Correlation and Application of Statistics to Problems of Heredity 29 



not described at length*, and I have ventured to modify it in one or two 

 directions, which I believe will make it somewhat clearer. The main difficulty 

 Ibave is to interpret what Galton meant by the column headed "Generants." If 

 he meant by " Generant " the hypothetical individual that I have represented 

 by U above, a sort of " midancestor," replacing the whole stirp, then I think 

 the variability of this midancestor should be given by o-j vl — i?, where <r x is 

 the standard deviation of the population for the given character. For stature, 

 using not cr, but the quartile, this would be Galton's b or l" - 179, or the 

 value which Galton selects for b, i.e. l"'06. In his diagram, we have under 

 the " Generants " column " Probable deviation " 0""8 ; this number does not 

 occur, as far as I can see, anywhere else in the paper. One solution I can 

 suggest is that Galton was thinking of the variability of pairs of his new 

 population; in this the variability of these paired generants would be b/-j2, 

 and , 8x\/2 = ri31, almost the mean between the above values of b. Another 

 explanation may be that Galton had not reached the comprehensive idea of 

 the single midancestor, which I have defined by the " generant " above, but 

 that his generant depended solely on the midparent and was to be taken as 

 an individual with f of the character of the midparentage. In this case the 

 variability of the generant group would be § of that of the midparental 

 group, i.e. § (l //- 2) = r/, 8. If this be true the generant would be only a 

 hypothetical individual who produced offspring varying about his own, and 

 not about a regressed type. I trust this latter solution may be erroneous, 

 as I should like Galton to have conceived the idea of a single individual — 

 not one depending only on the parents — who would represent the whole 

 stirp or ancestry. At any rate let us preserve in future the good word 

 " generant " for the hypothetical individual who possesses, in the manner 

 indicated by the function TJ, all the midancestral characters which are 

 capable of showing a blending inheritance. Such a generant is a sort of mean 

 man for the stirp, who for statistical purposes represents the whole ancestry. 

 If Galton had not this idea, he provided at least the origin from which it 

 sprung! If his generants are the receded midparents, let us ourselves use 

 generantsfor the midancestry, who will notof necessity involve regression at all. 



Of the Birmingham Lecture on "Chance and its Bearing on Heredity" 

 little need be said, it only adds to what we have already discussed, emphasis 

 on the point that in a stable population the whole inheritance of any blending 

 character depends on the knowledge of three constants: (i) the mean character 

 in any generation, (ii) the corresponding variability, and (iii) a single here- 

 ditary correlation. 



Galton gave a further account of his researches on regression in stature 



* Galton is explaining how the new generation is a reproduction of the old and writes: 

 " the process comprises two opposite sets of actions, one concentrative and the other dispersive, 

 and of such a character that they neutralise one another and fall into a state of stable 

 equilibrium (see Diagram [on our p. 28]). By the first set, a system of scattered elements is 

 replaced by another system which is less scattered ; by the second set, each of these new 

 elements becomes a centre whence a third system of elements is dispersed" (loc. cit. p. 256). 

 This is the only reference to the diagram or its interpretation I have noticed. 



