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 + w)‘. 
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,! 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. 
