1886.] 



Family Likeness in Stature. 



6L 



special data. The reason is that this inaccuracy cannot be ascribed 

 to an uncertainty of equal + amount in every entry, such as might 

 be due to a doubt of "shoes off" or "shoes on." If it were so, the 

 quartile deviate of the R.F.F. would be greater than that of- the 

 specials, whereas it proves to be the same. It is likely that the in- 

 accuracy is a result of the uncertainty above mentioned, which would 

 increase the value of the quartile deviate, combined with a tendency 

 on the part of my correspondents to record medium statures when 

 they were in doubt, and which would reduce the quartile deviate. 

 What the effect of all this might be on the value of w in Table IV, 

 which is a datum of primary importance, I am not prepared to say, 

 except that it cannot be great. While sincerely desirous of obtaining 

 a revised value of w from new and more accurate data, the provisional 

 value I have adopted may be accepted as quite accurate enough for 

 the present. 



Separate Contribution of each Ancestor to the Heritage of the Child. — 

 I here insert a short extract from my paper in the " Journ. Anthrop. 

 Inst.," with slight revision, as this memoir would be incomplete with- 

 out it. 



When we say that the mid-parent contributes two-thirds of his 

 peculiarity of height to the offspring, it is supposed that nothing is 

 known about the previous ancestor. But though nothing is known, 

 something is implied, and this must be eliminated before we can learn 

 what the parental bequest, pure and simple, may amount to. Let 

 the deviate of the mid-parent be x (including the sign), then the im- 

 plied deviate of the mid-grandparent will be ^r, of the mid- ancestor 

 in the next generation and so on. Hence the sum of the deviates 

 of all the mid-generations that contribute to the heritage of the off- 

 spring is + J + i + &c.)=af . 



Do they contribute on equal terms, or otherwise ? I have not 

 sufficient data to yield a direct reply, and must, therefore, try the 

 effects of limiting suppositions. First, suppose the generations to 

 contribute in proportion to the values of their respective mid-deviates; 

 then as an accumulation of ancestral deviates whose sum amounts to 

 x z •> yields an effective heritage of only a'-f , it follows that each piece of 

 heritable property must be reduced, as it were, by a succession tax, to 

 ± of its original amount, because -f x -§=-§-. 



Another supposition is that of successive proportionate diminutions, 

 the property being taxed afresh in each transmission to 1/r of its 

 amount, so that the effective heritage would be — 



1 6 



and this must, as before, be equal to a'f, whence -= — 



