396 Oll the Laivs of /nheritanre in .Ifmi 



influciicc, ;ui(l tho chanjjc is of a niai,niitu(ii', wliioli woiild acciiiinilate, if it be 

 seciilar, witliiii a comparativcly fcw coiitiuics into inost sigiiiticaiit differuncos. 



(iv) Thore is a qiiite unexpected amouiit of sexual selection even of the 

 physieal charactere in man. There is probably ])refi>rL'ntial niating, there is most 

 certainly a hirgu ainount of assortative inatiiig, and this not only in the same but 

 in cross charactei-s. The modus operandi of this assortative niating is not clear ; 

 it can hanlly in any great part bc due to conscious selection: it may be the result 

 of repnidnctive selection, i.e. a snbtle combination of physieal oliaracters in male 

 and feniale being niost likely to givo a pair witli a ninnher of aduit children. Be 

 the source what it niay, the existence of this a.'^sortative niating most siibstantially 

 niodifies tho form of biparental inheritance, and its existence can lianlly in futnre 

 bc ueglected when we are considcring the problems of heredity. 



(v) The coefficient of pareutal heredity varies to some extent from character 

 to character in man, having a mean value of about 46. This value is, however, in 

 (luite ciose agrecment with the resnlts obtained for other species, and we may 

 roughly say that parentai heredity in the species hitherto dealt with is close to '5. 



(vi) Fraternal cornlation for the physieal characters of man dealt with in 

 this memoir is also close to 'ö. This is in good agreemeut with the result 

 obtained for eight physieal and eight mental characters compared in pairs of 

 brothers in schools. While, however, parentai correlations are in good accord for 

 ditferent species, fraternal correlations in such species have a much wider ränge. 

 This curiovis resnlt is being further considered, but the tentative Suggestion is 

 made that it is due cither to different degrees of uuit or of intermittent 

 prepotency in tho menibers of these species. 



(vii) For the tirst time in tliis papcr statistics of an extensive kind are given 

 for answoring the problems of cross heredity, and an empirical formula is given for 

 detcrmining cross heredity from direet heredity and organic correlations. Some 

 years ago, I proposed for cross heredity a formula whiili auiounted in the Dotation 

 of the prosont monioir to 



r,y = i (>•„■ 7\w + ?v ?•,.,) 



where 1, 2 are the orgaiis in the first, 1', 2 the like organs in the second relative. 

 This formula Wiis based on a theory involving the constancy of the heredity 

 coefficient for all characters (cf. (v) above). It is shown in the present paper that 

 on the average ^ must be replaced by "öT for parentai and by "06 for fraternal 

 cross correlations. With these numbers we obtain from the direet and organic 

 correlations valnes of the cro.ss heredity cocfficients well within the errors of 

 random sampling. Thus at any rate in the case of man, we are in a position to 

 dctermine cross-heredity for the physieal characters without direet investigation. 

 A further rcseareh on cross-heredity will, I liope, shortly be published. 



(viii) The values of the parentai ronclations determined for man, sliow that 

 two or three generations of selection would suftice to raise the mean of the 

 oftspring to the selected standanl. Further with quite reasonable values of the 

 grandparentiil correlations no regression would take place, and the stock breed true. 



