190 NATURAL INHERITANCE. [CHAP 



variously after different and unlike progenitors. But 

 the difference between 5 in a mixed breed such as we 

 have been considering, and the value which we may 

 call /3, which it would have in a pure breed, w r ould be 

 very small. Suppose the Prob: Error of the implied 

 Stature of each separate Grand-Parent to be even as 

 great as the Q of the general Population, which is 1 7 

 inch (it would be less, but we need not stop to discuss 

 its precise value), then the Prob : Error of the implied 

 Mid- Grand-Parental stature would be \/ J x 1-7 inch, or 

 say 0'8 inch. The share of this, which would on the 

 average be transmitted to the child, w T ould be only J as 

 much, or 0'2. From all the higher Ancestry, put 

 together, the contribution would be much less even than 

 this small value, and we may disregard it. It results 

 that & 2 is a trifle greater than /3 2 +0'04. But 6 = 1'0; 

 therefore /3 is only a trifle less than 0'98. 



Simplification of Hereditary Inquiry. These 

 considerations make it probable that inquiries into 

 human heredity may be much simplified. They assure 

 us that the possibilities of inheritance are not likely to 

 differ much more than the varieties actually observed 

 among the members of a large Fraternity. If then we 

 have full life-histories of the Parents and of numerous 

 Uncles and Aunts on both sides, we ought to have a 

 very fair basis for hereditary inquiry. Information of 

 this limited kind is incomparably more easy to obtain 

 than that which I have hitherto striven for, namely, 

 family histories during four successive generations. 



