MUTATIONS OF BACTERIA 505 



However, in all but one case the experimental ratio is greater than the value 

 calculated from the theory — that is, the variability is even greater than pre- 

 dicted. 



Table 3 

 Distribution of the numbers of resistant bacteria in series of similar cultures. 



EXPERIMENT NO. 2 2 2\ 



Number of cultures 

 Volume of cultures, cc 

 Volume of samples, cc 



87 



Resistant 

 bacteria 

 o 

 1 

 2 

 3 

 4 

 5 

 6- 10 

 11- 20 

 21- 50 

 51- 100 

 101- 200 

 201- 500 

 501-1000 



Number of 



cultures 



57 



20 



5 

 2 



3 



1 

 7 

 2 

 2 

 o 



Resistant 

 bacteria 



o 



1 



2 



3 



4 



5 



6- 10 



11- 20 



21- 50 



51- 100 



101- 200 



201- 500 



501-1000 



Number of 

 cultures 

 29 

 17 

 4 

 3 

 3 

 2 



5 

 6 

 7 

 5 



* Cultures in synthetic medium. 



A part of this discrepancy may be accounted for by the fact that the 

 time t , mutations occurring prior to which were disregarded by the theory, 

 was chosen in such a manner that on the average one mutation would occur 

 prior to time t . This mutation, if it occurs, will of course tend to increase the 

 variance, and in some of the experiments the high value of the experimental 

 variance can be traced directly to one exceptional culture in which a mutation 

 had evidently occurred several generations prior to time to. Unfortunately, 

 there is no general criterion by which one might eliminate such cultures from 

 the statistical analysis, because, in a culture with an exceptionally high count 

 of resistant bacteria, these do not necessarily stem from one exceptionally 

 early mutation, but may also be due to an exceptionally large number of 

 mutations after time to. 



There may also be other reasons why the observed variances are higher than 

 the expected ones. First of all, the simplifying assumption that the mutation 



