80 GEOMETRICAL EATIO OF IXCEEASE. [Chap. HI 



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 theoretical calculations, namely, the numerous 

 recorded cases of the astonishingly rapid increase of 

 various animals in a state of nature, when circum- 

 stances 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 introduced 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 winch now range in India, as I 

 hear from Dr. Falconer, from Cape Comorin to the 

 Himalaya, which have been imported from America 

 since its discovery. In such cases, and endless others 

 could be given, no one supposes, that the fertility 



