THE EVOLUTION OF LIVING BEINGS. 73 



,the above that after the second fertilization: 



^2» l\" 



y = (i x i) = ^ = (i) 2 * 



2 M 



2 - (i x |) + ft x i) = § = (*)• + (|) w+1 



„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). 



„v = 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 n = the number of successive self-fertili- 

 zations and m = the number of pairs 

 of characters, 



*=(—), (I) 



y = (\) mn , (2) 



2 = 1 — (x + y), (3) 



V = I — X— (4) 



