No. 575] SHORTER ARTICLES AND DISCUSSION 695 



After obtaining x, or the proportion of homozygotes for any 

 one pair of characters, the proportion y for any number m of 

 pairs is obtained simply by raising x to the with power, that is : 



Thus, after two generations of brother X sister mating, the 

 proportion of homozygotes for three pairs of characters is 

 (1/2) 3 = 1/8, or 12.5 per cent. After 8 generations of such 

 inbreeding the proportion homozygotic for 10 pairs of char- 



The corresponding value in the case of continued self-fertili- 

 zation is 99.61 per cent. (4, p. 491). 



"Whether it may be possible to obtain a similar formula for 

 the coefficient of homozygosis in the cases of mating of cousin X 

 cousin or of parent X offspring, remains to be discovered. 



Pearl's "coefficient of inbreeding" gives the percentage of 

 lacking ancestors in a given pedigree, as compared with the 

 number that would be present if all the parents were unrelated. 

 In order to compare self-fertilization with inbreeding in this 

 respect, Pearl's formula' for the coefficient of inbreeding may be 

 expressed in terms of the number of successive inbreedings (n) ; 

 for many purposes the formula appear more convenient so ex- 

 pressed. The following gives these formulae for self-fertilizatioo 

 and the three types of inbreeding, together with those, so far as 

 worked out. for the proportion of individuals homozygotic with 

 respect to a given character. In all these, n is the number of 

 successive self-fertilizations or inbreedings. 



Cousin x Cousin — . )n ■ 



It will be observed that in self-fertilization the value of the 

 coefficient of inbreeding is, curiously, the same as that of the 

 coefficient of homozygosis. while in the other cases there is no 

 evident simple relation between the two. Further, the coefficient 



