THE REALITY OF MOLECULES 101tury studies on Brownian motion, not least because he had remained in touch with
Felix Exner, a comrade from student days who had done very good experimental
work on the subject. Indeed, Smoluchowski's paper of 1906 contains a critique of
all explanations of the phenomenon prior to Einstein's. Like Einstein (but prior
to him) Smoluchowski also refuted the Naegeli-Ramsey objection, pointing out
that what we see in Brownian motion is actually the average motion resulting
from about 1020 collisions per second with the molecules of the ambient liquid. He
also countered another objection: 'Naegeli believes that [the effect of the collisions]
should in the average cancel each other.. .. This is the same conceptual error as
when a gambler would believe that he could never lose a larger amount than a
single stake.' Smoluchowski followed up this illustrative comment by computing
the probability of some fixed gain (including sign!) after a prescribed number of
tosses of a coin.
Smoluchowski began his 1906 paper [S3] by referring to Einstein's two articles
of 1905: 'The findings [of those papers] agree completely with some results which
I had... obtained several years ago and which I consider since then as an impor-
tant argument for the kinetic nature of this phenomenon.' Then why had he not
published earlier? 'Although it has not been possible for me till now to undertake
an experimental test of the consequences of this point of view, something I origi-
nally intended to do, I have decided to publish these considerations....' In support
of this decision, he stated that his kinetic method seemed more direct, simpler, and
therefore more convincing than Einstein's, in which collision kinetics plays no
explicit role. Whether or not one agrees with this judgment of relative merits (I
do not) depends to some extent on familiarity with one or the other method. In
any case, Smoluchowski's paper is an outstanding contribution to physics, even
though the priority of Einstein is beyond question (as Smoluchowski himself
pointed out [S6]).
Smoluchowski treats the suspended particles as hard spheres with a constant
instantaneous velocity given by the equipartition value. He starts out with the
Knudsen case (the mean free path is large compared with the radius a), uses the
kinematics of hard-sphere collisions, calculates the average change in direction per
collision between the suspended particle and a molecule of the liquid, and there-
from finds an expression for (x^2 ) (different from Eq. 5.18 of course). He must
have treated the Knudsen case first since it is kinetically much easier than the
Stokesian case, for which the free path is small compared with a. For the latter
case, he arrived at Eq. 5.18 for (x^2 ) but with an extra factor 27/64 on the rhs.
This incorrect factor was dropped by Smoluchowski in his later papers.
Six letters between Einstein and Smoluchowski have survived. All show cor-
diality and great mutual respect. The correspondence begins with a note in 1908
by Einstein informing Smoluchowski that he has sent Smoluchowski some reprints
and requesting some reprints of Smoluchowski's work [E18]. The next commu-
nication, in November 1911, is again by Einstein and deals with a new subject to
which both men had been drawn: critical opalescence.
It had been known since the 1870s [A2] that the scattering of light passing