148 MODES OF RESEARCH IN GENETICS 



in very convenient form as follows (loc. cit., p. 

 490): 



"Let x = the proportional number of organisms 

 that are pure homozygotes (with re- 

 spect to all the characters considered) , 

 y = proportion that are heterozygotic 

 with respect to all the characters 

 considered, 

 s = the proportion that are mixed, 

 v = the proportion that have any heterozy- 

 gotic characters. 



Then, if n = the number of successive self- 

 fertilizations 

 and m = the number of pairs of characters, 



x 'Kir) ' (1) 



y = (h) mB , (2) 



z = 1 - (x + y); (3) 



2"»_ (2*_ i)« 

 v — 1 — x = * >—, (4) 



At 



With continued brother X sister mating the 

 present writer l has shown that the proportion of 

 homozygotes also increases, in the manner shown 

 in the following table. 



1 Pearl, R. "On the Results of Inbreeding a Mendelian Popu- 

 lation : A Correction and Extension of Previous Conclusions." Amer, 

 Nat., Vol. XLVIII, pp. 57-62, 1914. 



Since this was written a paper by Fish announcing an independent 

 working out of the same point has appeared (Amer. Nat., 1915). 



