596 PRACTICAL PROBLEMS 



. By this we see that the individual inherits from no less than 

 2046 individuals within ten generations of ancestry, and that, 

 on the average, characters possessed by a single individual of 

 the tenth generation back have an influence amounting to not 

 over one ten thousandth of one per cent of the total heritage, 

 representing a probability of about one in a million certain to 

 be heard from but of little consequence as a foundation. 



We must remember that besides the "foundation" there are 

 1023 other ancestors of the tenth generation, and some 1022 

 intervening ancestors, each more powerful by far than the 

 so-called foundation. Six generations back the influence is but 

 1.5 per cent for the sixty-four individuals involved, or about 

 -Q of one per cent for each. This is an amount of influence 

 which for practical purposes may be considered as a negligible 

 quantity, and it is for this reason that in many lines the dictum 

 has gone out, " The sixth cross is pure," this meaning that 

 nearly 99 per cent is covered by the "top." We have seen 

 already that this agrees perfectly with mathematical theory. 



The so-called foundation is therefore not a foundation, but 

 only a beginning, and it is the /<?/, and not the bottom, that gives 

 character to the pedigree. 



This is not intended to disparage purity of pedigree even to 

 the tenth generation and beyond, but it is intended as a protest 

 against the blind following of certain pedigrees because of the 

 "foundation." 



Nor is it to be construed as a criticism directed against breed- 

 ing along approved lines ; far from it ; but it is a plea for the 

 careful study and rational valuation of pedigrees. 



What deceives the breeder is the fact that the "short form 

 pedigree," as it is often presented, runs only on \kefemale side, so 

 that, of the 2046 ancestors of the first ten generations, only eight 

 or ten females and their sires would appear the other 2026 

 not being noted. They exist, however, and their influence is to 

 be reckoned with. Of course it is true that in close breeding 

 the same individual appears many times in a pedigree, and thus 

 his or her influence is multiplied ; but the point here made is 

 that a single individual ten or even six generations back counts 

 for little so far as its personal influence is concerned. 



