vii.] DISCUSSION OF THE DATA OF STATURE. 135 



to be equally taxed ; then, as an accumulation of ances- 

 tral contributions whose sum amounts to Df yields an 

 effective heritage of only Df , it follows that each piece 

 of heritable property must have been reduced to f of its 

 original amount, because f x f = f . 



Secondly, suppose the tax not to be uniform, but to 

 be repeated at each successive transmission, and to be 



equal to -- of the amount of the property at each 

 stage. In this case the effective heritage would be 



D r~ + ^-2 + K2^+ ) = D o -T ' wnicn miist > as 

 V r 3r* 3V / 3r 1 



-i / 



before, be equal to Df ; whence = - 



Thirdly, it might possibly be supposed that the Mid- 

 Ancestor in a remote generation should on the average 

 contribute more to the child than the Mid-Parent, but 

 this is quite contrary to what is observed. The descend- 

 ants of what was " pedigree wheat," after being left to 

 themselves for many generations, show little or no trace 

 of the remarkable size of their Mid- Ancestors in the 

 generations just before they were left to themselves, 

 though the offspring of those Mid-Ancestors in the first 

 generation did so unmistakably. 



The results of our only two valid limiting suppositions 

 are therefore, (l) that the Mid-Parental peculiarities, 

 pure and simple, influence the offspring to ^ of their 

 amount ; (2) that they influence it to T 6 T of their amount. 

 These values differ but slightly from ^, and their mean 

 is closely ^, so we may fairly accept that result. Hence 



