404 



Prof. Karl Pearson. 



Galton's unmodified law. Now the direct correlations as given by that 

 law certainly appear somewhat small for both stature and cephalic 

 index in man. Hence it is quite possible that when more extensive 

 data are forthcoming, it will be found necessary to modify Mr. Galton's 

 form and take 7 less than unity. The above table will suffice to indicate 

 the general direction of the correlation changes which result when 7 

 is varied. One point should be noticed, the total regression on an 

 individual mid-parent (note, not the partial regression) continually 

 increases as we go further back, and will ultimately be greater than 

 unity; in our case this will happen at the 10th generation. JSTow in such 

 a generation an individual has 1024 10th great-grandparents, and,, 

 were they independent, the mean of these could hardly differ widely 

 from the population mean. Hence the total regression coefficient 

 being greater than unity is not so significant as it might at first 

 sight seem. What it amounts to is this : that if we only knew of an 

 individual that his mid-parent in a very distant generation had more 

 of a character than the then population mean, and knew nothing* 

 about his other mid-parents, then the individual would probably bave 

 more of that character than the mid-parent. The apparent paradox 

 arises from the very small variability of a distant mid-parent, and 

 hence the extreme improbablility of a mid-parent differing very 

 widely from the population mean. Of course with close in-and-in 

 breeding the modification introduced by assortative mating could 

 not be neglected, and our whole investigation would need modifica- 

 tion.* Until, however, we have more measurements to deal with, it 

 is idle to develop at length all the consequences which flow from the 

 generalised form of Galton's law. 



(10) Collateral Heredity. — There is another point on which the 

 law of ancestral heredity gives us full information, namely, the cor- 

 relation between brothers, cousins, and all other collateral relatives. 

 In my memoir of 1895, I felt bound to reject Mr. Galton's regression 

 coefficient for brothers, because its value seemed to me in contradic- 

 tion with experience. I wrote (p. 285) : — 



" There is not, I think, sufficient ground at present for forming 

 any definite conclusion as to the manner in which lineal is related to 

 collateral heredity. It does not seem to me necessary that the 

 coefficient for the former should be half that for the latter, as sup- 

 posed by Mr. Galton." 



And again : — 



* I hope to return to this point again. We have neglected e in equations (ii) 

 and (iv). In endeavouring to follow back my own family to its fourth, and even 

 sixth great-grandparents, I was surprised to find only one first and one second 

 cousin marriage among the ascertainable ancestors. According, however, to O. 

 Lorenz (' Lehrbuch der Genealogie,' s. 305), the present German Emperor has only 

 44 instead of 64 sixth parents, and 275 instead of 4096 twelfth parents ! 



