THE EVOLUTION OF LIVING BEINGS. 73 



,the above that after the second fertilization: 



2 n 



y = (ixi)= T v=(i) 2 ' 



* = ft x i) + (I x j) = = (t) + (D-+ 1 



,,These are the formulae for % and jy 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,ifw = the number of successive self-fertili- 

 zations and m = the number of pairs 

 of characters, 



y = ft)"", . (2) 



z = i (x + y), (3) 



= i-x= 



