MATHEMATICAX. 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 PearPs 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 vdih. a Jersey 

 bull, the product of a similar system of inbreeding (^ = 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 A"=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 applyinc: 

 the laws of probability to Mendelian formula?. 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 



