76 ON MAGNITUDE [ch. 



Their motions are erratic, independent of one another, and 

 devoid of common purpose*. This is nothing else than a 

 vastly magnified picture, or simulacrum, of the Brownian move- 

 ment; the parallel between the two cases lies in their complete 

 irregularity, but this in itself implies a close resemblance. One 

 might see the same thing in a crowded market-place, always provided 

 that the busthng crowd had no business whatsoever. In like 

 manner Lucretius, and Epicurus before him, watched the dust-motes 

 quivering in the beam, and saw in them a mimic representation, 

 rei simulacrum et imago, of the eternal motions of the atoms. Again 

 the same phenomenon may be witnessed under the microscope, in 

 a drop of water swarming with Paramoecia or such-Hke Infusoria; 

 and here the analogy has been put to a numerical test. Following 

 with a pencil the track of each little swimmer, and dotting its place 

 every few seconds (to the beat of a metronome), Karl Przibram 

 found that the mean successive distances from a common base-hne 

 obeyed with great exactitude the "Einstein formula," that is to 

 say the particular form of the "law of chance" which is apphcable 

 to the case of the Brownian movement f. The phenomenon is (of 

 course) merely analogous, and by no means identical with the 

 Brownian movement; for the range of motion of the little active 

 organisms, whether they be gnats or infusoria, is vastly greater than 

 that of the minute particles which are passive under bombardment ; 

 nevertheless Przibram is inclined to think that even his compara- 

 tively large infusoria are small enough for the molecular bombard- 

 ment to be a stimulus, even though not the actual cause, of their 

 irregular and interrupted movements {. 



* Nevertheless there may be a certain amount of bias or direction in these 

 seemingly random divagations: cf. J. Brownlee, Proc. R.S.E. xxxi, p. 262, 

 1910-11; F. H. Edgeworth, Metron, i, p. 75, 1920; Lotka, Elem. of Physical 

 Biology, 1925, p. 344. 



t That is to say, the mean square of the displacements of a particle, in any 

 direction, is proportional to the interval of time. Cf. K. Przibram, Ueber die 

 ungeordnete Bewegung niederer Tiere, Pfliigefs Archiv, cliii, pp. 401-405, 1913; 

 Arch. f. Entw. Mech. xliii, pp. 20-27, 1917. 



X All that is actually proven is that "pure chance" has governed the movements 

 of the little organism. Przibram has made the analogous observation that 

 infusoria, when not too crowded together, spread or diffuse through an aperture 

 from one vessel to another at a rate very closely comparable to the ordinary laws 

 of molecular diffusion. 



