106 ANALYSIS OF THE FOUR PRINCIPLES. 
Method of Testing Table A. 
Let M=10; m=7; c= a then © —2 according to the table. 
We now place under pure-breeds any number, and under cross- 
breeds 34 times that number. 



Pure-breeds. Cross-breeds. = 
In nth generation, 2 | In nth generation, 7 = 
Gr. xt = 2(M — Mc)'= 15 | In(n+ 1)th gen., 49+ 2 Z 
(n+ 2)th ‘ | 2N(Fa5) i. a Mien (15s on] 2 
(one {= ar24 Nonagenss aay ies pari A 
= 2(M — Mc)? \ ] = 2(56.4) = 343-+ 244 + 26} \ 

Starting with the fraction 7 given in Table A, as correct for the 
2’ 
nth generation, we find that 5= Z is correct for all subsequent gene- 
rations; and this proves the formula to be correct. 
If the denominator of the fraction representing the value of ois 
o, or less than o, the disproportion increases with each generation ; 
that is, cross-breeds become the overwhelming element. 
In this case by which we are testing the correctness of Table A, 
suppose the pure-breeds to be 2 and the cross-breeds to be 7 in the 
generation with which we commence. In the next generation, which 
we designate as the (n+ 1)th generation, the pure-breeds will be 
2x (M —Mc)!=2 co 10 | 
l 4 J 
the pure-breeds = 2 X (M — Mc)? = 2 X (7.5)? = 112.5. 
The cross-breeds in the (7+ 1)th generation = 7 X< the cross- 
breeds of the previous generation, plus 7 < one-quarter of the pure- 
In the (n + 2)th gen- 
— 15. In the (n+ 2)th generation 
5 
breeds of the previous generation = 7? + 
lb | 
eration the cross-breeds will be 7 x the cross-breeds of the (m * 1)th 
generation, plus 7 * one-quarter of the pure-breeds of the (m + 1)th 
(15 
4 
‘ : 
generation = 73 + r+ x 7| = 303-75- 
\ 
