CHAP. III.] GEOMETEICAL RATIO OF INCREASE. 47 



season or occasional year, otherwise, on the principle of geometrical 

 increase, its numbers would quickly become so inordinately great 

 that no country could support the product. Hence, as more indi- 

 viduals are produced than can possibly survive, there must in every 

 case be a struggle for existence, either one individual with another 

 of the same species, or with the individuals of distinct species, or 

 with the physical conditions of life. It is the doctrine of Malthus 

 applied with manifold force to the whole animal and vegetable 

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

 food, and no prudential restraint from marriage. Although some 

 species may be now increasing, more or less rapidly, in numbers, 

 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 less than a thousand years, there would literally not 

 be standing-room for his progeny. Linnaeus has calculated that 

 if an annual plant produced only two seeds and there is no plant 

 so unproductive as this and their seedlings next year produced 

 two, and so on, then in twenty years there 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 goes 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 740 to 750 years there would be nearly nineteen 

 million elephants alive, descended from the first pair. 



But we have better evidence on this subject than mere theore- 

 tical calculations, namely, the numerous recorded cases of the 

 astonishingly rapid increase of various animals in a state of nature, 

 when circumstances have been favourable to them during two or 

 three following seasons. Still more striking is the evidence from 

 our domestic animals of many kinds which have 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 would have been 

 incredible. So it is with plants ; cases could be given of intro- 

 duced plants which have become common throughout whole islands 

 in a period of less than ten years. Several of the plants, such as 

 the cardoon and a tall thistle, which are now the commonest over 

 the wide plains of La Plata, clothing square leagues of surface 

 almost to the exclusion of every other plant, have been introduced 

 from Europe ; and there are plants which now range in India, as I 

 hear from Dr. Falconer, from Cape Comorin to the Himalaya, 



