lO FUNDAMENTALS OF SUBMI C ROSCOPIC MORPHOLOGY I 



But colloid chemistry was not content with these qualitative con- 

 clusions ; it tried to obtain quantitative facts as to the size of the par- 

 ticles. Some information was provided by ultrafiltration, but apart from 

 that, much more accurate methods were available. 



If the number of particles per unit volume is determined in the 

 ultramicroscope, the particle size can be calculated from the con- 

 centration of the sol. Moreover, there exist mathematical relations 

 between Brownian movement (Einstein's formula), velocity of sedi- 

 mentation (Stokes' formula) or diffusion on the one hand, and particle 

 size on the other. These make it possible to determine the diameter 

 of spherical colloid particles. The ultramicroscope plays an important 

 part in these investigations (Zsigmondy, 1925), since the particles 

 have to be observed when counting or measuring the Brownian 

 movement. In many cases, however, the colloid particles cannot be 

 observed ultramicroscopically, not only because their dimensions are 

 frequently too small but, above all, because their refractive power is 

 often only sUghtly different from that of the dispersing medium, so 

 that light scattering is insufficient. This usually applies to biological 

 sols with their organic colloid particles, which means that the limit of 

 visibility of these sols in the ultramicroscope is reached long before 

 that of inorganic sols (compare Fig. i, p. 2). 



The method of sedimentation is free from this difficulty, because the 

 change in concentration of the solution as a result of sedimentation 

 of the particles can be determined by analytic means or, still more 

 simply, by the change in refractive index. Moreover, the sedimentation 

 velocity can be increased at will by applying stronger centrifugal 

 forces. The ultracentrifuge, which was developed by Svedberg (1938a) 

 into an instrument of the highest accuracy and great power (cen- 

 trifugal fields which are 750,000 times that of the gravitational field!) 

 allows of the determination of particle weights down to amicroscopic 

 molecules. 



The various methods referred to have revealed much of the 

 morphology (size and shape) of submicroscopic particles, so that the 

 electron microscope has only confirmed by direct micrographs the 

 results obtained by indirect means. 



Fig. 2 represents a series of submicroscopic particles of biological 

 importance, facilitating comparison with the microscopic and amicro- 

 scopic regions. The size and shape of the particles were determined by 



