54 LOGARITHMIC ORDER OF DEATH 



V. BIOLOGICAL CONSEQUENCES OF THE LOGARITHMIC 

 ORDER OF DEATH 



Importance of the Number of I n - 

 dividuals. Let us consider again the case discussed 

 on page 16 of a million bacteria per cubic centimeter 

 dying at the rate of 90% per minute. The survivors at 9 

 consecutive minutes will be : 



100,000 10,000 1,000 100 10 1 0.1 0.01 0.001 



(This last number means that there is one bacterium left 

 alive in 1,000 c.c. If the bacterial suspension were dis- 

 tributed in ampules of 10 c.c. each, one ampule out of a 

 hundred would still contain one living bacterium.) If 

 instead of a million, we had only 1,000 bacteria per c.c. 

 at the outset, the same degree of sterilization would 

 have been reached in 6 minutes instead of in 9. The expo- 

 sure time for sterilization thus depends upon the amount 

 of contamination. It is a logarithmic function of the 

 number of cells present. If we have two suspensions 

 of the same bacterium, one with a cells and the other 

 with ma, and if the death times required to reach the 

 same degree of sterilization in the two cases are, respec- 

 tively, ti and to, we have the equations 



Kt, = log ^ 



Kt2 = log 



a-x 

 ma 



ma-y 



X and y being the number of bacteria dead at the times, 

 t, and to, respectively. The same degree of sterilization is 

 reached when a-x=m-y. Subtracting the second equation 

 from the first we obtain : 



K(t2-t,)=logm 

 This means that if one inoculum is m times as large as 

 the other, the increase in death time (to-ti) is propor- 

 tional to log m, and inversely proportional to the rate 

 of death. 



