94 C.B.VANNIEL 



results becomes superfluous ; every experiment automatically yields data 

 in which individual variations are represented. This will be obvious if it 

 be realized that with bacterial cultures populations of about lo® organ- 

 isms per ml. are the rule, and that even for pure cultures of protozoa 

 numbers up to lo*^ per ml. are far from rare. 



That not all individuals in a culture behave in an identical manner, 

 and that the results obtained really express statistical averages, follow 

 from the fact that growth curves of microorganisms are always smooth 

 even if cultures are started with a single individual, where one might 

 expect a discontinuity such as was first observed by Ellis and Delbruck 

 (4) in their studies on bacteriophage multiplication. More direct evi- 

 dence for the existence of variation among individuals in bacterial cul- 

 tures can be found in the investigations of Vaas (5) and Doudoroff (6). 



In spite of these advantages, the kinetic approach has not yet been 

 used very effectively or extensively. It is probable that this must chiefly 

 be ascribed to the unwieldy and laborious methodology that used to be 

 necessary for the determination of a growth curve, requiring either 

 many sets of culture plates, or the actual counting under the microscope 

 of thousands of cells for each point on the curve. The newer method- 

 ology of determining population densities by turbidity measurements 

 with the aid of photoelectric apparatus, though not always entirely free 

 from objections, may well bring about a renewed interest in this line of 

 work, as is foreshadowed by the important studies of Monod (7) during 

 the last few years. 



Kinetic investigations on cultures of microorganisms are eminently 

 suited for establishing relations between growth and environmental 

 factors, especially the nature and amount of nutrients. Based upon the 

 concept developed by Liebig about a century ago, it could be anticipated 

 that in microbial cultures growth would be limited by those ingredi- 

 ents which are present in "minimum" quantity. Experiments such as 

 those of Meyer (8) on the growth of Aspergillus niger in media with 

 graded concentrations of phosphate and ammonium sulfate have gone 

 far towards establishing the validity of Liebig's "law of the minimum" 

 for microorganisms. But these were not, strictly speaking, kinetic 

 studies ; the measurements dealt with total crops as dependent upon 

 nutrient concentrations rather than with rates of growth. Furthermore, 

 these researches were carried out at a time when little was known con- 

 cerning the exact mineral requirements of the organism used, which 

 makes the interpretation of the results somewhat difficult. 



Decidedly more conclusive in this respect have been the recent studies 



