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 = 1, 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 — Mc = — , which makes the half-breeds = the pure forms x 

 10 ' 



cm: and cm = — . Let M = 2, m = 1, c = - -; then half-breeds = 

 10 ' ' 100' 



pure forms x - — . Let M = 2, m = 1, c = ; then the infinite 

 r 100 2 



progression = 1, M — Mc — 1, and the pure forms in each genera- 

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



pure-breeds x 



1 



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 (1 — 2c)m , fi — 2c)m "1 2 , f "I 3 , f ] , ] 



p=m^mc x { i + j^mc + 1 -M=m\ +!J + H J' 



When (1 — 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 5 = — — . Applying this 



formula we have 



H _ mc 1 



P ~ M — Mc x ~_ (i — 2c)m 

 I— M — Mc 



mc M — Mc 



x 



M — Mc M — Mc — m+ 2mc 

 mc 



tj r-7— w> Formula ( 1 ) 



M — w+(2j»- M)c 



mc 



M — m+ (2W — M)c 



H = P x us u?^_ njr\, Formula (2) 



