THE REALITY OF MOLECULES 99is larger by many orders of magnitude than {x^2 ) /t^2 , the squared average velocity
computed from Eq. 5.18 for reasonable values of t. Is this paradoxical? It is not,
since one can estimate that the instantaneous velocity changes magnitude and
direction in periods of about 10~^7 s; (v^2 ) is therefore unobservable in Brownian
motion experiments. Here is also the answer to the Naegeli-Ramsey objection.
4) 1908. At the suggestion of the physical chemist Richard Lorenz, Einstein
writes an elementary expose of the theory of Brownian motion [E12].
This completes the account of Einstein's contributions to Brownian motion in
the classical domain. Applications to the quantum theory will be discussed in Part
VI. I conclude with a few scattered comments on the subsequent history of clas-
sical Brownian motion.
Einstein's relation (Eq. 5.18) is now commonly derived with the help of the
Langevin equation (derived by Paul Langevin in 1908 [L3]). The first review
article on Brownian motion appeared in 1909 [Jl]. In later years, the subject
branched out in many directions, including the behavior for small values of t, the
non-Stokesian case, and the presence of external forces [W4]. Brownian motion
was still a subject of active research in the 1970s [B9].
The rapid experimental confirmation of Einstein's theory by a new generation
of experiments, in particular the key role of Jean Perrin and his school, has been
described by Nye [Nl]. Perrin's own account in his book Les Atomes [P9], first
published in 1913 (and also available in English translation [P10]), remains as
refreshing as ever.* This work contains not only an account of the determination
of TV from Brownian motion but also a summary of all methods for determining
N which had been put to the test at that time. It is remarkable that the method
proposed by Einstein in his thesis is missing. I mentioned earlier that a commu-
nication by a pupil of Perrin had led Einstein to discover a mistake in his thesis.
Perrin must have known about this, since Einstein wrote to him shortly afterward
to thank him for this information and to inform him of the correct result [El3].
Einstein's very decent value for ./V (Eq. 5.14) was published in 1911. Its absence
in Perrin's book indicates that Einstein's doctoral thesis was not widely appreci-
ated in the early years. This is also evident from a brief note published by Einstein
in 1920 [El4] for the sole purpose of drawing attention to his erratum published
in 1911 [E7] 'which till now seems to have escaped the attention of all who work
in this field.'
'I had believed it to be impossible to investigate Brownian motion so precisely,'
Einstein wrote to Perrin from Zurich late in 1909 [El5]. This letter also shows
that, by that time, Einstein's preoccupation had moved to the quantum theory. He
asked Perrin if any significance should be attached to the 15 per cent difference
between the values of ./V obtained from Planck's blackbody radiation law and from*Perrin's collected papers are also strongly recommended [Pll].