PHENOMENA OF MOTION 53 



It is evident that these values are free from any hypothetical con- 

 siderations. It has, however, been shown that the coefficient of 

 diffusion for crystalloids bears a certain relation to the molecular 

 weight. Small molecules diffuse rapidly, large ones slowly. When 

 suitable formulas are used there is very satisfactory correspondence, 

 provided the molecular weights are not smaller than 50 nor larger 

 than 500. A further advance was made by seeking to calculate from 

 the coefficient of diffusion the molecular weights of colloids whose M 

 was unknown. The results were not concordant because the moving 

 units in colloidal solutions are not "molecules" but "particles," that 

 is, complexes of molecules. 



If we connect the fact that the coefficient of diffusion decreases 

 with increase in the size of the molecule, with what we know about 

 the Brownian-Zsigmondy movement, the relationship is surprising. We 

 have seen that the movement is smaller as the particles grow larger 

 and it is evident that, when we layer water over a metal hydro- 

 sol, the strong translatory movements which we observe under the 

 ultramicroscope must carry the hydrosol into the pure water. In 

 coarser suspensions possessing only vibratory movements, we do 

 not expect diffusion to occur. 1 SVEDBERG measured the diffusion 

 coefficient in different solutions of colloidal gold and calculated the 

 size of the particles from the very simple relation (particle size in- 

 versely proportional to diffusion coefficient). The experiments were 

 carried out with two gold solutions which contained particles of 

 I-SJJL/JL and of 20-30/^, directly measured ultramicroscopically. 

 There was a relatively good agreement between the results as cal- 

 culated and determined. A direct relationship between the Brown- 

 ian-Zsigmondy movement and the coefficient of diffusion cannot be 

 experimentally established by methods free from criticism, because 

 the hydrophobe hydrosols (e.g., colloidal gold, platinum and the like) 

 which may be counted under the ultramicroscope cannot be prepared 

 entirely free of crystalloids. Since every crystalloid molecule which 

 is attached to a colloid particle must greatly accelerate the diffusion 

 of the latter, we are confronted with a source of error that is uncon- 

 trollable. 



A series of coefficients of diffusion have also been measured for 

 hydrophile colloids, which though they have not the exactitude 

 possessed by those of crystalloids, reveal a remarkable constancy 

 so that they may be considered characteristic for the substance 

 under consideration (Sv. ARRHENIUS, R. 0. HERZOG, EULER, 

 OHOLM). 



1 For the mathematical relations between diffusion coefficient, molecular 

 weight and molecule or particle diameter see R. O. HERZOG and L. W. OHOLM. 



