5° 



GROWTH CURVES OF BACTERIA 



If the numbers of cells present at any two times during the period of logarithmic 

 growth are determined, the values of n and g may be readily derived. Nomograms for 

 such determination have been developed by the writer/ If the numbers of bacteria 

 are plotted against time a curve will be developed whose equation is (3) (see Fig. 5). 



Equation (5) may also be written 

 in the form, 



log&=— ^+Iog5 



(6) 



This indicates that if the logarithms 

 of the numbers of bacteria are plotted 

 against time a straight line will be 



developed, with slope 



log 



and with 



Time 



Fig. 5. — A. Growth curve during logarithmic 

 growth phase. B. Plot of logarithms of numbers of 

 bacteria against time. 



the intercept on the y-axis at log B 

 (Fig. 5). This is a convenient criterion 

 for determining whether or not a cul- 

 ture is in the logarithmic phase. 



For some purposes it is advisable 

 to determine the rate of growth per 

 cell. If the cells are increasing regu- 

 larly in geometrical progression, the 

 rate of increase in the number of cells 



-,- ) is constantly proportional to the 

 at J 



number of cells, i.e., 

 db 



dt 



= kb 



(7) 



in which k is the proportionality constant termed the "velocity coefficient" of the rate 

 of growth. Since 



db 



k=dt 



b 



the velocity coefficient is the rate of growth per cell. Integration of (7) gives the rela- 

 tionship 



In Z) = ^/+ Constant of integration 



When i = o, the constant of integration is equal to l)i B, and 



In b = kl+ln B 



1, h ^ 



(8) 

 (9) 



' Buchanan, R. E.: Iowa Stale College J . Sc, i, 63. 1926. 



