154 MODES OF RESEARCH IN GENETICS 



paper has given a general formula for the deter- 

 mination of the percentage of homozygotes (which 

 he calls the coefficient of homozygosis) after n 

 generations of inbreeding. His results are as 

 follows : 



"Let X = the coefficient of homozygosis, 



n = the number of inbred generations (the 

 number of times successive brother 

 by sister mating has occurred), 



/ij /2j /sj etc., = the successive terms of the Fibo- 

 nacci series (thus/i = 0, /2 = 1, etc.). 



Then the formula for the coefficient of homozy- 

 gosis is : 



2^"i +/i . 2"-2 + f2 . 9,^-K . . etc. 

 X = 



(The terms in the numerator are continued until 

 the exponent of 2 becomes 0)." 



It is clear that for further analysis of the problem 

 of inbreeding there will need to be much more com- 

 prehensive work done upon this second phase, i.e. 

 the theoretical Mendelian consequences of the 

 operation of inbreeding. One of the chief results 

 of the present study, in the writer's opinion, is to 

 bring out clearly the importance of a problem 

 which has not yet been considered at all in any of 

 the discussions of the subject which have hitherto 

 appeared. This problem may be put in the follow- 

 ing way : 



What is the mathematical probability that the 



