vii.] DISCUSSION OF THE DATA OF STATURE, 135

to be equally taxed ; then, as an accumulation of ancestral contributions whose sum amounts to D-- yields an effective heritage of only D3, it follows that each piece of. heritable property must have been reduced to 4 of its original amount, because 3 x 4=2.

Secondly, suppose the tax not to be uniform, but to be repeated at each successive transmission, and to be equal to 1 of the amount of the property at each

r

stage. In this case the effective heritage would be

D ( r + 3r2 + 7, + - j = D 3r3 1 which must, as before, be equal to DR.; whence r =11

Thirdly, it might possibly be supposed that the MidAncestor 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 descendants 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, (1) that the Mid-Parental peculiarities, pure and simple, influence the offspring to 4 of their amount ; (2) that they influence it to - 6 of their amount. These values differ but slightly from , and their mean is closely Q, so we may fairly accept that result. Hence