BROWNIAN MOTION 217
meine
Untersuchung
im Wesentlichen
nur
das Gesetz
des osmotischen Druckes
voraus-
setzt").[71]
Smoluchowski obtained
the
same
final
result
as
Einstein for the
mean square
displace-
ment
of
a
particle
suspended
in
a
fluid,
apart
from
a
numerical factor. In
1908,
this
nu-
merical
discrepancy
was
the
starting point
of
Langevin's
analysis.[72]
Langevin
not
only
asserted
that
Smoluchowski's
method leads to the
same
result
as
Einstein's if
correctly
applied,
he
also
presented
a new
derivation
of
the
mean square
displacement
formula.
Einstein's
work
on
Brownian motion
was
also noticed
by
others outside the small circle
of
physicists
with
a specialized
interest in the
phenomenon.
Between 1905 and the
middle
of
1906,
it
brought
him into contact with Heinrich
Zangger,
Professor
of
Forensic Medi-
cine at the
University
of
Zurich,
who had
a strong
interest in the
physical
properties
of
membranes,[73]
and who
apparently
had
made measurements
of
Brownian motion, which
led to his
acquaintance
with
Einstein.[74]
Zangger
continued to discuss the
topic
with
Einstein.[75]
In
a
letter
of
18
September
1906,
Wilhelm
Röntgen
asked Einstein for his reaction to
the
"objection
already expressed by Gouy
...
that
is
directed
against
the
assumption
of
molecular
impulses as
the
source
of
motion
of
small bodies. This is
quite
difficult to
bring
into
harmony
with the second law
of
thermodynamics"
("bereits
von Gouy geäusserten
Bedenken
...
dass sich
gegen
die Annahme
von
Molekularstössen als Ursache der
Bewegungen
kleiner
Körperchen
richtet. Dieselbe ist wohl
schwer
mit dem zweiten
Hauptsatz
der
Thermodynamik
in
Einklang zu
bringen").
In his
papers,
Einstein
never
directly
addressed this and other
objections
raised
to
the kinetic
interpretation
of
Brownian
motion,[76] although they are indirectly
addressed in
attempts
to make the
fundamental
[71]
Einstein
to
Carl
Seelig, 15 September
1952. In this
letter,
Einstein recalled that Smo-
luchowski's work
only
concerned
Brownian
motion in
gases
and "has
not achieved
the de-
gree
of
acuity (precision)
to be
desired"
("nicht
den wünschbaren
Grad
von
Schärfe
(Genauig-
keit)
erreicht hat").
[72]
See
Langevin
1908. For
a
critical discus-
sion
of
various
approaches
to
Brownian
motion,
see
Infeld
1940. For
a comparative
discussion of
Einstein's
and
Smoluchowski's
work
on
Brown-
ian motion,
see
Teske 1969.
[73]
See
Zangger 1906,
1907.
[74]
In
sketchy
notes
probably
written in the
1950s, Zangger
recalled how he met Einstein:
"Stodola
[Professor
of
Mechanical
Engineering
at the
ETH]
told
me
he
could
say
nothing
concrete
about
my
counting
of Brownian
m[olecular]
motion.
(1905/06
...)
I
should
go
to Einstein in
Bern"
("Stodola
sagte
mir,
dass
er
über
meine
Zählung
der Brown M
Bewegung
nichts Bestimmtes
sagen
könne.
(1905/06
...)
Ich solle
zu
Einstein nach Bern").
[75] A
reference to their discussion
of
Brown-
ian motion
is
found in Einstein
to
Heinrich
Zangger, 7
November 1911.
Zangger
continued
his research
on
Brownian motion in collabora-
tion with
a
doctoral
student,
Paul Böhi
(see
Zangger 1911
and
Böhi
1911).
For evidence of
a
letter from Einstein
to Böhi,
see
Böhi
1911, p.
212.
[76]
Einstein later used the
example
of
Brown-
ian motion in
discussing an apparent
contradic-
tion between
phenomenological thermody-
namics and the kinetic
theory
of
heat
(Einstein
1915a,
pp.
261-262). He
emphasized
that,
from
the
phenomenon
of
Brownian motion, it
is
clear
"that
the laws
of
phenomenological thermody-
namics
only possess approximate
validity"
("daß die Gesetze der
phänomenologischen
Wärmelehre
nur angenäherte Gültigkeit
be-
sitzen"), and concluded: "Thus,
according
to
Boltzmann, the
averaged
laws
of
experience
simulate the
irreversibility
of
thermal
processes
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