PRINCIPLES OF BREEDING. 119 



1 4-0 

 mally expressed thus: = 0.50, or J. C. is a 



heifer, and is put to another pure Short Horn, when 



' , 1-1-0.50 1.50 

 the calculation will stand thus : , or —^=.75, 



or three fourths pure blood. We will now proceed 

 to another generation. The progeny is still a heifer 

 put to a pure Short Horn, as before ; and the result 



1 -{■ 0.50 175 

 will be now as follows : 5- — , or -^ = .875 = .7 



pure blood. The fourth generation, the same course 



1-1-0.875 1.875 

 being pursued, will stand thus : -^ , or — ^ — 



= .9375, or }-f. The tenth generation would give, 

 as the reader may work out for liimself, if he pleases, 

 ^0 24 pure blood; and the twentieth generation 

 would possess x^tHfu of pure blood; or, in other 

 words, an animal of the twentieth generation, in ofie 

 million, forty-eight thousand, five hundred and sev- 

 enty-six parts of blood, would have one million, for- 

 ty-eight thousand, five hundred and twenty-five that 

 was pure ; and though, by farther progress, we 

 should approach nearer and nearer the unit that rep- 

 resented the bull, it would never be quite reached. 

 The deficiency would indeed be slight, but the pure 

 blood could never be attained or absolutely repro- 

 duced ; and this fact, though apparently of little con- 

 sequence, is of vast importance to the breeder, and 

 should be always kept in mind. 



It results from this mathematical demonstration 

 of the eff"ects of crossing in breeding, or breeding 

 from pure and common animals, that every breed 

 brought to a certain state of excellence by a suc- 

 cession of improvements, may sustain itself in this 

 state without having recourse to the pure breed from 

 which it was derived, and in which were its first 

 principles of improvement. All that is necessary in 



