LOGARITHMK' ORDER OF DEATH 29 



It is inconvenient to express the rate of dying- as the 

 percentage of survivors or deaths per time unit since the 

 time intervals may vary even within one experiment. It 

 has become customary to compute a constant, the ''death 

 rate constant," which is analogous to the reaction con- 

 stant of chemical reactions. If, at the time t, x bacteria 

 out of a initial bacteria have died, the number of sur- 

 vivors is a-x, and the rate of death is 



= k (a - x) 



which, upon integration, gives 



a-x 



The constancy of k in this formula is frequently used as 

 a criterion for the logarithmic order. But, for the pur- 

 pose of testing the constancy of the k values, it is cus- 

 tomary to use decimal logarithms instead of natural log- 

 arithms as the equation requires. This gives rise to a 

 new constant, which will be designated by K. 



K = 0.434k = A_log initial number 

 t survivors 



Tables 1 and 7 show that K (and therefore k) in- 

 creases with time in the case of multicellular organisms, 

 but is constant or decreases in the case of bacteria. 



The percentages of survivors per time unit can be 

 found from the equation 



K = logJ^ 



log s = 2 - K 



This substitution of decimal for natural logarithms 

 may not be permissible if the constants are to be used 

 for further mathematical calculations. 



