118 OF THE RATE OF GROWTH [ch. 



character in every cross between a bantam and a larger breed. 

 The bantam is not produced by selecting smaller and smaller 

 specimens of a larger breed, as an older school might have supposed ; 

 but always by first crossing with bantam blood, so introducing the 

 "character" of smallness or retarded growth, and then segregating 

 the desired types among the dwarfish offspring. In fact. Darwinian 

 selection plays a small and unimportant part in the process*. 



From the whole of the foregoing discussion we see that rate of 

 growth is a specific phenomenon, deep-seated in the nature of the 

 organism; wolf and dog, horse and ass, nay man and woman, grow 

 at different rates under the same circumstances, and pass at different 

 epochs through like phases of development. Much the same might 

 be said of mental or intellectual growth ; the girl's mind is more 

 precocious than the boy's, and its development is sooner arrested 

 than the man's f. 



On variability, and on the curve of frequency or of error 



The magnitudes which we are dealing with in .this chapter — 

 heights and weights and rates of change — are (with few exceptions) 

 mean values derived from a large number of individual cases. We 

 deal with what (to borrow a word from atomic physics) we may 

 call an ensemble; we employ the equaUsing powei^ of averages, 

 invoke the "law of large numbers J," and claim to obtain results 

 thereby which are more trustworthy than observation itself §. But 

 in ascertaining a mean value we must also take account of the 

 amount of variability, or departure from the mean, among the cases 

 from which the mean value is derived. This leads on far beyond 

 our scope, but we must spare it a passing word ; it was this identical 

 phenomenon, in the case of Man, which suggested to Quetelet the 



* Cf. Raymond Pearl, The selection problem, Amer. Naturalist, 1917, p. 82; 

 R. C. Punnett and P. G. Bailey, Journ. of Genetics, iv, pp. 23-39, 1914. 



t Cf. E. Devaux, L'p,llure du developpement dans les deux sexes, Revue gindr. 

 des Sci. 1926, p. 598. 



X S. D. Poisson, following James Bernoulli's Ars Conjectandi (op. posth. 1713), 

 was the discoverer, or inventor, of the law of large numbers. "Les chos^s 

 de toute nature sont soumises a une loi universelle qu'on pent appeler la loi des 

 grands nombres" {Recherches, 1837, pp. 7-12). 



§ See p. 137, footnote. 



