MATHEMATICAL CONSIDERATIONS 87 



its function from that of the Coefficient of Inbreeding, 

 since it is a measure of the community of ancestry of the 

 dam and the sire. 



These two coefficients taken together, then, give us 

 the first quantitative measure of inbreeding as a system 

 of mating, but obviously they do not tell anything con- 

 cerning the actual germinal constitution of any individual 

 resulting from a given system of inbreeding. This fea- 

 ture of the relationship coefficients is nicely illustrated 

 by one of Pearl 's examples. Clearly, a Holstein cow pro- 

 duced by continued brother x sister matings (K = 100) is 

 very different in its germinal constitution from a cross- 

 bred animal obtained by mating this cow with a Jersey 

 bull, the product of a similar system of inbreeding (K = 0). 

 Yet the Coefficients of Inbreeding in each case form iden- 

 tical series, with the maximum possible value of Z when 

 K=0 one generation farther removed than when 7T=100. 



Without question the germinal (or may one call it the 

 Mendelian ?) composition of any individual can be deter- 

 mined only by actually testing its breeding qualities, its 

 transmissive powers ; and the effect this composition may 

 have had upon its development can be measured only by 

 comparison with other individuals of known genetic con- 

 stitution. But an indication of the germinal constitution 

 of an individual produced by any long-continued system 

 of inbreeding, as far as the degree of heterozygosity or 

 homozygosity is concerned, can be obtained by applying 

 the laws of probability to Mendelian formulae. In other 

 words, the laws of probability applied to Mendelian 

 formulae show the probable homozygosity or heterozygos- 

 ity of the generation as a whole for any number of Men- 

 delian allelomorphic pairs with any given system of 



