yZ THE EVOLUTION OF LIVING BEINGS. 



J2 n l\ m 2 mn (2 n l) m 



V 



2 n ) 2 mn 



„These formulae may readily be deduced algabrai- 

 „cally, 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 {^. 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 AB ab + 



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



ab = 16. 



„It will be observed that of the entire 16, the 

 „first four are pure homozygotes, the second four 

 M 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 — i, z = \, of all. 

 „Now, b^ an analysis of the sort already given, it 

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

 „remains x ; y breaks up, 2 / 4 of these becoming x, 

 „ l l 2 of these becoming z, and x / 4 remaining y ; z breaks 

 >,up, V2 of these becoming x, 1 / 2 remaining z. 



„Now, when we recall that before the second ferti- 

 lization x was J / 4 ; y 1 I±, and z, 1 / 2 oi all, we see from 



