GEOMETRICAL RATIO OF mCRBA8E. 61 



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 circumstances have been favor- 

 able 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 ex- 

 clusion of every other plant, have been introduced from 

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

 I hear from Di\ Falconer, from (Jape Comorin to the 

 Himalaya, which have been inported from America since 

 its discovery. In such cases, and endless others, could be 

 given, no one supposes, that the fertility of the animals or 

 plants has been suddenly and temporarily increased in any 

 sensible degree. The obvious explanation is that the con- 

 ditions of life have been highly favorable, and that there 

 has consequently been less destruction of the old and 

 young and that nearly all the young have been enabled to 

 breed. Their geometrical ratio of increase, the result of 

 which never fails to be surprising, simply explains their 

 extraordinarily and rapid increase and wide diffusion in their 

 new homes. 



In a state of nature almost every full-grown plant an- 

 nually produces seed, and among animals there are very 

 few which do not annually jiair. Hence we may confi- 

 dently assert that all plants and animals are tending to in- 

 crease at a geometrical ratio — .that all would rapidly stock 

 every station in which they could anyhow exist — and that 

 this geometrical tendency to increase must be checked by 

 destruction at some period of life. Our familiarity with 

 the larger domestic animals tends, I think, to mislead us; 



