N. Hlanciiard 229 



stood tho tost of tiiuo. 'l'liis siuipUn' liyputhesis, discvissed in tliu presoiit [i.ipiT, still swm.s tc> fiie 

 to stand thc tcst uf time. La.stly, I tliink, tlie roader of Jlr V'ule'.s papoi- would bclievo fniiii tlie 

 words : "Selective matiiig, iiatui-al .selectiou, i'oproductivo selection, tho cffcct of uircuiiistance, 

 had all in turn to be recognised as causcs aflecting tlic valucs of the constant« of hci-cdity," tliat 

 these factors were introduced post hoc, i.e. after Observation had failod to give fixity of constant», 

 whereas ahnest the rover.se is tlie true citse. Tho definition of solective mating was given in niy 

 lirst paper to tho Royal Society on bipai-ontal inlioritanco in 1895* before I had applied the 

 forniula' to actiial data at all. Reproduetivo selection was considered in 189Gt, and the influcnco 

 of natural selection on correlation (including tho coetticionts of heredity) was given in (.'ollege 

 Lectures of the .ses.sion 1896-7, and put into a form ideutical with that of the nienioir just issued J 

 in August 1897. The mernoir of 1898 on the law of ancestral heredity wa.s writteu with a 

 knowledge of thc influence of the threo factors of selective mating, natural selection and repro- 

 duetivo selection on the constants of heredity. As a matter of fact tliey had boen biometrically 

 detincd in or Ijefore the mernoir of 189G, and were not " all in turn recognised as causes aflecting 

 tho vahies of the uonstants of heredity," or used to bolster up some theory which had not stood 

 the test of time. 



What I feit in 1896, 1 still fcel, naniely : that the problem of heredity from the purcly Statistical 

 Standpoint is an extremely difficult one, that the factors of selective mating, natural selection, 

 reproductive selection, en\-ironmental influence are extremely coniplex, espocially when we place 

 plants or insects in very artiticial surroundings for the purpcjse of experinienting on their laws of 

 reproduction. Still these foctors do not invariably tend in one direction, and when we take long 

 series, as free from their influence as is practically possible, we shall be able to judge from the 

 clustering of the heredity coefficients round eertain values — a phenomenon which I think is 

 obvious in existing results — what in broad linos is tlie quantitative intensity of heredity for 

 ditterent relationships, and for diftercnt characters in diflerent species. Mr Yule indicates that 

 he has a theory which allows hirn to determiue the influence of the environmental, reproductive, 

 selective and mating factors ; I can only say that I, as well as most biometricians, will heartily 

 welcome its publication, if it not only allows, in the case of any heredity statistics which it is 

 feasible to collect, for the correcting of the heredity constants for all these influences, but achieves 

 this by some hypothesis which is ä priori as reasonable, and <( posteriori as justified as the simple 

 one that ancestral correlations diminish in a geometrical progression. 



Appendix II. On Inheritance (Grandparent and Offspring) in 

 Thoroughbred Racehorses. 



Bt NORMAN BLANCHARD, B.A. 



(1) At the Suggestion of Professor Ivarl Peai'son I liave recently worked out the remaining 

 four cases for the inheritance of eoat-colour in thoroughbred horses, viz. those between 

 foals — colts or tillies— and their paternal and maternal grandams. The work was done in a 

 somewhat diflerent manner to that on the four earlier tables. In order to consider the bearing 

 of coat-colour inheritance on Meudel's theory, actual colour pedigrees were formed going back to 

 the great-great-grandparents and in some cases to the fifth and eighth generation of ancestry. 

 Further, in order to get more striking colour contrasts than are now-a-days possible, the first 

 threo volumos of the stud-book were dealt witli, I thus went back to the earliest records of coat 

 colour in thoroughbreds. Here we find 2 to 3 per cent. of black horses and 9 to 10 per cent. of 



* "Ou KeRressiou and Inheritance in the case of two l'arents," R. S. Proc. Vol. 58, 1895. 

 t " On Keprodiictive Selection," E. S. Proc. Vol. 59, p. 301, 189G. 

 t Phil. Tniiis. Vol. 200, pp. 1— UC>, 1902. 



