72 THE EVOLUTION OF LIVING BEINGS. 



(2 I\ m 2 mn (2 n T.) m 

 I _ _ 

 2 n j 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 {b- 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 

 ,,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 : 

 *= i, y = i, z = i f all. 



/ 



,,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, 1 / 4 of these becoming x, 

 ,,V 2 of these becoming z, and 1 / 4 remaining y ; z breaks 

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



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

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



