416 Mathematical Contributions to the Theory of Ecolution. 



kinship. The probable errors are, as might be expected from such 

 small series, large. Putting aside the paternal relationship, we are 

 justified in drawing certain general conclusions, which may be thus 

 summed up : — 



(a) The coefficients of heredity, as determined from the cephalic 

 index, differ in all cases from those determined for stature by less 

 than their probable error, and therefore by less than the probable 

 error of their difference. The stature coefficients were obtained for 

 the English middle classes.* We thus conclude that these results 

 confirm Galton's law, in so far as they tend to show that the strength 

 of inheritance is not a character of race or organ. 



Cephalic index is clearly not more strongly inherited than stature. 

 Its variability is also very much that of stature. It is accordingly 

 difficult to see why it should be considered as peculiarly a racial 

 character. 



(6) The divergences between the observed values for the coeffi- 

 cients of inheritance for the cephalic index, and the theoretical values 

 obtained on the basis of Galton's law of ancestral heredity, are 

 greater than the divergences between the former and the coefficients 

 for stature. f They do not, however, exceed the limits of errors of 

 observation. In the case of mothers and sons the divergence is 

 very slightly above the probable error ; the observed and theoretical 

 values are identical in the case of mothers and daughters ; they are 

 less than the probable error for brothers and brothers and only 

 slightly larger than it for brothers and sisters ; for sisters and sisters 

 the divergence is about one and a half times the probable error. 

 The mean weighted values of the coefficients for direct and collateral 

 kinship are 0*3366 and 0*4004, the former differing by less than half 

 its probable error from the theoretical value 0*3000, and the latter 

 sensibly identical with its theoretical value, 0*4000. 



We conclude, therefore, that Galton's law of ancestral heredity 

 gives values for the inheritance within the limits of the probable 

 errors of observation. But, 



(c) As in the case of stature there is, on the whole, a tendency of 

 the coefficients for cephalic index to be somewhat greater than their 

 values as given by Galton's law. It is therefore reasonable to sup- 

 pose that the heredity constant 7 (introduced in the foregoing paper 

 " On the Law of Ancestral Heredity ") is not, as Mr. Galton takes it, 

 unity, but has some slightly less value. 



Other conclusions which may be drawn from the above table are : 



(d) Among Indians of mixed blood the women are more braclry- 



* 'Phil. Trans.,' A, toL 187, pp. 270 and 281. 



f It is to be noted, that, putting paternity aside, the order of relative magnitude 

 of the coefficients of heredity is precisely the same for both cephalic index and 

 stature. 



