THE SIZE OF AMERICAN FAMILIES. 67 



other a species of restricted families with a range from to 3 or 4 

 and a preponderance of 2's and O's. 



In so far as growing incapacity is the cause, it will show itself 

 not by a disturbance of the form of the distribution of the different- 

 sized families, but by a shifting of the whole distribution back toward 

 a lower point, with probably a reduction of its variability or spread. 



If now we turn to the actual facts we shall see that restriction of 

 this type is utterly inadequate to explain them^ while a growing inca- 

 pacity would explain them very well. 



The comparison of what has actually occurred with what would 

 have occurred as a result first of growing restriction and second of 

 decreased fertility may be more conveniently made by the use of graphic 

 representations than by the numbers.' There are thus presented: (A) 

 the changes that would have occurred if the real fertility of this spe- 

 cies of individuals had decreased to a bit less than one half what it 

 was in 1803-1835, the variability being reduced in proportion to the 

 square root of their average; (B) the actual changes in the size of 

 families of college graduates from 1803-1874, and (C) the changes 

 that would have occurred if the reduction in the average size of fam- 

 ilies had been due to an increase in the number of families in which 

 the natural fertility had been restricted to from to 4 children. In 

 the last case I have calculated the result upon the hypotheses that 2 

 would be favored by forty per cent., and 3 by twenty per cent, each, 

 and 1 and 4 by ten per cent. each. But any other distribution of the 

 restrictions would lead just as emphatically to the same general con- 

 clusions. Still more so would a restriction to families of from to 3 

 children. 



This conclusion is that the changes in distribution actually found 

 decade by decade have far more likeness to those that would result 

 from a decrease in fertility, than to those that would result from re- 

 striction. Indeed, the likenesses in the first instance are so close as to 

 force upon us the conviction that the causes are identical. If one for- 

 got the common opinions about the prevalence of restriction and looked 

 directly at the facts he would say: The general fertility sinks from 

 5 to 2-3; the very large families become impossibilities, the range of 

 possibility which was from 12 to — 2 has changed to from 8 to • — 3 or 

 — 4 ; this species, whatever it is, is dying out. The facts are surely suffi- 

 cient to rule out restriction of the type described, but before jumping 

 to the conclusion that the obvious explanation of the statistics by a 

 steady decrease in fertility is the true one we must seek other possible 

 explanations of them. 



Among such explanations that have been suggested to the writer 

 none seems satisfactory. It might be thought that restriction was to 

 3, 4 and 5 in the early decades, to 2, 3 and 4 in 1835-55, and finally 



