LOOARITHMIG PHASE 



89 



The increase in the living organisms would still occur by geometrical progression, 

 and the resultant curve of plotting the logarithms against time would still fall 

 on a straight line ; the only difference would be that instead of the number of 

 organisms being doubled in each generation, their factor of increase, or generation 

 index, would be 1-6. 



Thus in Table 2 it is supposed that only 50 per cent, of the organisms inoculated 



V 



are viable. The ratio of viable to total organisms, i.e — , increases with each 



generation. After about ten generations, it rapidly approaches the value f — \, 

 where ]) = the generation index. The value of p can therefore be obtained with 

 fair accuracy towards the end of the logarithmic phase by simply calculating the 

 viable : total ratio and adding 1. In the example quoted it is approximately 1-6, 



TABLE 2 



Calculations of Viable and Total Organisms with a 20 per cent. Death-bate peb 



Genebation 



If the viable and total counts are known both at the start and at the end of 

 regenerations, then p can be ascertained at any time during the logarithmic phase, 

 since 



T. -T, 



= ^-1 



(3) 



V = m F;r+ 1 



(4)1 



T, - To 



where Vq and Tq = number of viable and total organisms respectively at the 

 start, and V^. and T^. = number of viable and total organisms respectively at the 

 end of X generations. 



Experiments on the growth of Salm. typhi-murium in broth have shown that 

 the average ratio of viable to total organisms at the end of the logarithmic phase 

 is about 0-8. This corresponds to a death-rate of about 10 per cent, per generation, 

 and to a generation index of 1-8. Hence in calculating the generation time, formula 

 (1) has to be changed to 



^ ^ l og 6 - log g 

 log 1-8 

 Employing this formula, the number of generations is greater than by the old 

 formula, and the generation time necessarily shorter. 



It must be understood that the factor of increase to be used in the formula 

 may vary with each experiment, and can only be ascertained by the performance 

 of a total and a viable count on each culture. 



* For this formula we are very much indebted to Dr. H. G. W. Hoare. 



