88 THE GROWTH AND DEATH OF BACTERIA 



dividing ; and (c) that during this lag phase the cells are undergoing a rapid 

 metamorphosis, resembling that perhaps described by Child (1915) in the rejuven- 

 escence of infusoria, flat worms, and marine algae, which renders them similar to 

 the young actively dividing bacilli of the logarithmic 2:)hase : it may be concluded 

 that the lag phase is essentially a period in which the protoplasm of the old, but 

 still viable, bacteria in the inoculum is acquiring the characteristics of young 

 protoplasm. The lag phase appears to be a phase of rejuvenescence. 



Logarithmic Phase 



The logarithmic phase is that period during which regular and maximum 

 multiplication is occurring. Increase in the number of organisms is by geometrical 

 progression, so that, if the logarithms of their numbers are plotted against time, 

 they will fall along an ascending straight line. If counts are made at intervals, 

 it is easy to calculate the number of generations during the phase, and the length 

 of each generation. 

 Thus if a = number of organisms at the beginning of a given time 



and = ,, ,, ,, ,, ,, end ,, ,, ,, ,, 



then at the end of the first generation, 



6 = a X 2 

 at the end of the second generation, 



5 = a X 2 X 2 

 at the end of n generations, 



6 = a X 2" 



To find the value of n, i.e. the number of generations, we may write 



log h = log a-\- n log 2 



log h — log a 



or n= ^- -^- ........ (1) 



log 2 



Further, if there have been n generations in time T, the generation time G can be 



calculated from the formula 



T 

 G=- (2) 



n 



It has generally been held that during the logarithmic phase all the bacteria 

 are alive and all are actively dividing. Thus, as represented in formula (1), 2 

 bacteria give rise to 4, 4 to 8, 8 to 16, and so on. If this assumption were correct, 

 then all the organisms present during this phase should be viable, and the total 

 count would be identical with the viable count. 



This may be true when, as Kelly and Eahn (1932)' have found, organisms are 

 growing under optimal conditions and are followed for a few generations only. 

 Observations, however, on ordinary broth cultures have shown that the total 

 number of organisms generally exceeds the number of viable organisms, even during 

 the logarithmic phase (Wilson 1922, 1926, Regnier, David, and Kaplan 1932, Buice 

 1933-34, Jordan and Jacobs 1944). 



The most probable explanation of this fact is that during the period of maximum 

 growth some of the organisms that are generated fail to survive. If, for example, 

 80 per cent, of the organisms produced during a given generation continued to live 

 and divide, while 20 per cent, died, then at the end of the logarithmic phase the 

 total number of organisms alive and dead would exceed the number of living. 



