RATE OF GROWTH OF BACTERIA 19 



unexpended in the given universe (or area) of actual and potential 

 resources for the support of growth." 



Growth curves of bacteria are obtained by counting the number 

 of cells in a culture by one or another method, usually plating, at 

 regular time intervals during the growth of a culture. The results 

 may be plotted in various ways. The actual number of cells may 

 be plotted against time, as has been done in Fig. 9. This serves to 

 show the absolute increase or decrease, but not the rate of change, 

 and has the disadvantage that where the numbers are small, at the 

 beginning and end, slight but relatively important changes are not 

 shown. The usual method, illustrated in Fig. 1, is to plot the loga- 

 rithms of the numbers of cells against time. Such a curve shows the 

 proportional increase or decrease in the number of cells, and the slope 

 of the curve is a measure of the rate of change; it possesses the ad- 

 vantage that variations at the beginning and the end, when the 

 numbers are small, are plotted on a scale such that these variations 

 are clearly distinguishable. Since, after the maximum growth period 

 has passed, changes in the rate of increase or decrease occur at an 

 increasingly slower rate, it is sometimes advantageous to plot the 

 logarithms of the numbers of cells against the logarithms of the time 

 intervals. This serves to magnify the scale of the abscissae during 

 the early stages of growth when changes are occurring rapidly. Such 

 a curve cannot be used to measure the rate of growth, but still serves 

 to show clearly the division into phases. It has been necessary to 

 follow this procedure in Fig. 25 and Fig. 33 simply to obtain space 

 for the cells forms and the growth curve on the same graph. 



The rate of growth has also been expressed in terms of generation 

 time, i.e., the time required for the cells to double in number. The 

 mean generation time may be computed for any time interval by 

 dividing the time by the number of generations, and the latter quan- 

 tity may be determined from the cell counts at the beginning and 

 the end of the time interval according to the formula 



log. b — log. a 



n = ; 



log. 2 



where n is the number of generations and a and b are the first and 

 last cell counts, respectively. The mean generation times for the 



