158 THE RATE OF GROWTH [ch. 



fall again, of growth which has its sequel in decay. The growth 

 of a child or of a nation; the history of a railway*, or the speed 

 between stations of a train; the spread of an epidemic]", or the 

 evolutionary survival of a favoured type J — all these things run 

 their course, in its beginning, its middle and its end, after the fashion 

 of the S-shaped curve. That curve represents a certain common 

 pattern among Nature's "mechanisms," and is (as we have said 

 before), a "mecanisme commun aux phenomenes disparates§." 



At the same time — and this is a very interesting part of the story 

 — the S-shaped curve is no other than what Galton called a curve of 

 distribution, that is to say a curve of integration or summation- 

 curve, whose differential is closely akin to the Gaussian curve of 

 error. 



Such, to a first approximation, is our S-shaped population-curve, 

 and such are the many phenomena which, to a first approximation, 

 it helps us to compare. But it is only to a first approximation that 

 we compare the growth of a population with that of an organism, 

 or for that matter of one organism or one pbpulation with another. 

 There are immense differences between a simple and a complex 

 organism, between a primitive and a civihsed population. The 

 yeast-plant gives a growth-curve which we can analyse; but we 

 must fain be content with a qualitative description of the growth 

 of a complex organism in its complex world ||. 



There is a simphcity in a colony of protozoa and a complexity in 

 a warm-blooded animal, a uniformity in a primitive tribe and a 

 heterogeneity in a modern state or town, which affect all their 

 economies and interchanges, all the relations between milieu interne 

 and ex^rne. and all the coefficients in any but the simplest equations of 

 growth which we can ever attempt to frame. Every growth-problem 

 becomes at last a specific one, running its own course for its own 

 reasons. Our curves of growth are all alike — but no two are ever 



* Raymond Pearl, Amer. Nat. lxi, pp. 289-318, 1927. 



t Ronald Ross, Prevention of Malaria (2nd ed.), 1911, p. 679. 



j J. B. S. Haldane, Trans. Camb. Phil. Soc. xxm, pp. 19^1, 1924. 



§ Cf. {int. al.) J. R. Miner's Note on birth-rate and density in a logistic population, 

 Human Biology, iv, p. 119, 1932; and cf. Lotka, ibid, in, p. 458, 1931. 



II Cf. {int. al.) C. E. Briggs, Attempts to analyse growth- curves, Proc. E.S. (B), 

 en, pp. 280-285, 1928. 



