TABLE IV WITH FORMULA. l8l 



Let us now consider cases in which the segregation is incomplete, 

 but segregate fecundity comes in to modify the result. Let M = 2, 



Substituting these values in our formula from Table 



9 18 

 III, we shall find that the sum of the infinite progression is - = 



1 8 

 And M Me = , which makes the half-breeds = the pure forms x 



cm; and cm = . Let M 2, m = i, c = ; then half-breeds == 



IO 100 



pure forms x . Let M = 2, m = i, c = ; then the infinite 



progression = i, M Me = i, and the pure forms in each genera- 

 tion will equal A , and the half-breeds Ax. Therefore, half-breeds = 



pure-breeds x 

 2 



TABLE IV. Simplified Formulas for the Proportions in which Half-breeds stand to 

 Pure-breeds when all forms of Segregate Survival are considered. 



In each formula M may represent the ratio of those coming to 

 maturity in each generation of the pure-breeds, and m may represent 

 the ratio of success or failure of the cross-breeds in coming to maturity 

 in each generation. 



From Table III we learn that 



H mc f 4. 2c)m fi 2c)m i 2 , ri 3 _,ri i 



P~M-Mc X ~ M Mc^ \ M Mc \ 



*- L J^JLJJ 



When (i 2C)m is less than M Mc, the series within the brack- 

 ets is a decreasing geometrical progression, and we may obtain the 



value of the whole series by the formula S = - . Applying this 



I T 



formula we have 



