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, 



m = i, c = . Substituting these values in our formula from Table 



9 18 

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



o 



18 



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

 10 



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



10 100 



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



100 2 



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

 tion will equal A , and the half-breeds A > - . 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 me \ (i 2c)ui fi 2c)m 1 2 , f 1 3 , f 1 1 

 P = M=Mc X ( l+ W^JIc + [M-Mc] + [\ + [\+\' 



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

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



value of the whole series by the formula 5 = - - . Applying this 



I Y 



formula we have 



M Me M Me m+ 2mc 



_ me 



~Ti~/r~ _i_/ n/r\ ........... Formula ( i ) 



M m+(2m M)c 



H = P x mr~ n^ Formula (2) 



M m + (2m ~ M)c 



