M. Schlesinger 



Therefore, a coli bacterium killed by heating to 70° is capable of irreversibly 

 adsorbing an average maximum of 130 to 140 bacteriophages. 



Calculation of the Particle Size of the Bacteriophage from the Adsorp- 

 tion Velocity and from the Saturation Capacity. Conclusions: 



a) Calculation of Particle Size from the Adsorption Velocity. The assumption 

 was made in the derivation of equation (1), a formal description of the adsorption 

 kinetics, that contact between one phage and one bacterium occurs entirely by 

 chance and without benefit of any orienthig or attractive forces whatsoever. The 

 collisions were thought to be mainly due to the Brownian movement of the 

 particles^, to which, obviously the movement of the much smaller bacteriophages 

 made the principal contribution. Since there exist well-known relations between 

 Brownian movement, the diffusion coefficient, and the particle size, it is thus 

 possible theoretically to correlate the latter with the adsorption velocity of the 

 phage. It is, however, first necessary to make an assumption concerning the 

 relation which might exist between the Brownian movement collision frequency 

 of phages and bacteria and the number of adsorptive events which actually ensue 

 as a consequence of these coHisions. 



The simplest assumption in this connection is that every collision leads to an 

 irreversible fixation. If this assumption is valid, then the relation of the adsorp- 

 tion velocity to the diffusion constant, D, of the phage follows at once from the 

 formula on which M. v. Smoluchowsky has based his theory of the kinetics of 

 coagulation^. This formula states that the quantity Jdt of a solute which diffuses 

 in a time dt onto a sphere of radius R capable of fixing solute particles which touch 

 it is 



Jdt = AirDRcdt 



where c is the concentration of the substance^. If we efjuate R to the radius of a 

 supposedly spherical bacterial cell, substitute for c the number of free bacterio- 



^It is also possible that convection or mechanical agitation of the fluid could play a certain 

 role. The error arising from neglecting the Brownian movement of the bacteria depends on the 

 ratio of the bacterial diameter to that of the phage, and probably causes the estimate of the 

 phage diameter to be too small by 10% in the following calculation. 



^Z. Phy.nk. Chem., 92, 140 (1917). An attempt — though insufficient — to apply the formula 

 of the V. Smoluchowsky coagulation theory to bacteriophage adsorption has already been made 

 by V. Angerer [Arch. f. Hyg., 92, .312 (1924)]. 



^The complete formula is 



Jdt = 4DRc 



R 



1 +-J^ 



dt 



where I indicates the time which has elapsed since the start of the experiment. As in the 

 coagulation experiments of Zsigmondy analyzed bv v. Smoluchowsky, so also, under our 



R ' 



experimental conditions is the quantitv , small compared to imity, and can be neglected 



yJTrDt 



without significant error. Incidentally, Jdt represents in v. Smoluchowsky's application, as 



well as in ours, not the number of particles which actually diffuse onto the sphere in the time dt 



(after all, in our experiments there is only one bacteriophage for every hundredth or thousandth 



bacterial cell), but onh' the probability of an encounter of a particle with the adsorbing sphere. 



32 



