108 THE RATE OF GROWTH ' [ch. 



twenty the women begin to outnumber the men, and at eighty-five 

 there are twice as many women as men left in the world*. 



Men have pondered over the likeness and the unhkeness between 

 the short lifetimes and the long; and some take it to be fallacious 

 to measure all alike by the common timepiece of the sun. Life, 

 they say, has a varying time-scale of its own ; and by this modulus 

 the sparrow hves as long as the eagle and the day-fly as the manf. 

 The time-scale of the living has in each case so strange a property 

 of logarithmic decrement that our days and years are long in 

 childhood, but an old man's minutes hasten to their end. 



On pre-natal and post-natal growth 



The rates of growth which we have so far studied are based on 

 annual increments, or "first differences" between yearly determina- 

 tions of magnitude. The first increment indicates the mean rate of 

 growth during the first year of the infant's life, or (on a further 

 assumption) the mean rate at the mean epoch of six months old; 

 there is a gap between that epoch and the epoch of birth, of which 

 we have learned nothing; we do not yet know whether the very 

 high rate shewn within the first year goes on rising, or tends to fall, 

 as the date of birth is approached. We are accustomed to inter- 

 polate freely, and on the whole safely, between known points on 

 a curve: "si timide que Ton soit, il faut bien que Ton interpole," 

 says Henri Poincare; but it is much less safe and seldom justifiable 

 (at least until we understand the physical principle involved and 

 its mathematical expression) to "extrapolate" beyond the limits of 

 our observations. 



We must look for more detailed observations, and we may learn 

 much to begin with from certain old tables of Russow's J, who gives 



* Cf. F. E. A. Crew's Presidential Address to Section D of the British Association, 

 1937. 



+ Cf. Gaston Backman, Die organische Zeit, Lunds Universitets Arsskrift, xxxv, 

 Nr. 7, 1939. 



J Quoted in Vierordt's Anatomische . . . Daten und Tabellen, 1906, p. 13. See 

 also, among many others, Camerer's data, in Pfaundler and Schlossman's Hdb. d. 

 Kinderheilkunde, i, pp. 49, 424, 1908; Variot, op. cit.; for pre-natal growth, R. E. 

 Scammon and L. A. Calkins, Growth in the Foetal Period, Minneapolis, 1929. Also, 

 on this and many other matters, E. Faure-Fremiet, La cinetique du developpement, 

 Paris, 1925; and, not least, J. Needham, Chemical EinJbryology, 1931. 



