370 PROTOPLASM 



negative charges balance each other, but in the diffuse double 

 layer there is, over a time average, an excess of ions of one sign 

 in any unit volume. The difference of potential (f ) across the 

 double layer depends upon the thickness of this ionic atmosphere 

 (which in turn depends upon the concentration) and the number 

 of adsorbed charges within the plane of slippage per unit area. 

 It is f which determines the speed of a particle moving under the 

 influence of an electric field. It is, therefore, f that should 

 express the potential in the Helmholtz formula. 



In addition to the f potential there is the e or thermodynamic 

 potential, e is usually considered to be the total potential between 

 the surface and the body of the solution, whereas the electro- 

 kinetic potential f is the potential drop between the plane of 

 slippage and the body of the solution. The curve in Fig. 161B 

 shows the fall of these potentials with distance from the particle, 

 f and € do not bear a clear relationship to each other ; e is treated 

 by thermodjaiamics, whereas f is not. The Gouy theory deals 

 only with f. f is much more sensitive to the effects of salts 

 than e. 



The field strength near the particle is, on the basis of estimates 

 by H. Miiller, exceedingly great. For this reason the "layer" of 

 ions is greater than ionic dimensions ; and for this reason all heat 

 motion of the nearer ions is nullified. Furthermore, there are 

 probably distortions of the ions, and also orientation of the 

 water molecules. These latter, functioning as electric dipoles 

 (Fig. 177), will be held in definite orientation (Fig. 161^). 



Abramson has been able to show that when quartz particles 

 are placed in certain protein solutions they behave like protein 

 molecules; i.e., they become coated with a film of protein. Since 

 these quartz particles are of microscopic dimensions, whereas 

 protein molecules are not, use of this method facilitates the 

 investigation of proteins by the microscopic method of cata- 

 phoresis. By measuring the cataphoretic mobilities of these 

 protein-coated particles, Abramson has calculated their charge 

 by the Gouy theory and also thermodynamically. A comparison 

 of the two values obtained by different methods reveals essential 

 agreement, thus confirming the Gouy theory. 



In laboratory practice, it is more convenient, and for most 

 purposes as satisfactory, to express cataphoretic observations in 

 terms of rate of migration (in microns per second per volt per 



