November 6, 1908] 



SCIENCE 



631 



tBe dark. For a time the CO, production 

 of these non-growing structures remains 

 uniform, and then it begins to fall off in a 

 logarithmic curve. We interpret both 

 phenomena in the same way: in the 

 initial level phase the respirable ma- 

 terial in the leaf is in excess, and the 

 amount of catalytic protoplasm limits the 

 respiration to the normal biological level; 

 in the second falling phase some supply of 

 material is being exhausted, and we get a 

 logarithmic curve controlled by the law of 

 mass, as much, it would seem, as when 

 cane-sugar is hydrolyzed in aqueous solu- 

 tion. 



After these two illustrations of the ac- 

 tion of the law of mass from the more 

 simple case of respiration we return to the 

 consideration of the totality of metabolic 

 reactions 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 com- 

 plex of reactions catalyzed by protoplasm? 

 Let us consider, first, the simplest possible 

 ease, that of a bacterium 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 expectation 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 typhosiis in 

 broth at 37° C. five small samples were 

 withdrawn at intervals of an hour, and the 

 number of bacteria per unit volume de- 

 termined by the usual procedure. The 

 number of organisms per drop increased 

 in the following series: 6.7, 14.4, 33.1, 

 70.1, 161.0.3 This shows a doubling of the 

 mass of bacteria in every fifty-four min- 

 utes and actually represents a strictly 

 logarithmic curve. 



We may quote some observations made 

 by E. Buchner* of the rate at which bac- 

 teria increase in culture media. Bacillus 

 coli communis was grown at 37° C. for 

 two to five hours, and by comparison of 

 the initial and final numbers of bacteria 

 the time required for doubling the mass 

 was calculated. Out of twenty-seven 

 similar experiments a few were erratic, 

 but in twenty cases the time for doubling 

 was between 19.4 and 24.8 minutes, giving 

 a mean of 22 minutes. This produces an 

 increase from 170 to 288,000 in four hours. 

 No possible culture medium will provide 

 for prolonged multiplication of bacteria at 

 these rates. 



Cohn'^ states that if division takes place 

 every sixteen minutes, then in twenty-four 

 hours a single bacterium 1 fi. long will be 

 represented by a multitude so large that it 

 requires twenty-eight figures to express it, 

 and placed end to end they would stretch 

 so far that a ray of light to travel from 

 one end to the other would take 100,000 

 years. The potentialities of protoplasmic 

 catalysis are thus made clear, but the ac- 

 tualities are speedily cut short by limiting 

 factors. 



' For this unpublished experiment on bacterial 

 growth I am indebted to Miss Lane-Claypon, of 

 the Lister Institute of Preventive Medicine. 



* Buehner, Zuwachsgrossen u. Wachsthumsge- 

 sohmndigkeiten, Leipzig, 1901. 



" Cohn, Die Pflanze, Breslau, 1882, p. 438. 



