ACTIVE FROM INACTIVATED BACTERIOPHAGE 



123 



nigrosin were made without fixation, and, after the slides were dried, 764 

 cells were measured with an ocular micrometer (Filar). The distribution of 

 lengths is given in figure 8, and will be referred to as the "B distribution." 

 Measurements on five cultures gave similar distributions. 



For the purpose of obtaining the distribution of phage particles adsorbed 

 per bacterial cell, or "P distribution," we shall split the bacterial population in- 



300 



MEAN= L = 25.717 MICROMETER UNITS 

 VARIANCE = 109.36 (MICROMETER UNITs)^ 



0.1653 L 



T I 



150 



T — r 



200 



50 100 



MICROMETER UNITS 



Figure 8. — The distribution of bacterial lengths in standard cultures of 

 Escherichia coli strain B containing 10^ cells per ml. 



to a number of subpopulations, each comprehending one of the length classes 

 in figure 8, and assume that the adsorption capacity of all cells within each 

 subpopulation is constant. 



By the calculation given at the end of this paper, the following properties 

 of the P distribution are derived: 



a) its arithmetic mean is equal to x, that is, to the multiplicity of infection, 

 as for a Poisson distribution. 



b) its variance is equal to the variance x of the Poisson distribution, plus a 

 term equal to the variance of the B distribution: var(P) = a;+var(B). 



If we express the variance in terms of the mean x taken as the unit of meas- 

 ure, we obtain for our experimental cultures: va,T(P) = x-\-0.1653x^. This equa- 

 tion expresses the relation between the variance of the P distribution for an 

 ideal population with uniform capacity of adsorption and the variance for a 

 real population with a capacity of adsorption distributed with a given variance. 



The P distributions for several values of x, calculated from the actual 

 B distribution, are given in table 8, together with the Poisson distributions 



277 



