156 THE RATE OF GROWTH [ch. 



An analogous S-shaped curve, given by the formula L^ = kg^, 

 was introduced by Benjamin Gompertz in 1825* ; it is well known to 

 actuaries, and has been used as a curve of growth by several writers 

 in preference to the logistic curve. It was devised, and well devised, 

 to express a "law of human mortality", and to signify the number 

 surviving at any given age (x), "if the average exhaustions of a 

 man's power to avoid death were such that at the end of infinitely 

 small intervals of time he lost equal portions (i.e. equal proportions) 

 of his remaining power 'to oppose destruction." The principle 

 involved is very important. Death comes by two roads. One is 

 by cha^ce or accident, the other by a steady deterioration, or 

 exhaustion, or growing inability to withstand destruction; and 

 exhaustion comes (roughly speaking) as by the repeated strokes of 

 an air-pump, for the life-tables shew mortality increasing in geo- 

 metrical progression, at least to a first approximation and over 

 considerable periods of years. Gompertz relied wholly on the 

 experience of "life-contingencies," but the same deterioration of 

 bodily energies is plainly visible as growth itself slows down; for 

 we have seen how growth-rate in infancy is such as is never after- 

 wards attained, and we may speak of growth-energy and its gradual 

 loss or decrement, by an easy but significant alteration of phrase. 

 To deal with the declining growth-rate, as Gompertz did with the 

 falling expectation of life, and so to measure the remaining energy 

 available from time to time, would be a greater thing than to record 

 mere weights and sizes; it raises the problem from mere change of 

 physical magnitudes to an estimation of the falling or fluctuating 

 physiological energies of the bodyf. We have seen how in only 



* Benjamin Gompertz, On the nature of the function expressive of the law of 

 human mortality, Phil. Trans, xxxvi, pp. 513-585, 1825. First suggested for use 

 in growth-problems by Sewall Wright, Journ. Amer. Statist, Soc. xxi, p. 493, 

 1926. See also C. P. Winsor, The Gompertz curve as a growth curve, Proc. Nat. 

 Acad. Sci. XVIII, pp. 1-8, 1932; cf. {int. al.) G. R. Da vies. The growth curve, 

 Journ. Amer. Statist. Soc. xxii, pp. 370-374, 1927; F. W. Weymouth and S. H. 

 Thompson, Age and growth of the Pacific cockle, Bull. Bureau Fisheries, xlvi, 

 pp. 63f3-641, 1930-31 ; also Weymouth, McMillen and Rich, in Journ. Exp. Biol. 

 vni, p. 228, 1931. 



t A bold attempt to treat the question from the physiological side, and on 

 Gompertz's lines, was made only the other day by P. B. Medawar, The growth, 

 growth-energy and ageing of the chicken's heart, Proc. R.S. (B), cxxix, pp. 332- 

 355, 1940. Cf. James Gray, The kinetics of growth, Journ. Exp. Biol, vi, pp. 248- 

 274, 1929. 



