TABLES FOR CALCUI^ATING C0E;FFICIENTS OF INBREEDING. I93 



The totals of this table are the quantities (p^^^ — 1n+i) 

 of (i). To get from them the successive values of Z it is 

 necessary only to divide by p ^^i- 



It is obvious from equation (i) that (p ^^^ —q „+i ) must 

 in practice always be something less than p^^^ — i. Further- 

 more p ^ -^ , the maximum possible number of ancestors in "any 

 generation, presents a definite seriea of values, namely the 

 successive powers of 2. If then there were available tables 

 which would give for each successive value of />„_,. j , the quo- 

 tients obtained from dividing each integer smaller than p^^^ 

 by this same quantity, evidently the value of Z for any partic- 

 ular case could be read off from the table, without the necessity 

 for any arithmetical work whatever. 



The tables accompanying this paper are of just the sort 

 described. For the first ten ancestral generations, beginning 

 with the second, all possible values of 



ioo(/'n+i— 9n+l) 



Pn+l 



are tabled, to 3 places of figures. 



The arrangement of the tables is as follows : In the right 

 hand columns are the successive value of (» ,, — a ,, )=iA.* 



^L n + 1 J n+1 -' 



These columns are headed A. The values in the A columns of 

 the tables correspond to the "Totals" of such pedigree elimina- 

 tion tables as is shown above in Table i for Figgis 20th, Over 

 against these A columns are given the corresponding values of 

 the coefficient of inbreeding Z. 



Example Showing Use of Tables. 



We may take, as an example to show the method of using 

 these tables, the case of Figgis 20th, for which the pedigree 

 elimination table has been given above. We see that in this 

 case the first entry is for the third ancestral generation and is i. 

 Turning to the table for the third ancestral generation we find 

 that iov A^=i,Z=.i2.^oo. Thus we may write at once, ^2^ 12.500. 

 For the fourth ancestral generation the total is 2 From the 

 table for this generation it is seen, on the second line of this 

 table, that Z= 12.500 when ^=2. Hence, Z3= 12.500, 



*Used merely for convenience to save printing the longer expression. 



