HEREDITY 539 



If this same line of argument be carried on, so that the fourth 

 generation of back ancestry is selected, 



h = o-9375 -#! 

 Likewise, if the fifth generation be selected, 



h = 0.9687^. 

 And if a sixth generation be selected, 



h = 0.9844 HI. 



The significant point in all this is that six generations of 

 selection, even on a mediocre stock, establish the selected 

 character to within about 1.5 per cent. The full significance of 

 this point will appear later. 



Finally, if selection of the character of deviation H^ be made 

 for n generations, and if we may assume mediocrity in the 

 ancestry beyond the #th generation, the amount of the charac- 

 ter established is given by 



Making no assumptions as to mediocrity in back ancestry. 



It has been shown both by experimental and by theoretical 

 methods that if mid-parents with character H^ are selected, the 

 offspring will, on the average, exhibit about 0.6 H^ of the 

 character in question. The inquiring reader will ask here why 

 this differs from the 0.5^ obtained from Galton's law. It 

 should be remembered that 0.5^ is what we obtained by 

 assuming mediocrity back of the first mid-parents. In general, 

 if we select parents of character H v their special ancestry will 

 exhibit this character to a greater degree than ancestry in 

 general from which the selection is made. It is therefore only 

 common sense to expect a higher value than 0.5 ff l under the 

 present assumption. 



Granting, then, if we can make no assertion about back 

 ancestry, that an offspring will exhibit 0.6 of the deviation of 



* 1 1 -- I is the sum of the geometrical progression | | --- 1 --- \~ ' ' ' ~^~ 

 t See p. 533; also Proceedings of the Royal Society, LXII, 396. 



