28 LOGARITHMIC ORDER OF DEATH 



III. THE CAUSE OF THE LOGARITHMIC ORDER OF DEATH 



T h e D e a t h r a t e Co n s t a n t . The outstanding 

 feature of the death of bacteria is the constancy of the 

 deathrate. "Constant deathrate" means that the num- 

 ber of bacteria which die per time unit is a constant per- 

 centage of the number of living cells at the beginning of 

 this time unit. (One may notice that the number of bac- 

 teria dying in each of the successive time units decreases 

 continuously when the percentage in question remains 

 constant.) The constancy of the death rate leads to the 

 geometrical progression mentioned above (p. 16) for the 

 successive number of survivors : 



^ ''Tor ""Kiw) \~im~) '" ^\ 100 



where a is the initial number and s the percentage of 

 survivors. After t time units, the number of survivors is 



b =a 



\ 100 / 



or 



t log-^^^ = log b- log a 



In this equation, s is constant, and therefore log s/100 

 may be called Ci; a is also constant, and log a may be 

 called C2 ; ?> is variable and is a function of the exposure 

 time t. Thus, we have 



logb = Cit + C2 



which means that the logarithms of the numbers of 

 survivors plotted against the time of exposure lie on a 

 straight line. 



