•220 The Laie of Anrestral Hcreditif 



Mr Galton 's evidencc from stature only gave a rough test of the series ^, J. J, ... 

 having the right trend. He di<l not himself claini nioic for it than this; thus 

 aftcr .suggesting that J, = i and J. = J, lie writes : " It would, however, be 

 liazardous to extend this seiiuence with confidence to nioro distant generations*." 



Referring again to this point, Mr Galton says in 1897 : " I stated it briefly and 

 with hesitation in niy book on Xatural Inheritaiicef." 



When I pei-sonally first came to investigate the matter from the more puiely 

 mathematical side, it seemed to me better to start with the coefficients of coiTe- 

 lation and make no assumption as to the values of the regression coefticients 

 in the /-series of p. 217^. Each coefficient found wouhl serve as the basis of a 

 limited amount of prediction, and we must plod away finding coefficients for as 

 many generations for as many charactere in as many races as we pos.sibly conld. 

 When thcse werc known, wc sbouid possibly be able to prcdict the relationship 

 between the correlation coefficients of succes.sive generations even beyond the 

 liniits of Observation and experiment. If wc had to make an hypothesis at all, it 

 seemed to me most reasonable to suppose the correlation not tlie rcgrc.s.sion 

 coefficients of each generation of ancestry to diininish in a geometrical series. 

 This view I kcpt steadily before me, bnt it was very difficult tu lind material 

 going sufficiently far back to test it. Theoretically I shewed that if these corrc- 

 lations formed a geometrical series then the regression coefficients, or J'a, would 

 also form a geometrical series, if we neglected the efiects of assortative mating§, 

 but the data I had coUected did not as far as they went jnstify Mr Galton's 

 proposed ^, \, J ... series. 



Takiiig the matter broadly we maj' say that the Law of Ancestral Heredity 

 implied two ideas : 



(o) That ihe iJiiiin r iiictliml to procced in heredity within ihe raco is by 

 the Statistical theory of multiple correlation — this does not exclude the truth of 

 <any physiological theory, althoiigh it may scrvc to confirm <>r rcfutc such a theory. 

 The correlation between parcnt and utispring in man will remain about '4.5 to '5, 

 whatever theory of gametes may eventually be accepted, and the prediction of 

 probable character in son from actual character in father remains equally valid. 



(6) That a knowlcdge of the ncarcr coefficients of correlation, i.e. tho.'je 

 between offspring, and j)arents, grandparents, and possibly great-grandparents, 

 will suggest the more distant ones, and that probably these, and consequently the 

 multiple regression coefficients, arc expressible as a geometricaily decrcasing 

 series. 



This is the hypothesis involved in my own expression of the Law of Ancestral 



* Natural Inheritance, p. 136. 



t I<- S. Proc. Vol. xLi. p. 401. I have clsewlicrc shewn that the cvidence from Basset Honnds admits 

 of other interpretations. R. S. Prof. Vol. Gü, p. 140 et seq. 



X " HcRression, I'anmixia and Heredity." Phil. Tram. Vol. 187, p. 25H ff >eq. 

 § " On the Law of Ancestral Heredity." R. S. Proc. Vol. 62, p. 394. 



