AhicK Lkk 



235 



yroni Table I. I find in thc fourfold divisiou hitherto adopted : 



GreatOrandparents. 





O 



Honco 

 and tlie cquation is : 



/t = -671,102, ({■ = ■423,602, 



•198,115 = /- + -141, 81 3f-' + -07.".,l(l6/-H-085,182;-' + etc. 



;-=-1922. 



Froni Table IL \ve have : 



Oreat-great-( Irandparents. 



bo 



_c 



A 



o 



I find 

 and the eqiiation 



wliich gives 



/i = -725,258, /■= -361,420, 



-149,992 = /- + ■131,061/-' + •068,681r' + •077,532/'' + eto. 

 /• = -1469. 



We see from thesc rcsults tliat the ancostral relationships in coat-coloTir for the horse are far 

 niorc intciise than was originally supposed for the like grades of relation.ship. Wo have in 

 round numbers : 



Parental correlation =-50. 



Grandparental correlation ='30. 



Great-grandparental con-elatioii ... =-20. 

 Great-great-grandparental correlation =-15. 



As far as thi.s series goes, not the coofiicient itself, l>ut the difference appears halved at each 

 ascent, and it is clear that the |, j, J, i^,... .series caunot possibly hold for the rcgression 

 coefficients uf the multiple correlation seriea. 



30—2 



