130 MODES OF RESEARCH IN GENETICS 



indicate in a distinctive way every primary 1 

 reappearance of individuals. Then form a table 

 on the plan of Table 4, the character of which is 

 so obvious as not to need detailed explanation. 

 This table is to be read in the following way : 

 Because of the reappearance of Sisera's Stoke 

 Pogis in the 2d ancestral generation Bess Weaver 

 has 1 fewer ancestors in that generation than she 

 would have had in the entire absence of inbreed- 

 ing; 2 fewer in the 3d generation, and so on. 

 The totals of the columns of this table are the 

 values, for each generation, of 



Pn+l ~ Qn+V 



in (i). These totals, multiplied by 100, have then 

 merely to be divided by p^i in order to obtain 

 the successive Z's. The whole operation may be 

 very quickly carried out. It is not necessary, 

 in fact, to fill out the whole of the later columns 

 of the table; the entries may be cumulated. 

 For the present pedigree we have 



Z = 0, as always. 2 



Z\ = — = 25 per cent, 



4 



1 By "primary" reappearance in the pedigree is meant a reap- 

 pearance as the sire or dam of an individual which has not itself 

 appeared before in the lower ancestral generations. Thus Patrick 

 Fawkes makes a primary reappearance in the fourth ancestral genera- 

 tion as the sire of General Kelly, a bull which is not found in any 

 generation below the third. 



3 The apparent paradox implied in the fact that Zq must always 



