72 GEOMETRICAL RATIO OF INCREASE. Chap. III. 



become so inordinately great that no country could support the 

 product. Hence, as more individuals are produced than can 

 possibly survive, there must in every case be a struggle for 

 existence, cither one individual with another of the same spe- 

 cies, or -with the individuals of distinct species, or with the phys- 

 ical conditions of life. It is the doctrine of Malthus applied 

 with manifold force to the whole animal and vegetable king- 

 doms ; for in this case there can be no artificial increase of 

 food, and no prudential restraint for marriage. Although some 

 species may be now increasing, more or less rapidly, in num- 

 bers, all cannot do so, for the world would not hold them. 



There is no exception to the rule that every organic being 

 naturally increases at so high a rate, that, if not destroyed, the 

 earth would soon be covered by the progeny of a single pair. 

 Even slow-breeding man has doubled in twenty-five years, and 

 at this rate, in a few thousand years, there would literally not 

 be standing-room for his progeny. Linnasus has calculated 

 that if an annual plant produced only two seeds — and there is 

 no plant nearly so unproductive as this — and their seedlings 

 next year produced two, and so on, then in twenty years thei'C 

 would be a million plants. The elephant is reckoned the 

 slowest breeder of all known animals, and I have taken some 

 pains to estimate its probable minimum rate of natural increase: 

 it will be safest to assume that it begins breeding when thirty 

 years old, and go'es on breeding till ninety years old, bringing 

 forth six young in the interval, and surviving till one hundred 

 years old ; if this be so, after a period of from seven hundred 

 and forty to seven hundi'ed and fifty years, there would be alive 

 nearly nineteen million elephants descended from the first pair. 



But we have better evidence on this subject than mere 

 theoretical calculations, namely, the numerous recorded cases 

 of the astonishingly ra\nd increase of various animals in a state 

 of nature, "when circumstances have been favorable to them 

 during two or three following seasons. Still more striking is 

 the evidence from our domestic animals of many kinds which 

 liave run wild in several parts of the world : if the statements 

 of the rate of increase of slow-breeding cattle and horses in 

 South America, and latterly in Australia, had not been well 

 authenticated, they Avould have been incredible. So it is with 

 plants : cases could be given of introduced plants which have 

 b(>come common throughout whole islands in a period of less 

 than ten years. Several of the plants, such as the caitloon, 

 and a tall thistle, now most numerous over the wide plains of 



