72 CHEMICAL ENVIRONMENT 



varies much with the kind even under good conditions. 

 The most rapid rate so far observed is a division in eighteen 

 minutes. A great many reproduce every half-hour, and this 

 may be taken as a good average rate. If such division 

 could proceed without interruption, a little calculation will 

 show that in about sixty-five hours a mass as large as the 

 earth would be produced. 



Starting with 1 coccus, 1 m in diameter, 



its volume = . 0000000000005 cc. 



Such a rate of increase evidently cannot be kept up long 

 on account of many limiting factors, chief of which is the 

 food supply. 



The foregoing calculation is based on the assumption that 

 the organism divides in one plane only. If it divides in two 

 or three planes the rate is much faster, as is shown by the 

 following formulae which indicate the theoretical rate of 

 division: 



S = number of bacteria after a given number of divisions, 

 a = number at the beginning and n = number of divisions. 



1 plane division S = 2"a 



2 " " S = 22«a 



3 " " S = 23"a 



With two-plane or three-plane division, assuming that 

 each organism attains full size, as was assumed in the first 

 calculation, the "mass as large as the earth" would be 

 attained in about thirty-two and twenty-two hours respec- 

 tively. 



This extraordinary rate of increase explains in large 

 measure why bacteria are able to bring about such great 

 chemical changes in so short a time as is seen in the rapid 



