72 THE RISE AND FALL OF BACTERIAL POPULATIONS 



5. THE PHASE OF DECREASE 



From the earliest days of bacteriology it has been noted that the decrease in bac- 

 terial numbers under the influence of an unfavorable environment (such as is present 

 for one reason or another on the descending side of the curve of the population cycle) 

 followed a gradual and more or less orderly course. This was at first attributed to a 

 process of natural selection, the surviving organisms being assumed to be of a specifi- 

 cally more resistant character. With the work of Koch (1881), Paul and Kronig (1896), 

 Kronig and Paul (1897), Ikeda (1897), Madsen and Nyman (1907), and Chick (1908, 

 1 9 10) on the action of chemical disinfectants the mortality curve was given a new in- 

 terpretation as an expression of a more fundamental chemical phenomenon. As sum- 

 marized by Phelps (191 1), these researches have shown that "the rate of dying, 

 whether under the influence of heat, cold or chemical poison, is unfailingly found to 

 follow the logarithmic curve of the velocity law, if the temperature be constant." 



The general slope of the mortality curve during the period of rapid decline is 

 therefore the same as that of the curve for the increase of a bacterial population dur- 

 ing its period of rapid multiplication. In the phase of increase the logarithm of the 

 number of new cells formed from a single initial cell in a given time is proportional to 

 the lapse of time ; in the phase of decrease the logarithm of the proportion of the cells 

 present which perish in a given interval is proportional to the length of that interval. 

 In other words, increase and decrease alike bear a direct relation to the number of 

 cells present at the beginning of a unit period and a logarithmic relation to any time 

 period of greater duration. 



The formula for the rate of decrease is, therefore, in the form used by Chick (1908), 

 as follows: 



t2-h "= n 



where /i is the initial and (2 the final time and n^ and «. the corresponding numbers of 

 bacteria present. Phelps, taking the elapsed time (as /) instead of the initial and final 

 time readings (/j — ^i) and B as the initial and b the final number of bacteria, expresses 

 the formula as: 



log J = Kt 



which is of course the formula for a monomolecular reaction.^ 



The results presented by Chick (1908) in regard to the regularity of the process of 

 disinfection were very striking and seemed to justify her conclusion that "a very com- 

 plete analogy exists between a chemical reaction and the process of disinfection, one 

 reagent being represented by the disinfectant, and the second by the protoplasm of 



' This formula is written by Falk and Winslow, 



o.434/v.= i// log —-^ 



where a = 7i, of Chick and a—x = niOi Chick because A'i= i/l \ogc ^^ and K=\/t log,o — - when 



