io6 



ANALYSIS OF THE FOUR PRINCIPLES. 



Let M = 10; m 



Method of Jesting Table A. 



i\ c- ; tlicn = ' according to the tabic. 

 4 P 2 



We n<>\\ place under pure breeds any number, and under cross- 

 breeds ;\ times that number. 



Starting with the fraction -, given in Table A, as correct for the 



>7th generation, we find that = = - 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 = is 



o, or less than o, the disproportion increases with each generation; 

 that is, eross breeds become the overwhelming clement. 



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 I i)th generation, the pure-breeds will be 



2 x (M -Mc) 1 



2 1 10 

 t 



^ 



4 J 



', = 15- 



In the (n t 2)th generation 



the pure breeds = 2 X (M — Mc) 2 = 2 ■ (70) 2 = 112. 5. 



The crossbreeds in the (w+i)th generation 7 the cross- 

 breeds of the previous generation, plus 7 one quarter of the pure- 



breeds of the previous generation 7-' '. In the (»t+2)th gen- 



2 



eration the cross breeds will be 7 x the cross-breeds of the (n • i)th 

 generation, plus 7 x one-quarter of the pure-breeds of the (n + i)th 



> ration 



7 3 + Z + 



15 



4 x 7 I 



! 



