238 HISTORY OF THE SHORT-HORNS. 



Grandson of Bolingbroke, the Galloway cross so frequently mentioned. 

 This daughter of Lady had one-sixteenth part of Galloway blood, 

 and she being put to a bull having the same amount of that blood, 

 the produce would contain the same fraction of impurity. Or, 

 let the female produce be put to another bull having even a lesser 

 fraction of the blood for bulls were used with one-sixteenth, one- 

 thirty-second and one-sixty-fourth part of it, and very much less, 

 in a descending ratio, from that day to this all of them having a 

 taint of it. We ask how many crosses of that tainted blood will 

 have to be made before it is entirely eradicated ? We shall not 

 undertake to compute it, and yet to settle the fact, a month's labor 

 or more may have to be exhausted in finding it out ; while half the 

 number of crosses in some other animal may carry a pedigree back 

 into its original parents without finding the most distant taint of any 

 other than pure Short-horn blood. We mention this without preju- 

 dice to the tainted pedigree, but only to show that its value must be 

 judged by the qualities of the animals through which it has run as 

 well as its length, or the number of pure crosses it contains. 



To further elucidate the matter of blood, let us reckon the de- 

 grees of impurity in the number of crosses a pedigree may contain, 

 by taking a continuation of descent from well-bred Short-horn bulls 

 and a common cow, or one of other blood. The 



1st cross gives 1-2 blood Short-horn. 



2d " 3-4 " 



3d " 7-8 " 



4th " 15-16 " 



5th " 31-32 " 



6th " 63-64 " 



7th " 127-128 " 



8th " 255-256 " " 



Qth " 511-512 " " 



loth " 1023-1024 " " 



nth " 2047-2048 " " 



I2th " 4095-4096 " " 



I3th " 8191-8192 " 



I4th " 16383-16384 " " 



I5th " 32767-32768 " " 



i6th " 65535-65536 " 



So, this sixteenth cross contains 1-65536 fraction of impure to all the 

 other parts of good blood. How much damage, let us ask, in ordi- 

 nary probability, will that do the creature possessing it ? And yet the 

 bull or cow possessing this 1-65536 part of impure blood, according to 



