1907).

[31]

Perrin

1911,

p.

157.

[32]

Smoluchowski

was

the first to discuss the

impossibility

of

measuring

the

velocity

of

sus-

pended particles (see

Smoluchowski

1906).

For

Einstein's

discussion

of

this

problem,

see

Ein-

stein

1907c

(Doc. 40).

[33]

For

a

more

detailed discussion

of

Ein-

stein's

introduction

of

this

quantity,

see

the fol-

lowing

section.

[34]

See

Einstein

1907c

(Doc. 40).