648 



THE AMERICAN NATURALIST 



[Vol. XLII 



of mass from the more simple case of respiration we re- 

 turn to the consideration of the totality of metabolic re- 

 actions as exemplified in growth. 



What should we expect to be the ideal course of growth, 

 that is, the increase of the mass of the plant regarded 

 as a complex of reactions catalyzed by protoplasm? Let 

 us consider, first, the simplest possible case, that of a bac- 

 terium growing normally in a rich culture solution. When 

 its mass has increased by anabolism of the food material 

 of the culture medium to a certain amount it divides into 

 two. As all the individuals are alike, counting them would 

 take the place of weighing their mass. The simplest ex- 

 pectation would be that, under uniform conditions, growth 

 and division would succeed each other with monotonous 

 regularity, and so the number or mass of bacteria present 

 would double itself every n minutes. This may be ac- 

 cepted as the ideal condition. 



The following actual experiment may be quoted to show 

 that for a time the ideal rate of growth is maintained, and 

 that at the end of every n minutes there is a doubled 

 amount of protoplasm capable of catalyzing a doubled 

 amount of chemical change and carrying on a doubled 

 growth and development. 



From a culture of Bacillus typhosus in broth at 37° C. 

 five small samples were withdrawn at intervals of an 

 hour, and the number of bacteria per unit volume deter- 

 mined by the usual procedure. The number of organisms 

 per drop increased in the following series: 6.7, 14.4, 

 33.1, 70.1, 161.0. 6 This shows a doubling of the mass 

 of bacteria in every fifty-four minutes and is the case ac- 

 tually represented in the strictly logarithmic curve of 

 Fig. 2. 



We may quote some observations made by E. Buchner 7 

 of the rate at which bacteria increase in culture media. 

 Bacillus coli communis was grown at 37° C. for two to 



T Buchner. Zuwachsgrossen u. Wachsthumsgoschwindigkeiten. Leipzig, 

 1901. 



^ "For this unpublished experiment on bacterial growth I am indebted to 



