II], THE BROWNIAN MOVEMENT 47 



movement described by Doflein, and the undulating or rotating 

 movement described by Schaudinn, are just such as may be easily 

 and naturally interpreted as part and parcel of the Brownian 

 phenomenon. 



While the Brownian movement may thus simulate in a deceptive 

 way the active movements of an organism, the reverse statement 

 also to a certain extent holds good. One sometimes lies awake of 

 a summer's morning watching the flies as they dance under the 

 ceiling. It is a very remarkable dance. The dancers do not 

 whirl or gyrate, either in company or alone ; but they advance 

 and retire; they seem to jostle and rebound; between the rebounds 

 they dart hither or thither in short straight snatches of hurried 

 flight; and turn again sharply in a new rebound at the end of each 

 little rush. Their motions are wholly "erratic," independent of 

 one another, and devoid of common purpose. This is nothing else 

 than a vastly magnified picture, or simulacrum, of the Brownian 

 movement; 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 bustling 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 simulacrmn ef 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 

 suchlike 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-line obeyed with great exactitude the "Einstein 

 formula," that is to say the particular form of the "law of chance" 

 which is applicable to the case of the Brownian movement*. 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 



* Ueber die ungeordnete Bewegung niederer Thiere, Pfliiger^s Archiv, CLin, 

 p. 401, 1913. 



