62 
MendeV s Laws of Inheritance. 
* 
Where a dominant and a recessive character belonging to 
different pairs are in combination, then it is a two to one 
chance that any given animal is pure with regard to the 
dominant character, and the only method of discriminating 
in snch cases is to test by further breeding. This becomes 
a serious matter, for to ensure picking a pure male and a pure 
female, on the average nine matings must be made. Unfortu- 
nately there seems no possibility of this further breeding test 
being avoided, though it may be simplified by crossing the 
types to be isolated with a pure recessive. If the type is pure, 
all the offspring will show the dominant character ; if not, half 
will show the corresponding recessive. If the pairs of char- 
acters are A a and Bb , such an animal may be Ab , the pure, or 
Aab , the impure, type . 1 On crossing with an animal such as the 
parent showing the recessive in question, a , in the former case, 
Ab on meeting a will give all Aab ; in the latter, where two 
types of gametes Ab and ab, are being produced, it will give 
Aab and ab in equal proportions. The pure types, when 
isolated, form the starting point of a new breed. 
Finally, the case has to be considered where two pairs 
of dominant characters are combined. On the average this 
occurs nine times in every sixteen individuals in the genera- 
tion bred from the cross-bred. These animals all appear to 
be similar, yet constitutionally they fall into four types. 
Using the same notation, Aa and Bb, for the pairs of charac- 
ters, such animals may be AB, AaB, ABb or AaBb. The 
type which will breed true when mated with its like is the 
one in which both dominant characters are pure, namely AB. 
This only occurs once in every nine individuals. As one 
would require a pure male and female to start such a breed, 
it is evident that the chances of drawing both are too remote 
for practical purposes. If such a combination had to be 
effected and the type fixed the simplest plan would be to take 
animals showing both recessive characters, ab’’ s, from the 
generation bred from the cross-breds and mate these with the 
series having the appearance of AiTs. The pure type would 
then throw only animals similar to itself {AaBb resembling 
AB). On the average this would mean nine matings to find 
a single pure type, and in the case of animals which give but 
one descendant a year this would have to be continued for at 
least three years before one could be reasonably sure of its 
purity. Once a pair of such animals have been isolated the 
1 This combination occurs three times on the average in sixteen individuals. 
See Journal R.A.S.E., Vol. 65, 1904, pp. 337-345. The corresponding com- 
bination aBb or aB , where a is recessive and B dominant, occurs in the same 
proportion, and the pure type may be distinguished in the same fashion by 
crossing with an animal showing the recessive b. 
