70 



On the Mathematical Theory of Evolution. [Nov. 28, 



types of sexual selection resulting from tribal and individual tastes, 

 and leading respectively to a preferential and an assortative mating. 

 The mathematical measurement of the latter (which seems a sensible, 

 if small, quantity in the case of stature in man) is not quite identi- 

 cal with Darwin's conception of sexual selection, which approximates 

 rather to preferential mating. The memoir develops Bravais' theory 

 of correlation, determining the probable error of the determination 

 of a coefficient of correlation and the relation of a coefficient of 

 correlation to coefficients of variation. The analytical forms for 

 two, three, or four correlated variables are given, and a proof of 

 Edge worth's theorem. These results are applied to the problems 

 of correlation in local races, of biparental inheritance, collateral 

 inheritance, morbid inheritance, and some problems in ' cross ' 

 heredity. Finally, the problem of panmixia is dealt with. The 

 following results among others are deduced; they are, however, 

 to be considered in each case as probable only, and matter for closer 

 investigation and observation* : — 



(«.) It is improbable that coefficients of correlation are absolutely 

 constant for local races. 



(b.) To judge by stature, the father, in the case of both sons and 

 daughters, is markedly more prepotent in inheritance than the mother. 

 Heredity is thus markedly stronger in the male than the female line. 



(c.) Fathers of sons are less variable than fathers of daughters. 

 Very tall or very short fathers have more daughters than sons. 



(d.) There is a sensible sexual selection in man. 



(e.) There is some evidence of reproductive selection. 



(/.) Regression is not the same in the case of ascent and descent 

 in the direct line. 



(g.) Elder sisters are shorter and less variable than younger 

 sisters. 



(/?,.) Biparental inheritance is sensibly influenced by sexual selec- 

 tion, the general tendency of the latter being to lessen the hereditary 

 tendency. 



(i.) The mathematical theory appears capable of covering such 

 phenomena as " skipped generations " and the " antedating of here- 

 ditary diseases." 



O'O Sports breed just as true as a race established by long and 

 continuous selection. 



(k.) According as the " focus of regression " is considered sta- 

 tionary or progressive with long-continued selection , panmixia will 

 or will not tend to reverse natural selection, both as to magnitude 

 of mean and amount of variation. 



(I.) A stationary focus of regression, besides an obvious difficulty 



* Conclusions (b) — (g) are based upon applications of the theory to family data 

 of stature kindly placed at my disposal by Mr. Galton. 



