72 THE EVOLUTION OF LIVING BEINGS. 



2mn (2» !)»» 



" = '-(—) 



„These formulae may readily be deduced algabrai- 

 „caUy, or verified, by a detailed analysis of a case of 

 „two or more characters. It may be worth while to 

 „indicate the method followed, by taking up the 

 „simpler case of two pairs of characters. Call these 

 „/^ and 1^. The gametes formed are AB, Ab, aB 

 „and ab. 



„When these combine in all possible ways (as 

 „indicated in the diagrams given in Bateson's Men- 

 delism), these give the following results: 

 I AB AB + I Ab Ab + I aB aB + I ab ab + 2 ABab + 



2 Ab aB + 2 AB Ab + 2 AB aB + 2 Ab ab + 2 aB 



ab = i6. 



„It will be observed that of the entire i6, the 

 „first four are pure homozygotes, the second four 

 „are pure heterozygotes (heterozygotic with res- 

 „pect to both characters) ; while the last 8 are mixed 

 „(homozygotic with respect to one character, hete- 

 „rozygotic with respect to the other). 



..Letting x = pure homozygotes, y — pure hete- 

 „rozygotes, z = mixed, we find thus that : 



x-=i, y = \,z = h of aU. 

 „Now, bij an analysis of the sort already given, it 

 „will be found that at the next self-fertilization, x 

 „remains x; y breaks up, ^j^ of these becoming x, 

 „ V2 of these becoming z, and ^4 remaining 3/ ; z breaks 

 ,.up, V2 of these becoming x, V2 remaining z. 



„Now, when we recall that before the second f erti- 

 „lization x was ^j^; y ^4. and 2, Vsof all, we see from 



