84 fjije ami Lcttrm of Fraurh fttiffon 



And then follows Galton's first onunciatioii of tlu' Law of Ancestral 

 Heredity. He writes : 



"The sharu a man rvtains in the constitution of his remote (lesciMuiiiiits is inconceivably 

 snudL The father transmits, on an average, one-hHif of liis nature, the grandfather one-fourth, 

 the great-grandfather one-eighth ; tlie share decreasing step by step in a geometrical ratio, with 

 great rapidity." (p. 32G.) 



Galton is clearly on the right track, but the nunibei-s he gives would 

 only be correct if he used mrentnl generation, gmnduarent-al generation, 

 gi-eat-gi"andj)areiital generation, instead of father, grandfather, great-gmnd- 

 father. He lias overlooked the* mother, and overlooked the multiplicity of 

 the ancestral individuals. The numbers as he gives them in a lateV j)ul)lica- 

 tion are one-fourtii for the parent, one-sixteenth for the gran<l))arent and 

 one-sixty-fourth for the great-grandparent, etc. (ialton's view was that this 

 rule held for either blended or alternative inheritance^ Thus in 1865 

 Galton had already in mind this law of ancestral heredity, although by an 

 obvious oversight he gave the wrong proportions. It has been suggested 

 by certain over-confident geneticists that Mendelism has for ever done away 

 with Galton's Law. I doubt the validity of this conclusion, as I doubt 

 whether hybridisation will explain variation, or mutation account for the 

 origin of species. The subject is, however, too controversial and technical 

 to be discussed here, although it must lie referred to as long as the tendency 

 is to belittle Galton's contributions to heredity*. 



Galton draws from his law the conclusion that there is nothing much to 

 be proud of in descent in a single line from a Norman baron for it would 

 contribute on the average only (;|:)**, if 26 generations intervened, to the 

 individual's natural aptitudes, 



"an amount ludicrously disproportioned to the value popularly ascribed to ancient descent. As 

 a stroke of policy, I question if the head of a great faii\ily, or a prince, would not give more 

 strength to his position, by marrying a wife who would bear him talented sons, than one who 

 would merely bring him the support of high family connections." (p. 327.) 



' See his Natural Itifieritance (pp. 138 and 151) where he applies it both to stature and to 

 eye colour; in the one case to deduce the average stature of the offspring, and in the other case 

 to deduce the distribution of eye colour in the offspring. 



' If Galton in 186.5 had applied his law to the following scheme of the crossing of two pure 

 races (Z)ZJ) and (Rli) to produce the liybrid (Z>^)— to u.se iMendclian notation — let us see what 

 it would have given hiui for the offspring of {DR) mated with (DR). The two parents are 

 {DR) and {DR), the four grandparents are (DD), (KR), (OD), {RR), the eight great-grandparents 

 are four {DD) and (our (HR) and so on. Hence according to Galton's Law applied to alternative 

 inheritance, the constitution of the offspring would be for a family of 4/" 



4/{J(2>^) + J(^*) + A[2(^^) + 2(^/?)] + A[* (DD) + i(RR)] + ,U [»{DD) + 8 (^^)]+ ••} 

 = /{2(DR) + (i + i + i+...)[{DI)) + (RR)]] 



=/{{DD) + 2{DR) + {JiR)). 



Or, this simple application of his law would have led Galton to the fundamentjil equation of 

 Mendelian hybridisation. On the other hand had Galton applied it to (DD) niatcsd with (DR) — 

 or to a pun? race mated with a hybrid — he would have obtained different results according to the 

 origin of the hybrid, i.e. whether it was an immediate result of crossing pure races or the product 

 of two hybrids, or the product of hybrid and pure race, i.e. whether it was not or was an 

 'extracted ' hybrid. And who shall say that he would not have been right? My own experience 

 certainly leads me to doubt whether all hybrids, 'extracted' or not, are of e<iual germinal valency. 



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