190 PHYSIOLOGY OF BACTERIA 



of the generation time (Appendix p. 399). Since the 

 generation time means the time required by bacteria 

 to double in number, it is smallest when multiplication 

 is most rapid. This necessitates thinking in reciprocals. 

 The formula is 



Hog 2 



g - 



log 6 — log a 



where a is the number of cells at the start, and 6 the 

 number after the time t. 



A direct method for measuring the growth rate has been 

 suggested by Slator (1916) who, by the application of 

 calculus (see p. 403), derived the following formula for a 

 growth rate constant : 



K = 1^ ^ ~ ^^ ^ = log 6 — log g ^ log 6 — log g 

 t tloge 0.434^ 



Comparing this with the formula for the generation 

 time, we see that the growth rate constant K of Slator 

 is nothing but the reciprocal of the generation time 

 multiplied with a constant factor: 



K = 1 !2S2 _ 0.694 

 ^ log e g 



The disadvantage of the growth rate constant is that 

 it cannot be defined descriptively; it has no easily 

 expressed meaning. It is just a number indicating the 

 relative growth rate. 



For comparison, the following relation between growth 

 rate constants and generation times might be useful: 



The generation time of 15 minutes corresponds io K = 2.776 

 The generation time of 20 minutes corresponds io K = 2.082 

 The generation time of 30 minutes corresponds io K = \. 388 

 The generation time of 60 minutes corresponds io K = Q. 694 

 The generation time of 120 minutes corresponds io K = 0.347 



