Ill] VERHULST'S LAW 145 



it draws slowly to an ill-defined and asymptotic maximum. The 

 two ends of the population-curve define, in a general way, the 

 whole curve between; for so beginning and so ending the curve 

 must pass through a point of inflection, it must be an S-shaped 

 curve. It is just such a curve as we have seen imder simple 

 conditions of growth in an individual organism. 



This general and all but obvious trend of a population-curve has 

 been recognised, with more or less precision, by many writers. It 

 is imphcit in Quetelet's own words, as follows: "Quand une 

 population pent se developper hbrement et sans obstacles, elle croit 

 selon une progression geometrique; si le developpement a heu au 

 miheu d'obstacles de toute espece qui tendent a Farreter, et qui 

 agissent d'une maniere uniforme, c'est a dire si I'etat sociale ne 

 change point, la population n'augmente pas d'une maniere indefinie, 

 mais elle tend de plus en plus a devenir stationnaire*.'' P. F. Verhulst, 

 a mathematical colleague of Quetelet's, was interested in the same 

 things, and tried to give a mathematical shape to the same general 

 conclusions; that is to say, he looked for a "fonction retardatrice" 

 which should turn the Malthusian curve of geometrical progression 

 into the S-shaped, or as he called it, the logistic curve, which should 

 thus constitute the true "law of population," and thereby indicate 

 (among other things) the hmit above which the population^ was not 

 likely to grow f . 



Verhulst soon saw that he could only solve his problem in a 

 prehminary and tentative way; ''la hi de la population nous est 

 inconnue, parcequ'on ignore la nature de la fonction qui sert de 

 mesure aux obstacles qui s'opposent a la multiphcation indefini de 

 I'espece humaine." The materials at hand were almost unbeUevably 

 scanty and poor. The French statistics were taken from documents 

 "qui ont ete reconnus entierement fictifs"; in England the growth 



* Physique Sociale, i, p. 27, 1835. But Quetelet's brief account is somewhat 

 ambiguous, and he had in mind a body falling through a resistant medium — which 

 suggests a limiting velocity, or limiting annual increment, rather than a terminal 

 value. See Sir G. Udny Yule, The growth of population, Journ. R. Statist. Soc. 

 Lxxxvm, p. 42, 1925. 



t P. F. Verhulst, Notice sur la loi que la population suit dans son accroissement. 

 Correspondence math. etc. public par M. A. Quetelet, x, pp. 113-121, 1838; Rech. 

 math, sur la loi etc., Nozw. Mem. de VAcad. R. de Bruxelles, xviii, 38 pp., 1845; 

 deuxieme Mem., ihid. xx, 32 pp., 1847. The term logistic curve had already been 

 used by Edward Wright; see antea, p. 135. footnote. 



