190 NATURAL INHERITANCE. [cnAr

variously after different and unlike progenitors. flut the difference between b in a mixed breed such as we have been considering, and the value which we may call $, which it would have in a pure breed, would 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 '/4 x 1.7 inch, or say 0.8 inch. . The share of this, which would on the average be transmitted to the child, would be only I 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 b2 is a trifle greater than 8'+ 0.04. But b =1.0 ; therefore # is only a trifle less than 0.98.

Simpl f cation 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.