1325 
SMoLcvcHowskKr (Sm. ID. While according to Sm. I e.g. the mean 
square of the deviation is inversely proportional to the square of 
the radius a of the particle, it is according to Sm. II inversely 
proportional to the first power of a. Further according to Sm. | 
the mean square of deviation in the Brownian movement in gases 
would be inversely proportional to the pressure of the surrounding 
gas, whereas according to Sm. II it would be independent of the 
pressure. According to von SMOLUCHOWSKI this does not imply any 
contradiction. He is, namely, of opinion that his formulae are 
applicable to different cases. According to him Sm. L will hold for 
the case that the free path / of the molecules of the medium is 
great compared with a, Sm. [ it will hold for the opposite case. The 
reason why according to von SMOLvCHOWSKL we get different formulae 
in those two cases is this, that in the first case the velocities of the 
surrounding molecules will be independent of the velocity of the 
Brownian particle, whereas in the second case the surrounding 
molecules will join the movement of the Brownian particle. 
Other writers (EINSTEIN '), Einstein and Horr *), LANGEVIN *)), who 
derive formulae, which just as Sm. II are based on the supposition 
of friction, do not give any information about the reason why they 
think that the motion of the particle is damped by friction, but 
probably they start from the same view as von SMOLVCHOWsKL For 
if the surrounding liquid (or gas) does not join the motion of tbe 
particle, there can be no question of friction according to the 
ordinary laws of liquid friction. But at the same time it is clear 
that the opinion that the surrounding substance should join the 
movement is in flat contradiction with the results of statistical mecha- 
nies. Gipps *) e.g. proves that for statistical equilibrium the velocities 
of the different particles forming a system, will be independent of 
each other, at least in the case that the kinetic energy is a homo- 
geneous quadratic function of the velocities, with coefficients which 
are independent of the coordinates. And this is certainly the case 
for the coordinates which determine the movement of a suspended 
particle and that of the molecules of the medium. 
But statistical mechanics teaches more. It also demonstrates that 
we should assume independence between the distribution in velocity 
and in configuration °). If we, therefore, assume that the molecular 
1) Erystern. Ann. d. Phys. 19. p. 371. Ann. 1906. 
2) EiNsTEIN und Horr. Ann. d. Phys. 33. p. 1105. Ann. 1910. 
5) LANGEVIN. Comptes Rendus. 146. p. 530. Ann. 1908. 
4) J. W. Gisps. Elementary Principles in Statistical Mechanics, p. 46—47. 
5) J. W. Gress, |. c. ch. VI. 
