LOGARITHMIC ORDER OF DEATH 



39 



The probability that a certain tube (or molecule) has 

 undergone a change at the time t is 



Px= 1 



1--P-V 



100/ 



This formula for the probability of inactivation ap- 

 plies to any one definite enzyme molecule, whether in 

 a separate small test tube or in the original large volume 

 of enzyme solution. The probability that tmo definite 

 molecules, either in the large volume or in the small test 

 tube, be inactivated is the product of the probabilities 

 of each separate event: 



Pa = Pi -Pi = 



1-1 



P 



100 



and the probability that n molecules be inactivated is 



P. = 



P 



100 



As was stated above, p is the percentage of molecules 

 inactivated per minute. The percentage not changed is 

 100 — p = s. If we introduce this into the above equa- 

 tion, we obtain 



R = 



100 



This is the same formula which we encountered on page 

 22. All calculations in Tables 3 and 4, and the curves 

 of Figures 4 and 5 apply to this case ; we merely have to 

 substitute the word ''molecule" for "cell." 



The conclusion is that a logarithmic order of death can 

 be obtained onl}^ if the death of the bacterium is brought 

 about by the reaction of one single molecule. This con- 

 clusion is absolute. The logarithmic order of death is 

 entirely impossible if more than one molecule must be in- 

 activated to produce the death of the cell. As Tables 3 

 and 4 and Figure 4 show, an approximation of the loga- 

 rithmic order is obtained if death is caused by inactiva- 



