76 MECHANISM OF DISINFECTION AND HEMOLYSIS 



where ^ is a constant. The latter equation is that of the monomo- 

 lecular reaction isotherm; but it gives a curve having unlimited range, 

 a condition which makes it undesirable in the case of a limited popu- 

 lation; it is better to use a curve of very similar appearance which 

 results if we put .Ti =0 in equation (1) above. We thus introduce the 

 necessary factor of limited range given by X2. The equation, so modi- 

 fied, becomes 



, . ,. (1 - i)' 



kx„ 



X 



while if — is made indefinitely great (i.e. if we consider only the first 



X2 



part of a curve with infinite range) it approaches an equation identical 

 with (2) above. 



Reichenbach has shown that if we imagine a constant fraction of the 

 bacteria of each generation to lose their power to divide, and sup- 

 pose that at each successive division there occurs a decrease in the 

 resistance of the dividing organisms, the individuals with the highest 

 resistance, i.e. those of the first generation, which have not since 

 undergone division, will be present in the smallest numbers, and that 

 those of succeeding generations (and which have therefore less resist- 

 ance), will be present in numbers increasing in geometrical proportion. 

 Under certain conditions such a culture would have nearly the type of 

 variation curve necessary to give the " monomolecular" curve of 

 killing; and Reichenbach finds in individual variation a complete 

 explanation of the observed curves of disinfection. This hypothesis 

 is not, however, applicable to the process of hemolysis, and can there- 

 fore have no general significance. The agreement of the middle 

 portion of hemolytic and other similar time curves with the monomo- 

 lecular reaction curve is probably only a coincidence, and is not of 

 fundamental significance. 



Yule^^ has shown that it is possible, theoretically at least, to account 

 for a time curve of hemolysis such as that which I have observed, 

 which, rather than a monomolecular curve, is probably characteristic 

 of the other processes here discussed, even if all the cells are assumed 

 to be equally resistant. This involves the assumption that a certain 

 small number, r, of independent changes suffices to cause lysis. Prob- 

 ably in the case of hemolysis r would not greatly exceed 2. If ;- = 1, 



i« Yule, G. U., /. Roy. Statist. Soc, 1910, Ixxiii, 26. 



