50 COLLOIDS IN BIOLOGY AND MEDICINE 



seen under the ultramicroscope are comparable to the dance of the 

 molecules in accordance with the Kinetic Theory of Gases. 



The speed of the particles is dependent on the viscidity of the 

 dispersing medium and increases with a rise in temperature. It is 

 very pertinent to enquire at this point whether we here see the move- 

 ments of the molecules themselves. In a certain sense, this may be 

 answered in the affirmative. Though we cannot yet say that this 

 movement is inherent in the particles, i.e., that it would be carried 

 out by the particles themselves, we may assert that it is caused by 

 blows from the molecules of the solvent. 



A. EINSTEIN and M. VON SMOLUCHOWSKI have independently de- 

 duced from the Kinetic Theory of Gases, laws for the Brownian 

 movement (extent of movement, influence of temperature and vis- 

 cosity). It might be assumed a priori, that a particle floating in a 

 fluid would remain at rest, for it simultaneously receives from all 

 sides an equal number of impacts from molecules. The fallacy of 

 this assumption is shown by M. VON SMOLUCHOWSKI in a very pretty 

 comparison. If we play roulette for a long time the chances for 

 gaining and losing are equal (disregarding the banker). If we play 

 only a short time we win one day and lose the next. In other words 

 the law of probabilities shows that the excess of molecular impacts 

 which reach a particle in a given quarter suffice to give it movement 

 one direction or another direction. The smaller the particle, the 

 greater is the probability that the impacts will not arrest it and the 

 stronger is its movement. 



The formula of VON SMOLUCHOWSKI as well as that of A. EINSTEIN 



demands that -- be constant for equal sized particles. 



A amplitude, Y) = viscosity, T = oscillation time. 



TH. SVEDBERG, by brilliantly devised methods, measured these 

 values on colloid metals, in various dispersing media, and estab- 

 lished the constants. It is true that the absolute figures for the 

 measured and for the calculated amplitudes do not exactly agree, 

 but they are of the same order of magnitude; i.e., the values found 

 are on the average three times as large as those calculated. SEDDIG, 

 also, confirmed the quantitative increase of amplitude accompany- 

 ing a rise in temperature. 



This is a remarkable agreement between the movements of small 

 particles seen with the eyes and the hypothesis of the movements 

 of gas molecules based on scientific imagination, which KROENIG in 

 1856 and CLAUSIUS in 1857 formulated mathematically (kinetic 

 theory of gases) . All investigations that have since been undertaken 



