144 THE RATE OF GROWTH [ch. 



common thing, and, apart from the free growth of a population or 

 an organism, we find it in many biological phenomena. An epidemic 

 dechnes, or tends to decline, at a rate corresponding to a geometrical 

 progression; the mortahty from zymotic diseases declines in geo- 

 metrical progression among children from one to ten years old; 

 and the chances of death increase in geometrical progression after 

 a certain time of Hfe for us all*. 



But in the ascending scale, the story of the horseshoe nails tells 

 us how formidable a thing successive multipHcation becomes f. 

 Enghsh law forbids the protracted accumulation of compound 

 interest; and hkewise Nature deals after her own fashion with the case, 

 and provides her automatic remedies. A fungus is growing on an 

 oaktree — it sheds more spores in a night than the tree drops acorns 

 in a hundred years. A certain bacillus grows up and multiphes by 

 two in two hoTlrs' time; its descendants, did they all survive, would 

 number four thousand in a day, as a man's might in three hundred 

 years. A codfish lays a million eggs and more — all in order that 

 one pair may survive to take their parents' places in the world. 

 On the other hand, the humming-birds lay only two eggs, the auks 

 and guillemots only one; yet the former are multitudinous in their 

 haunts, and some say that the Arctic auks and auklets outnumber 

 all other birds in the world. Linnaeus { shewed that an annual 

 plant would have a miUion offspring in twenty years, if only two 

 seeds grew up to maturity in a year. 



But multiply as they will, these vast populations have their 

 limits. They reach the end of their tether, the pace slows down, and 

 at last they increase no more. Their world is fully peopled, whether 

 it be an island with its swarms of humming-birds, a test-tube with 

 its myriads of yeast-cells, or a continent with its miUions of mankind. 

 Growth, whether of a population or an individual, draws to its 

 natural end; and Quetelet compares it, by a bold metaphor, to the 

 motion of a body in a resistant medium. A typical population 

 grows slowly from an asymptotic minimum; it multiphes quickly; 



* According to the Law of Gompertz ; cf. John Brownlee, in Proc. R.S.E. xxxi, 

 pp. 627-634, 1"911. 



t Herbert Spencer, A theory of population deduced from the general law of 

 animal fertility, Westminster Review, April 1852. 



X In his essay De Tellure, 1740. 



