THE PKOBLEMf^ OV HEREDITY AND THEIR SOLirTION. 571 



one-hiilf or (O.f)) of tho total boritag'e of the otfspriiio-; the four o-rand- 

 parents, one quarter or (»».5)''; the eight oroat-grandparents, one- 

 eighth or (0.5)^ and so on. Then the sum of the ancestral 

 contrilnitions is expressed by the series 



{((l.5) + ((l.5f + (().5f, etr.}, 



whicii. being equal to 1. accounts for the whole hei'itage." 



In the former case where ^1 and (/ are characters which can be denoted 

 by reference to a conuuon scale, the law assumes of course that the 

 inheritance Tvill be. to use (lalton's term, blended; namely, that the 

 zygote resulting from the union of ^1 with (f will on the average be 

 more like (f than if J had been united y^'ith A; and, conversely, that 

 an ^[(( zygote will on the average l)e more like .1 than an (h/ zygote 

 would be. 



But in the case of A's and i>\s, which are assumed to be mutuall}' 

 exclusive characters, we can not speak of blending, l)ut rather, to use 

 Galton's term, of alternative inheritance. 



Pearson, finding that the law, whether formidated thus or in the 

 moditied form in which he restated it," did not express the phenomena 

 of alternative inheritance known to him with sufticient accuracy to 

 justify its strict application to them, and also on general grounds pro- 

 posed tliat the phenomena of blended and alternative inheritance 

 should l)e treated apart — a suggestion'' thc> wisdom of which can 

 scarcely be questioned. 



Now the law thus imperfectly set forth and every modification of it 

 is incomplete in one respect. It deals only with the characters of the 

 resulting zygotes and predicates nothing in regard to the gametes 

 which go to form them. A good prediction may be mad(^ as to any 

 given g'roup of zygotes, but the various possible constitutions of the 

 gametes are not explicitly treated. 



Nevertheless a definite assumption is implicitly madi^ regarding the 

 gametes. It is not in question that diflerences l)etween these gametes 

 may occur in respect of the heritage they bear, yet it is as-umed that 

 these differences will be distributed among the gametes of any indi- 

 vidual zygote in such a way that each gamete remains capal)le on fer- 

 tilization of transmitting all the characters (both of the parent zygote 

 and of its progenitors) to the zygote which it then contrilmtes to form 

 (and to the posterity of that zygote) in the intensity indicated l)y the 

 law. Hence, the gametes of any individual are taken as collectively a 

 fair sample of all the racial characters in their appropriate intensities, 

 and this theory demands that there shall have ])een no qualitative 

 redistribution of characters among the gametes of any zygote in such 



« In Pearson's moditicatioii ihv parents t-ontriltuU' 0.',], the }j;ramlparents, 0.15. tlie 

 great-grandparents 0.075. 



''See the workiB referred to above. 



