1910-11.] The Rate of Multiplication of Micro-organisms. 655 
*}?fUb = ab lay a method of estimating nutritive values and possibly even 
(JiC 
of determining whether a particular substance acted as a food or as a mere 
accelerator. But it is at this point that the simplifying assumption breaks 
down, for obviously an extreme degree of concentration of food-stuff can- 
not cause an infinite rate of multiplication. The simplifying assumption 
ascribes to the organism the business of obtaining its food ; it presupposes 
a lightning rapidity of assimilation after it has come in touch with its food, 
and a lightning rate of multiplication after sufficient nutriment has been 
assimilated. These conceptions are impossible, and it is only where the 
period of a generation is large in comparison with the times required for 
assimilation and division that the simplifying assumption holds good. We 
have, in fact, applied molecular physics to molar vital phenomena, and we 
meet with necessary limitations. 
The rate of growth ( ab ) may, however, be applied to a comparison of 
bacteria as to their multiplying properties ; and it may also be most 
advantageously employed in the comparative investigation of fluid media 
(bouillon, sugar, etc.) with a view to their standardisation and improvement. 
The period of a generation can be deduced as follows : — One generation 
corresponds to a multiplication of the original number by 2 ; or to an 
addition of 0301 to its logarithm to base 10. But ab is the rate of 
change of log 10 y 0 , or change per unit time. Hence = number of 
generations per unit time. In curves 3, 4, 5, ab = 0*812, and unit time is 
one hour ; consequently the period of a generation is 22*27 minutes. 
Conclusions. 
1. The rate of multiplication of fast-growing micro-organisms is pro- 
portional to the number of organisms, and to the concentration of food- 
stuff*. 
2. The initial rate of multiplication affords a factor of comparison both 
of efficiency for media and of reproductive properties of organisms. 
3. Vaccines may be prepared in large quantities on the basis that 
a maximum number of organisms is attained to, this maximum being 
dependent on the concentration of nutriment, and independent of the 
amount of culture inoculated. 
{Issued separately October 24, 1911.) 
