332 CIVIC BIOLOGY 



and in many other ways. Fig. 163 expresses this relation to 

 the eye, showing how quickly the world may be covered or 

 any limit be reached, whether of space or food supply, by the 

 geometrical increase of a living species. 



Each species has its own formula or equation of increase, 

 its terms depending on the number of eggs, seeds, or offspring 

 and the length of life of a generation. Every species that 

 we need to control or exterminate, or which we wish to save 

 or increase, finds expression for its power of good or evil in 

 this law of increase. The mythical labors of Sisyphus typify 

 humanity struggling with these problems. He was condemned 

 to be eternally rolling a heavy stone up a mountain, the stone 

 slipping and rolling down again when he had almost reached 

 the top. Flies, rats, mosquitoes, or some other plague, become 

 unendurable, and the community tries to rid itself of them. 

 It rolls the stone almost to the top of the mountain. A little 

 more effort, and extermination would be complete, the stone 

 would be rolled over the summit and disappear; but those 

 who do not know this law say, " Never mind these few, 

 they can't do much harm." In a short time the work is all 

 to do over again. So effective control or conservation can- 

 not be developed until we have clear ideas of these equations 

 of increase. 



Work out formulas of increase for all sorts of types, good or bad, and 

 develop clearly their significance in solving local problems. 



The native American oyster-shell scale produces one generation (about 

 50 eggs) a year. Its equation of yearly increase is 2 (a pair) = 50. 



The Chinese (or San Jose") scale brings forth about 500 living young 

 in a period of 45 days, having four or five generations a season. Its 

 equation of increase for a year is 2 = 3,216,080,400. What bearing has 

 this upon thorough spraying of trees ? The native insect rarely injures 

 a tree perceptibly. The imported scale threatens to exterminate many 

 species of trees from the continent. 



The bobwhite has been known to produce 100 eggs in a season. 

 Suppose each pair rears 10 young a year ; how long would it take, if 



