When all of the environmental conditions necessary for the best development of a given bacterium are fulfilled, it will then develop to the limit of its capacity. This development is characterized essentially by its reproduction, which occurs by transverse division. The rate of this division 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, 1µ in diameter, its volume = 0.0000000000005 cc.
| ½ hour | = | 2 | ||
| 1 hour | = | 4 | ||
| 2 hours | = | 16 | ||
| 4 hours | = | 256 | ||
| 5 hours | = | 1024 | = | 103+ |
| 15 hours | = | 1,000,000,000 | = | 109 = 0.5 cc. |
| 35 hours | = | 1021+ | = | 500.0 cu.m. |
| About 65 hours | = | 2 × 1042+ | = | 5 × 1020 cu.m. = a mass as large as the earth. |
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 formulæ, 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 = 2na
2 plane division S = 22na
3 plane division S = 23na
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 respectively.
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 “spoiling” of food materials, especially liquids. The reactions brought about by bacteria on substances which are soluble and diffusible are essentially “surface reactions.” The material diffuses into the cell over its entire surface with little hindrance. The bacteria are usually distributed throughout the medium, so that there is very intimate contact in all parts of the mass which favors rapid chemical action. The following calculation illustrates this:
The volume of a coccus 1µ in diameter is 0.5236 × 10-13 cc.
The surface of a coccus 1µ in diameter is π × 10-8 sq. cm.
It is not uncommon to find in milk on the point of souring 1,000,000,000 bacteria per cc.