in] RAYMOND PEARL 149 



An estimate of the population of the world 

 (After W. F. Willcox) 



Mean rate of 

 1650 1750 1800 1850 1900 increase 



Europe 100 140 187 266 401 0-52 % per annum 



World total 545 728 906 1171 1608 0-49% „ 



Verhulst was before his time, and his work was neglected and 

 presently forgotten. Only some twenty years ago, Raymond Pearl 

 and L. J. Reed of Baltimore, studying the U.S. population as 

 Verhulst had done, approached the subject in the same way, and 

 came to an identical result; then, soon afterwards (about 1924), 

 Raymond Pearl came across Verhulst's papers, and drew attention 

 to what we now speak of as the Verhulst-Pearl law. Pearl and 

 Reed saw, as Verhulst had dope, that a "law of population" which 

 should cover all the ups and downs of human affairs was not to be 

 found; and yet the general form which such a law must take was 

 plain to see. There must be a limit to the population of a region, 

 great or small; and the curve of growth must sooner or later "turn 

 over," approach the limit, and resolve itself into an S-shaped curve. 

 The rate of growth (or annual increment) will depend (1) on the 

 population at the time, and (2) on "the still unutiUsed reserves of 

 population-support existing" in the available land. Here we have, 

 to all intents and purposes, the growth-factor and retardation-factor 

 of Verhulst, and they lead to the same formula, or the same 

 differential equation, as his*. 



A hundred years have passed since Verhulst dealt with the first 

 U.S. census returns, and found them verifying the Malthusian 

 expectation of a doubhng every twenty-five years. That "grande 

 vitesse d'accroissement " continued through five decennia; but it 

 ceased some seventy years ago, and a retarding influence has been 

 manifest through all these seventy years (Fig. 29). It is more 

 recently, only after the census of 1910, that the curve seemed to be 



* Raymond Pearl and L. J. Reed, on the Rate of growth of the population of 

 the U.S. since 1790, and its mathematical representation, Proc. Nat. Acad. Sci. 

 VI, pp. 275-288, 1920; ibid, vin, pp. 365-368, 1922; Metron, m, 1923. In the 

 first edition of Pearl's Medical Biometry and Statistics, 1923 (2nd ed. 1930), Verhulst 

 is not mentioned. See also his Studies in Human Biology, Baltimore, 1924, Natural 

 History of Population, 1939, and other works. 



