134 NATURAL INHERITANCE. [chap. 



heritages that blend and those that are mutually exclu- 

 sive, must be here borne in mind. It would be a poor 

 prerogative to inherit say the fifth part of the peculiarity 

 of some gifted ancestor, but the chance of 1 to 5, of 

 inheriting the whole of it, would be deservedly prized. 



Separate Contribution of each Ancestor. — In making 

 the statement that Mid-Parents whose Stature is P±D 

 have children whose average stature is P±§I), it is 

 supposed that no separate account has been taken of 

 the previous ancestry. Yet though nothing may be 

 known of them, something is tacitly implied and has 

 been tacitly allowed for, and this requires to be elimi- 

 nated before we can learn the amount of the Parental 

 bequest, pure and simple. What that something is, we 

 must now try to discover. When speaking of converse 

 Eegression, it was shown that a peculiarity in a Man 

 implied a peculiarity of ^ of that amount in his Mid- 

 Parent. Call the peculiarity of the Mid-Parent D, then 

 the implied peculiarity of the Mid-Parent of the Mid- 

 Parent, that is of the Mid- Grand-Parent of the Man, 

 would on the above supposition be ^D, that of the Mid- 

 Great- Grand-Parent would be ^D, and so on. Hence 

 the total bequeathable property would amount to 

 D(l+i + i + &c.)=Df. 



Do the bequests from each of the successive genera- 

 tions reach the child without any, or what, diminution 

 by the way ? I have not sufficient data to yield a direct 

 reply, and must therefore try limiting suppositions. 



First, suppose the bequests by the various generations 



