80 CHEMICAL ENVIRONMENT 



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, Ijx in diameter, 



its volume =0.0000000000005 c.c. 



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 2 or 

 3 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 diWsions 

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



1 plane division S = 2"a 



2 " " S = 2="a 



3 " " S = 2»"a 



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

 organism attains full size, as was assumed in the first calcu- 

 lation, the "mass as large as the earth" would be attained 

 in about 32 hours and 22 hours respectively. 



This extraordinary rate of increase explains m large 

 measure why bacteria are able to bring about such great 

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

 "spoiling" of food materials, especially liquids. The reac- 

 tions brought about by bacteria on substances which are 

 soluble and diffusible are essentially "surface reactions." 



