Ill] POPULATION OF THE UNITED STATES 151 



finding its turning-point, or point of inflection; and only now, since 

 1940, can we say with full confidence that it has done so. 



A hundred years ago the conditions were still relatively' simple, 

 but they are far from simple now. Immigration was only beginning 

 to be an important factor; but immigrants made a quarter of the 

 whole increase of the population of the United States during eighty 

 of these hundred years*. Wars and financial crises have made their 

 mark upon the curve; manners and customs, means and standards 

 of living, have changed prodigiously. But the S-shaped curve 

 makes its appearance through all of these, and the Verhulst-Pearl 

 formula meets the case with surprising accuracy. 



Population of the United States 



I In ten years 



A colony of yeast or of bacteria is a population in its simplest 

 terms, and Verhulst's law was rediscovered in the growth of a 

 bacterial colony some years before Raymond Pearl found it in a 

 population of men, by Colonel M'Kendrick and Dr Kesava Pai, who put 

 their case very simply indeed f. The bacillus grows by geometrical 



* Without counting the children born to those immigrants after landing, and 

 before the next census return. 



t A. G. M'Kendrick and M. K. Pai, The rate of multiplication of micro-organisms : 

 a mathematical study, Proc. R.S.E. xxxi, pp. 649-655, 1911. (The period of 

 generation in B. coli, answering to Malthus's twenty-five years for men, was found 

 to be 22^ minutes.) Cf. also Myer Coplans, Journ. of Pathol, and Bacleriol. xiv, 

 p. 1, 1910 and H. G. Thornton, Ana. of Applied Biology, 1922, p. 265. 



