62 



Mr. F. Galton. 



[Jan. 21, 



A third possible supposition of the mid-ancestral deviate in any one 

 remote generation contributing more than would be done by an equal 

 mid-parental deviate, is notoriously incorrect. Thus the descendants 

 of "pedigree wheat " in the (say) twentieth generation show no sign 

 of the remarkable size of their mid-ancestors in that degree, but the 

 offspring in the first generation do so unmistakably. 



The results of our only two valid limiting suppositions are therefore 

 (1) that the mid-parental deviate, pure and simple, influences the 

 offspring to f of its amount ; (2) that it influences it to the T b T of its 

 amount. These values differ but slightly from -J, and their mean is 

 closely -J, so we may fairly accept that result. Hence the influence, 

 pure and simple, of the mid-parent may be taken as -J, of the mid- 

 grandparent J, of the mid-great-grandparent -§-, and so on. That of 

 the individual parent would therefore be J, of the individual grand- 

 parent yg-, of an individual in the next generation and so on. 



[I do not propose here to discuss the reason why the effective 

 heritage of the child should be less than the accumulated deviates of 

 his ancestors. It is obviously connected with considerations that 

 bear on stability of type.] 



Pure breed. — In a perfectly pure breed, maintained during an in- 

 definitely long period by careful selection, w would become =0, and 

 the value of b would be changed, but apparently only a little. Call its 

 new value (3. It may be roughly estimated as follows. In mixed breeds 

 the value of b includes the probable uncertainty of the implied value 

 of the contributions inherited from the mid- grandparents, and from 

 the mid-ancestry of each preceding generation. This can be but a 

 trifle. Suppose the quartile of the uncertainty in the implied stature 

 of each grandparent to be even as much as 1*7 inch (we need not 

 wait to discuss its precise value), then the quartile of the uncertainty 

 as regards the implied mid-grandparental stature would be l/ \/4x 

 that amount, or say 08. The proportion of this, which would on the 

 average be transmitted to the child, would be only \ as much, or 0*2. 

 From all the higher ancestry put together, the contribution would be 

 much less than this, and we may disregard it. The result then is 

 63-02+0-04. Taking 5 = 1-07, this gives £=r05 inch. 



Probable Stature of the Child when the Statures of several of his 

 Kinsmen are known. — First we have to add their several contributions 

 as assessed in the last paragraph but one, and to these we have to add 

 whatever else may be implied. A just estimate of the latter requires 

 the solution of a very complex problem. Thus : — a tall son has a 

 short father ; this piece of knowledge makes us suspect that the 

 mother was tall, and we should do wrong to set down her unknown 

 stature as mediocre. Our revised estimate would be further modified 

 if we knew the stature of one of her brothers, and so on. Moreover, 

 the general equation w 2 p 2 +f%=p 2 may cease to hold good. The pos- 



