144 DOMESTICATED ANIMALS AND PLANTS 



no mixture had taken place in the field ; third, the coefficients 

 expressing proportion as well as the exponents expressing 

 infusions of blood stand in the exact form of the binomial 

 theorem, that is, we have here reproduced the binomial [y -f- w) 4 . 

 Knowing this general theorem, the student can readily write 

 the color or blood combination for any number of infusions 

 with any degree of mixed breeding. 



Another significant fact must be noted, namely, that although 

 this formula becomes rapidly complicated with successive genera- 

 tions, 1 there are always a few individuals remaining just as 

 pure as if no mixed breeding had been done, all of which means 

 that in free and unrestricted breeding all possible combinations 

 will take place. In systematic improvement it is the business 

 of the breeder to allow only such blood combinations to be made 

 as will result in desirable combinations and favorable results, 

 preventing all others. 



Characters that do not blend. When diverse characters are 

 thus brought together, two very different results may follow. 

 They may blend into a single new character, in which case 

 our figures show the proportions within the blood, or they may 

 remain distinct as two independent characters within the same 

 individual. Stature and size as well as many colors blend freely, 

 but not all characters behave in that simple way. For example, 

 white and black blend freely in the human race, and the off- 

 spring of white and negro are mulattoes of various shades, 

 according to the respective infusions ; but colors do not blend 

 in pigs, which are either black, white, or spotted, never roan 

 or mulatto. Some colors blend in horses (roan), some do not. 

 Some breeds of cattle have blended colors (Shorthorns) ; in 

 others the colors remain distinct (Holstein-Friesian). 



And so with characters generally. Many will blend and many 

 others will not. When they will not blend, then the appearance 

 is still less a guide to the real hereditary qualities, and under 

 these circumstances it is little or no index to what will happen 



1 " Principles of Breeding," p. 506. 



