THE EVOLUTION OF LIVING BEINGS. 73 



„the above that after the second fertilization: 

 x = i + (ix|) + iixi) = ^ = (?^^' 



^= (J X i) + (i X i) = 1= (!)« + (i)«+i 

 „These are the formulae for x and y that were ob- 

 „tained by the other method (since here n and m 

 „are each 2). This method however gives in addi- 

 „tion a direct formula for z. 



„It is easy to verify the formulae for three pairs 

 „of characters, though of course the conditions be- 

 „come here somewhat more complex. 



„We may now summarize our formulae, and show 

 „the results they give in certain examples. 



„Let X = the proportional number of organisms 

 „that are pure homozygotes (with respect to all 

 „the characters considered). 



„y = the proportion that are heterozygotic 

 with respect to all the characters 

 concerned, 

 z = the proportion that are mixed, 

 V = the proportion that have any hetero- 

 zygotic characters. 

 „Then,if« = the number of successive self-fertili- 

 zations and m = the number of pairs 

 of chara,cters, 



^ = (^)" 



(I) 



y = {\T\ (2) 



z = T—\x + y), (3) 



27»» — (2" I)"* 



V = T — X= —^ (4) 



