VIABLE BACTERIA IN YOUNG CULTURES 443 



Calculation of the generalion time 



Takinf? for granted that there is a normal death rate of the 

 organisms in vitro cultures, it is inmiediately apparent that the 

 generation time must be calculated afresh. Hitherto the number 

 of generations occurring dining a given period has been calculated 



from the formula n = — ^-i — -^ — - where n = the number of 



log 2 



generations, b = the number of organisms at the end of the given 

 period, and a = the number alive at the beginning of that period 

 (Chesney, 191G). This formula has been employed solely on the 

 assumption that the number of organisms doubles in each genera- 

 tion. But if, for instance, only 80 per cent are dividing, then the 

 increase in the number of organisms in each generation will only 



rise by 1 .6. Hence the formula must be altered to n = —, ^— ' 



log 1.6 



The result of this will be to give a larger number of generations in 



the particular period studied, and consequently a shorter time 



for the production of each generation. It is now seen that the 



generation time cannot be calculated with accuracy unless the 



number of both the total and viable organisms be known. In 



these experiments these numbers are known, at least for the latter 



part of the logarithmic phase. What has been done then, is to 



estimate the relation between the total and viable organisms at 



the end of the logarithmic phase. Assuming that this relation 



has persisted all through the phase — and it is difficult to dispute 



the probability of this considering that the viable count increases 



regularly — one can then deduce the percentage of organisms 



which has remained alive and divided in each generation, and 



hence the total number of generations. For instance, reverting 



to the figures given for experiment 12 (table 9). The number of 



organisms alive at the commencement of the logarithmic phase, 



namely, minutes, was 62,150 per cubic centimeter. At 240 



minutes, the close of the logaritlmiic phase, there were 43,290,000 



per cubic centimeter living and 50,780,000 per cubic centimeter 



total alive and dead. The proportion of viable to total is then 



85.23 per cent. The actual increase in the viable count per 



