148 



Prof. Karl Pearson. 



This shows us that the correlation with the individual ancestor is 

 halved at each backward step in the pedigree. We see at once that 

 (xii) can only be in agreement with (xxiv) — the letter c being 

 different in the two, and merely standing for a constant — provided 

 a + = 1, or by (i), provided 7 = Thus the condition that blended 

 and exclusive inheritance should lead to the same values for the corre- 

 lations with the ancestry is : that reversion should form a series starting 

 with the actual parent. If this condition should hold, then, for 

 example, the grandparental correlation must always be one-half the 

 parental either for blended or for exclusive inheritance. 



(5) Correction of an Error in Memoir on Ancestral Heredity. — It may 

 be of value to insert here the modifications required in my memoir on 

 blended inheritance, owing to the slip just referred to : they apply to the 

 results deduced from (xvii) on p. 403 ; these are the table on p. 403, 

 and the result immediately under (xviii) on p. 406. 



In the first place the law of ancestral heredity may now be written 



1+70-1 (1 + 7)'^ 0-2 (1 + 7)3 0-3 



a very simple form. 



In the second place we may replace the equation for c on p. 394 by 



27 + 1 



(xxvi) 



'272 + 27+1 



whence we find for the parental correlation caj J 2 or Jc 



1 27+1 . ... 



Each succeeding ancestral correlation will be obtained by repeated 

 halving of this value. 



Lastly, the result on p. 406 for the fraternal correlation becomes* — 



The following table indicates the effect of varying 7 on the intensity 

 of heredity, and should replace that on p. 403 of the memoir on the 

 ancestral law : — 



* Equation (xviii) on p. 406 of the memoir is correct, but the value of r in 

 terms of y below it, since it depends on the erroneous Equation (xvii) of p. 403, as 

 well as the limit given for y in the foot-note, must be cancelled. 



