146 Prof. Karl Pearson. 



Butpo= 1> .*. A1 + A2 == 1. Thus we may put 



Pn = + + ....(xii) 



where c is a constant. 



Let us substitute this in equation (ii) ; we find 



= ^ + 2y« I (1 - c)^ + 2a(l - c)i + U\l - 



o. =PM^^T^i^] 



Write 8 = a + ^8 - J, then by (i) we have 



ay = Ka-S)(l-2a) (xiv) 



Hence from (xiii) 

 and by (xiv) 



(l-2a8)(3-a ) , . 



(l-2S){(a-8)(l-2a)-(l-a)(l-2aS)} ^ ^ 



Suppose the parental and grandparental correlations observed, 

 then 



Pi = i(l-c) + c8 1 



> (xvi) 



will both be known. 



These will give c and 8 ; then (xv) will give a and (xiv) y, while 



P = S-a + J (xvii) 



will determine and the whole law of inheritance and reversion will 

 have its constants fully determined. 

 We have, indeed, from (xvi) 



'-'t^ 



(xi.) 



