LOGARITHMIC ORDER OF DEATH 27 



The above calculation has been made on the assump- 

 tion that we were dealing- with ''definite" cells, while 

 death of the multicellular organism will result from the 

 destruction of any ''random" cells. The inactivation of 

 n definite cells will take much more time than the inacti- 

 vation of n random cells. The correction factor which 

 changes the formula for definite to that for random 

 cells is 



a! 



(a-n)! n! 



The probability that any n cells out of a total of a cells 

 are inactivated, is then (see p. 21) 



P ' = 



a! 



(a - n) ! n ! 



1- 



\ 100 j _ 



With a— 10 cells, the probability that any one of these 

 10 cells dies is 10 times greater than the probability that 

 a definite cell, e.g., Number 3, dies. The probability of 

 death for any two cells is 



10-9-8-7-6-5-4-3-2-1 



8-7-6-5-4-3-2-lx2-l 



or 45 times as great as for any two definite cells. Table 

 6 gives the number of survivors in the case of definite 

 and of random cells for a survival rate of 90%. 

 Generally speaking, since 



(a-n) !n ! 



is a constant, it cannot alter the shape of the survivor 

 curves or of the mortality curves. The rate is greatly 

 increased, but only by a constant factor; the convex 

 curves remain convex, and the straight lines remain 

 straight. If more than one cell must become inactivated 

 to cause the death of an organism, the order of death is 

 not logarithmic, Avhether these cells are definite ones or 

 not. 



