APPENDIX 403 



The generation time is the reciprocal of the growth-rate, and is 

 least when the growth rate is greatest. In order to have a direct 

 measure of the growth rate, Slator (1916) suggested the ''growth- 

 constant." He computed this by starting from the assumption that 

 the growth at any time must be proportional to the number of cells 

 present. This leads to the equation 



db J, 







Upon integration, this changes to 



In b = kt + C 

 For ^ = 0, we have kt = and b = a 



Ina = + C 

 subtracting this equation from the preceding, we ehminate C: 

 \n b — In a = kt 

 I ^n u ^ \ 1 (log ^ — log a) 



k = -anb-lna) = -^ 0.434 



This value of k is called the growth-constant. Its meaning and its 

 relation to the generation time is explained on p. 190. 



The formula for the generation time is accurate only 

 in the exponential branch of the growth curve, i.e., 

 only as long as the rate of growth does not decrease. 

 If this is the case, the formula is based on the false 

 assumption of an exponential increase. Since we are 

 without accurate knowledge of the cause of the decreas- 

 ing growth rate, we cannot very well put it into a 

 correct mathematical equation. The assumption that 

 growth proceeds in a straight line will be more accurate 

 at this stage than the above formulas, be it the one for 

 generation time, or that of Slator. 



