540 TRANSMISSION 



selected mid-parents, Pearson has established, 1 by the theory of 

 multiple correlation, the following results : 



1. If selection be made of first and second generations of 

 ancestry, with no knowledge as to back ancestry, 



h = 0.5122 HI 4- 0.2927 H z . 



If we have a fixed standard of selection, H = H 2 ; 

 then h = 0.8049 H. 



2. If selection be made of three generations of ancestry 

 under similar conditions as to back ancestry, 



h = 0.5015 H 4- 0.2553 H z + 0.1459 ^s ; 

 with a fixed standard H lt 



h = 0.9027 HI. 



3. If selection be made of four generations of ancestry, 



h 0.5002 HI 4- 0-2507 H 2 4- 0.1276^7.5 + 0.0729^/4; 

 with a fixed standard H^ 



h = 0.95147/1. 



4. Similarly, for a selection of five generations, 



h = 0.5000^4-0.2501 77 2 + 0.1253 ^4-0.0638^4 4-0.0365 HS\ 

 and with a fixed standard H^ 

 /& = 0.9717^. 



5. Finally, for a selection of six generations, 



h = 0.5000 .//! 4-0.2500^2 4- 0.1250^3 + 0.0627 HI 

 4-0.0319^5 4- 0.0182 HS ; 



and with our fixed standard H ly 

 h = 0.9878 .#!. 



It should be noted that the coefficients which we obtain are 

 approaching more and more Galton's coefficients in the law of 

 ancestral hereditv, which means that if selection be carried 

 on for a very large number of generations it does not matter 

 whether the back ancestry of our selection be mediocre or 

 above mediocrity. 



1 Proceedings of the Royal Societv, LXII, pp. 397-398. 



