1 66 



ANAIvYSIS OF THE FOUR PRINCIPLES. 



Method of Testing Table A . 

 I ■ C 7 



Let M= lo; m= 7; c = -; then-= = - according to the table. 



4 F 2 



We now place under pure-breeds any number, and under cross- 

 breeds 3J times that number. 



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



»th generation, we find that 



C_7: 



is correct for all subsequent gene- 



rations ; and this proves the formula to be correct. 



C. 



If the denominator of the fraction representing the value of = is 



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 (w + i)th generation, the pure-breeds will be 



2 X (M-Mc)i = 2 [10---] 



L 4 J 



15. In the {n -\- 2)th generation 



the pure-breeds = 2 X (M — McY = 2 x (7.5)2 = 112. 5. 



The cross-breeds in the (« + i)th generation = 7 x the cross- 

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



breeds of the previous generation = 72 



In the (n + 2)th gen- 



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

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



generation 



73+^ + 



15 



393-75- 



