Correlation and Application of Statistics to Problems of Heredity 19 



trouble ourselves about the parents separately. The statistical variations of stature are extremely 

 regular, so much so that their general conformity with the results of calculations based on the 

 abstract law of frequency of error is an accepted fact by anthropologists. I have made much 

 use of the properties of that law in cross-testing my various conclusions and always with 

 success*." 



Galton considers the fact that stature is not a simple element, but a 

 compound of the accumulated lengths or thicknesses of more than a hundred 

 parts, to be a distinct advantage and a source of the beautiful regularity of 

 its frequency distributions f. He does not see that this may tend to screen 

 some fundamental law which may be obeyed by the simple components. 

 Thus we note that as a rule the parental correlations decrease as we take 

 characters based on fewer elements, e.g. the parental correlations for span 

 are less than those for stature, and those for forearm are less than those for 

 span. There might be — I on my part do not assert that there is — an alternate 

 inheritance in the simple components, which is screened in the complex 

 compound J. To this Galton might well have replied: Why should a single 

 bone be looked upon as an ultimate element, if it develops from a number 

 of centres of ossification, and pushing the matter further may we not be 

 driven to find the simple component ultimately in a cell? The "simple com- 

 ponents," which obey some equally simple law of inheritance, are still to find 

 in the bony skeleton of man. 



Two further terms defined by Galton may here be considered. 



He recognises that the individuals in what we now term an array (a column, 

 or row) of the correlation table are not in themselves blood kindred, they 

 are not, for example, all sons of the same parents, or all brothers of the same 

 individual. Their link is that they are all sons of a set of parents having the 

 same small range of any character, or again all brothers who have a brother 

 within the same small range of character. Thus these individuals probably 

 differ in both ancestry and nurture. Galton proposes to call them "co-kinsmen " 

 or more definitely according to the array type "co-filials" or " co-fraternals. " 

 By such terms he only means that their correlated variable (e.g. stature in 

 parent, brother or collateral) has the same value, or limited range of values. 

 Galton was thus fully aware that the variability within a family group of 

 brethren, a fraternity, was not the same as the variability within such an 

 array or co-fraternity, or co-kinship. Galton's terms have not come into 

 general use, it is, perhaps, awkward to call individuals co-kinsmen who are 

 not kinsmen at all. But the failure to distinguish between a fraternity in 

 the true sense, and a co-fraternity in Galton's sense, has not been unfruitful 

 of error§. It is, perhaps, best to stick to the words "filial array" or "fraternal 



* Journ. Anthrop. Instit. Vol. xv, p. 251. t Ibid. p. 249. 



X Those who assert that stature or cephalic index " mendelises," have not explained how 

 the bones on the dimensions of which they are formed themselves react to inheritance. If 

 these simpler elements " mendelise," how comes it that the compounds do, and what becomes 

 of the correlations between these components 1 



§ If r be the correlation coefficient of offspring on midparent and R be the multiple correlation 

 coefficient of offspring on the whole of its ancestry, then, o- being the standard deviation of off- 

 spring, o- VI - r 2 is the variability of a co-fraternity and <r \/l — B? the variability of a fraternity, 

 or group of blood brothers. 



3—2 



