Mathematical Contributions to the Theory of Evolution. 355 



conclusion would then be that, with increased civilisation, absolute 

 size* and variation tend to increase ; while correlation, to judge 

 by the males, is stationary ; to judge by the females, tends to 

 increase. 



It will be found somewhat difficult to reconcile these results with 

 any simple applications of the principle of natural selection. In the 

 first place increased variation undoubtedly suggests a lessening of 

 the struggle for existence, and there can be no question that this 

 increase has gone on among civilised races (see ' Variation in Man 

 and Woman'). The lessening of the struggle has probably been 

 greater for woman than man ; hence the principle of natural selec- 

 tion might help to explain the preponderance of variability in civi- 

 lised woman. The increase in size with civilisation seems, on the 

 average, also incontestable. But is it the effect of lessening the 

 struggle for existence ? The possibilities may, perhaps, be summed 

 up as follows : — 



(a) The civilised races may have survived owing to their superior 

 size. It may be a result of the struggle in the past. To this must be 

 objected that the increase of size appears to be a progressive change 

 still going on, and yet increase of variation should show a lessening 

 strnggle for existence. 



(6) The effect of suspending natural selection may be to increase 

 size. This would be a blow for panmixia, for we might naturally have 

 expected a regression to the smallness of the more primitive races. 

 It would leave unexplained the apparently smaller progress of women 

 as compared with men, for in their case we might argue from the 

 variation that the struggle for existence is relatively less than in the 

 case of man, 



(c) The larger size of the civilised races may be due to better food 

 supply and better physical training : in short it may be due, not to 

 evolution, but to better conditions of growth. This hypothesis does 

 not involve the assumption that acquired characters are inherited. 

 Diminish the food supply and abolish physical training and the size 

 would sink to the level at which natural selection had left it. Physical 

 training in civilised races being usually more adequate in the case of 

 man than of woman would, perhaps, explain why man has progressed 

 more rapidly in size than woman. It seems impossible, taking varia- 

 tion as a measure of the intensity of selection, to reconcile the rela- 

 tive increases in size of man and woman with any direct effect of 

 natural selection. 



* This is only generally true, not in every individual case. The French femur 

 is longer than that of the Aino, of neolithic man, and of the ancient inhabitants of the 

 Canary Islands. On the other hand, the French femur appears to be slightly less 

 than the Libyan, although the humerus is somewhat greater. The French women 

 appear in all long bones less than the Libyan women. 



