92 STATISTICAL PHYSICSviscosity in the Stokes regime. Equation 5.12 is the second relation for the two
unknowns N and a.
By a quite remarkable coincidence, Eq. 5.12 was discovered in Australia at
practically the same time Einstein did his thesis work. In March 1905 William
Sutherland submitted a paper that contained the identical result, arrived at by the
method just described [S2a]. Thus, Eq. 5.12 should properly be called the Suth-
erland-Einstein relation.
Note that the derivation of Eq. 5.12 is essentially independent of any details
regarding the motion of the solute particles. Therein lies the strength of the argu-
ment that, as a theme with variations, recurs a number of times in Einstein's later
work: a 'systematic force,' a drag force of the Stokesian type (that is, proportional
to the velocity) balances with a random, or fluctuating, force. In the present case,
as well as for Brownian motion, the fluctuating force is the one generated by the
thermal molecular motions in the environment, the fluctuations leading to a net
diffusion. Later, in 1909 and again in 1917, Einstein was to use the balance
between a Stokesian force and a fluctuating force generated by electromagnetic
radiation.
As to the contents of Einstein's thesis, all was quiet for the five years following
its publication. Then a Mr. Bacelin, a pupil of Jean Baptiste Perrin's, informed
Einstein of measurements which gave a value for 77 that was too high to be com-
patible with Eq. 5.7. As we shall see in the next section, by this time Perrin had
a very good idea how big TV had to be. Therefore, 77 could now be computed
(knowing a from other sources) and the result could be compared with experi-
ment! Upon hearing this news, Einstein set one of his own pupils to work, who
discovered that there was an elementary but nontrivial mistake in the derivation
of Eq. 5.7. The correct result is [E7]
With the same data that Einstein had used earlier to obtain Eq. 5.5, the new value
for TV is
a far better result, on which I shall comment further in the next section.
In conclusion, it is now known that Einstein's Eq. 5.13 is valid only for values
of ip < 0.02.* Theoretical studies of corrections 0(<p^2 ) to the rhs of Eq. 5.13 were
made as late as 1977. Effects that give rise to <p^2 terms are two-particle correlations
[B6] and also a phenomenon not yet discussed in the thesis: the Brownian motion
of the solute particles [B7],
*See the reviews by Rutgers, which contain detailed comparisons of theory with experiment, as well
as a long list of proposals to modify Eq. 5.13 [R5].