THE EEGULATION OF NUMBEES 291 



15. The discussion of historical races has been brief and was only 

 entered upon in order to round off the subject. There are other 

 points in connexion with the adjustment of numbers to which 

 allusion must be made. It will be convenient, however, first to 

 review shortly our conclusions regarding the problem of adjust- 

 ment as a whole and then to ask in respect of the various periods 

 in turn what we are led to think that the position must have been. 



Eeasons have been given for thinking that, if any general change 

 in fecundity has taken place in the course of history, it has been 

 in the direction of increase. In any case fecundity is very large — 

 the theoretical power of increase, that is to say, is very great. 

 Some figures were given at the end of the fourth chapter in 

 illustration of this fact. There is a tendency noticeable in nearly 

 all discussions of questions of quantity to under-estimate the 

 power of increase. Another calculation previously given may 

 therefore be recalled. It has been shown that at the present 

 average rate of increase of the population of the world — a rate of 

 increase which is obviously everywhere very severely restricted — 

 a single pair would produce in 1,750 years descendants equal in 

 number to the present population of the world. 



In connexion with the under-estimation of the power of increase, 

 is the over-estimation of the relief given by any factor which 

 allows of a growth of population — increase in skill or migration, 

 for example. It is constantly assumed that, when such a factor 

 can be detected in operation, there is, so to speak, a complete 

 outlet for fecundity. This is the idea which lies at the basis of 

 such statements as those which speak of ' surplus population ' 

 as being drawn off by migration. When, however, a calculation 

 is made, it is seen that the relief given is, except under very 

 unusual circumstances, almost negligible. It was shown on 

 p. 105 that under the circumstances mentioned a population of 

 1,000,000 would remain stable so long as to each married woman 

 there was born an average of two children. But if the average 

 was 2| children, then in a hundred years the population would 

 be 3,050,000. It follows, therefore, that most unusually favourable 

 circumstances only make room for a fraction of the possible 

 increase and that migration likewise only draws off an insignificant 

 fraction of the possible additions to the population. 



Startirig with such considerations and taking into account 

 the fact that, wherever social co-operation exists, there must 



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