9780192806727.pdf

where n(x, t) is the number of particles per unit volume around x at time t.

The essence of Einstein's attack on Brownian motion is his observation that, as

far as these three facts are concerned, what is good for solutions is good for

suspensions:

1. Van 't Hoff's laws should hold not only for dilute solutions but also for dilute
   suspensions: 'One does not see why for a number of suspended bodies the same
   osmotic pressure should not hold as for the same number of dissolved mole-
   cules' [E2].


2. Without making an explicit point of it, Einstein assumes that Stokes's law
   holds. Recall that this implies that the liquid is treated as a continuous medium.
   (It also implies that the suspended particles all have the same radius.)


3. Brownian motion is described as a diffusion process subject to Eq. 5.15. (For
   simplicity, Einstein treats the motion as a one-dimensional problem.)
   Now then, consider the fundamental solution of Eq. 5.15 corresponding to a
   situation in which at time t = 0 all particles are at the origin:

96 STATISTICAL PHYSICS

a scholium to the doctoral thesis. To this end, I return to the relation between the

diffusion coefficient D and the viscosity 17 discussed previously

where a is the radius of the hard-sphere molecules dissolved in the liquid. Recall
the following main points that went into the derivation of Eq. 5.12:

1. The applicability of van 't Kofi's laws (Eqs. 5.2 and 5.3)


2. The validity of Stokes's law (Eq. 5.10)


3. The mechanism of diffusion in the x direction, described by the equation (not
   explicitly used in the foregoing)

where n = \n(x)dx. Then, the mean square displacement (x^2 ) from the origin
is given by