TABLE IV WITH FORMUIvA. 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 - = —• 



18 

 And M — Mc = — , 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 = 1, c = ~; then the infinite 



'^ 100 ' 2 



progression = i, 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 -. 



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 



//_ mc r , (i — 2c)m f i — 2c)m 1 ^, T 1 ^ , f 1 1 



P-M-Mc'^[^'^ M — Mc^ ^M—Mc \ + }^ J U )' 



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 



formula we have 



H _ mc I 



P " M — Mc ^ (i — 2c)w 

 ^"^ M—Mc 



mc M — Mc 



X 



M — Mc M — Mc — m+2mc 



= iTf -rr? jrjT" Formula (i) 



M — w+(2m — M)c ^ ^ 



H = P X "tt? X"7 jTrC" • • • • Formula (2) 



^M — m+{2m — M)c ^ ' 



