124 S. E. LURIA AND R. DULBECCO 



for the same values of x. It is clear that for low multiplicities of infection 

 there is little difference between actual and Poisson distributions. For higher 

 multiplicities, the discrepancies increase; still, for :r=1.5, they only affect 

 relevantly the proportions of bacteria with 5 or more particles. 



Table 8 



The P distribution for various values of x 



"P" columns give the frequencies in the P distribution, "Poisson" columns give the fre- 

 quencies in the Poisson distribution. All frequencies are multiplied by 10^ 



The calculation of x from the bacterial survival — assuming {B unin- 

 fected) /5=e~^ — only gives reliable results for values of x up to about 2. For 

 higher multiplicities, it leads to an underestimation of x. 



THEORY 



The bacterial population is considered as a mixture of an infinite number of 

 subpopulations homogeneous in adsorption capacity. Within each subpopu- 

 lation there is a Poisson distribution of phage particles per bacterium, whose 

 frequency function is: 



jm = —^ (1) 



where Xj is the multiplicity of infection in thejth subpopulation. Xj is obtained 

 from the B distribution of bacterial lengths: if we call Ij the length of the bac- 

 teria in thejth class, we have: 



278 



