20 MORPHOLOGIC VARIATION 



various intervals of observation may then be plotted against time. 

 Such a curve has the advantage that it expresses more clearly than 

 the others changes in the rate of growth; it has the serious disad- 

 vantage that it tends to magnify small experimental errors in count- 

 ing, so that most data must be iirst smoothed by some method before 

 they can be used in this way. 



Mathematical analyses of the growth curves of bacteria have 

 been made by McKendrick and Pai, Ledingham and Penfold, Slator 

 (1917), and Buchanan; of yeasts by Slator (1913, 1918, 1919), and 

 by Carlson; of growth curves in general by Pearl and by Robertson; 

 and various empirical formulae have been derived to express these 

 curves. Where these are not interpreted in terms of organisms, sub- 

 strate, products of metabolism or other definite factors, they do not 

 seem to be very helpful to an understanding of the phenomena to 

 one who is not mathematically minded. 



For purposes of description and analysis it has been generally 

 found convenient to divide the growth curve of bacteria into phases. 

 This is in a sense unfortunate in that it makes what is essentially a 

 continuous process appear somewhat discontinuous, but is almost 

 necessary for intelligent discussion. Lane-Claypon described four 

 phases, an initial lag period during which the number of cells re- 

 mains constant or very slowly increases, a period of maximum growth, 

 a stationary or resting period, and a period of death. This phasing 

 has been followed by most succeeding authors, but Buchanan further 

 subdivided these phases, making seven in all, illustrated in Fig. 1, 

 which is taken from his paper. They are the initial stationary phase, 

 from the origin to a, during which the number of cells shows no 

 increase (it may actually decrease, according to Chesney) ; the lag 

 phase, or period of positive acceleration in growth rate, a-b; the 

 logarithmic growth phase when the rate of growth is constant and 

 maximum, the logarithms of the number of cells falling on a straight 

 line, b-c; the phase of negative acceleration, c-d] the maximum sta- 

 tionary phase, d-e\ the phase of accelerated death, e-j ; and the 

 logarithmic death phase, during which the cells are dying at a 

 constant rate, and the logarithms of the number of cells again fall 

 on a straight line, f-g. A final phase of negative acceleration in death 

 rate might have been added, for in many cases at least the death 



