228 The Law of Aiiresfral Ileredity 



than the desired amount of character, woiild give us niore than 92 per cent. of it. 

 After selection ceases a very slow regression sets in, which would be hardly 

 perceptible witliout very definite quantitative metisureineut for the fii'st three or 

 four generations of in-breediiig. 



No rough Classification like a Mendelian category would enable us to test 

 whethcr such slow regression is rcaliy takiiig place, i.e. whether "recessives" are 

 really breediiig true to theii- stock*. And above all no Mendelian tlieory cau 

 (a) replace the Statistical treatment unless it shows that offspring are absoliitely 

 deterniined by their parcnts, for if the correlation be not perfcct,a better prediction 

 must be oblainable by using the positively correlated ancestry, or (b) be proved 

 without careful quantitative analysis of the variations falling within the wide 

 categories adopted. 



Appendix I. Note on a paper by G. U. Yule. 



This pajjer wa.s written before I wius awaro that Mr O. U. Vule was writing some account 

 of the law of ancesti-al hcredity, and Wcvs sent to press before I had seen bis paper {The New 

 Phytologist, November and Deccmber, 1902). With much of his papei-, I agree, for example, 

 with his insistence on the point that the laws of intra-raeial heredity are not incompatible 

 with Mendelian priuciples holditig for hybridisation. I shoiild lay, however, far less stress than 

 he does on tlie valuo of the existing evidonce in favour of tho.se priiiciple.s. That evidence 

 certaiiily justitio.s the uiaking of new and crucial exporiniont.s, but these will have to be niade with 

 muüh greater caution and closer quantitative delinition of tlio categorie.s eniployed before we can 

 say with certainty how far either of the two principles of dominance and segregation actually 

 applies eveu to the Ciises of hybridisation already dealt with by the Meudelians. I shall be 

 siirpriscd if the laws wbich goveru intra-racial and inter-racial lieredity are not more clo.sely 

 related than ai)poars to me possible under the reccnt formulation of Mendelian Principles by 

 Mr Batcson. Furtber Mr Yule does not sceni to nie to liave clearly expressed tuy i)ei-sonal 

 Position with regard to the law of ancestral h(>rcility. I believe that iny nienioir of 189G was the 

 first in which the equatious of multiple regression were worked oiit aml applied to the problem of 

 hcredity. Such equatious are, I presume, what Mr Yule refers to and says may be termed the 

 law of ancestral heredity. But the objectiou to such form of the law is simply the inipossibility 

 of working it out for all the ancestry, and for all charactera of all races. The problenis that arise 

 at once in our uiinds are : Is tliere any relationship between the correlatious of ofispring and 

 succcssive ancestors i Are these corrclations in casos, where direct selection of the characters 

 is small or can be allowed for, the same or approximately the .saiue for diö'ereut characters of the 

 same race, or for divers characters of difl'erent races ? Is there any rclation l)etwecn the corrc- 

 lations, which appears fairly in accordance with Observation and yet will simplify the otherwise 

 appalling coniplexity of the multiple regression equatious ? The memoir of 1896 gave the 

 general regn.s.sion cquations, and indicated what results would flow supposing one or other of a 

 variety of hypotheses due to Galtoii, Weismann and otbers were true. The memoir of 1898 

 adopted the simpler hypothesis that the correlation cocfficients decrejise in geometrical progrcssion, 

 ü did not involvc thefixity of the numerical constants of lieredity which Mr Yule teils us has not 



* For example, if we gciccted extreme cliestiiut (towardB roanchestunts) fur two Renerations only in 

 the horse, j-ct if the progcny in.brcd for 10 generations, the ofispring would still be well in the chestnut 

 ränge of coat-colour, and no category like chestnut would teil us whether the horses were breeding true or 

 rcgrcssing. 



