356 Mathematical Contributions to the Theory of Evolution. 



8. To sum up, then, the following results seem suggested by these 

 measurements. 1 *, 



(i.) Civilised man has progressed generally on primitive man in 

 size, variation, and correlation. 



(ii.) This progression can hardly be accounted for by increased 

 selection (because of the increased variation), nor by decreased selec- 

 tion (because it is inconsistent with the relative changes in male and 

 female size). It might possibly be accounted for by decreased selec- 

 tion and improved physical conditions. 



(iii.) Woman is more variable than man in civilised races. 



(iv.) Woman is more highly correlated than man in civilised 

 races. 



(v.) In uncivilised races the sexes are more nearly equal in the 

 matter of size, variation, and correlation than in the case of civi- 

 lised races. 



(vi.) It is impossible to say that civilised woman is nearer to the 

 primitive type than civilised man, for while civilised man differs 

 more from the primitive type than civilised woman, so far, probably, 

 as absolute size is concerned, he has made only about half her 

 progress in variation, and hardly any progress at all in corre- 

 lation. 



(vii.) The causes {e.g., lessening of selection) which tend to increase 

 variation may also increase correlation. In other words, the intensity 

 of the struggle for existence is not necessarily a measure of the 

 intensity of correlation.* 



The measurements made by Mr. Warren on the Libyans, the 

 results of which he has kindly favoured us with, are, on the whole, 

 fairly in accordance with the above conclusions. He finds for the 



Mean of the sexual ratio of the means .... 1*092 

 „ ,, ,, the variations . 1*028 



,, ,, ,, the correlations 1*068 



The corresponding quantities for the French are : 1*109, 0*939, 

 0*956, or, we concluded, that in passing from uncivilised to civilised 

 peoples, from Libyan to French, the men gain on the women in size — 

 here very slightly, and the women gain upon the men very markedly 

 in variation and correlation. 



These results are merely suggestions, but they may possibly serve 

 to emphasise the importance of a careful measurement of the long- 

 bones of, say, 100 members of both sexes for a series of civilised and 

 uncivilised races. In the former case at least there does not appear to 

 be any real difficulty, except the need of co-operation, in obtaining 



* The mathematical theory of selective correlation shows that the close selection 

 of an organ, say th« femur, may actually tend to reduce the correlation between 

 two other organs, say the humerus and the radius. 



