TABLE IV WITH FORMULA. 181 
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 
a 8 
III, we shall find that the sum of the infinite progression is = = —. 
And M — Mc = = which makes the half-breeds = the pure forms x 
I 
cm; and cm = a Let M = 2, m = 1, c = —; then half-breeds = 
10 100 
I I iene 
pure forms x —-. Let M= 2, m = 1, c =~; then the infinite 
100 2 
progression = 1, M — Mc = 1, and the pure forms in each genera- 
tion will equal A, and the half-breeds A < - Therefore, half-breeds = 
I 
pure-breeds x -. 
TABLE 1V.—Simplified Formulas for the Proportions in which Half-breeds stand to 
Pure-breeds when all forms of Segregate Survival are considered. 
In each formula MM 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 ( (7—2c)m , (r1—20c)m)2 (6 13 °F 1) | 1 
SEs | ee =e Achaea price Wailccile. 
PYM =Me [ M — Mc | “@ Mc J L | Gaia 
When (1 — 2c)m is less than IZ — 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 = sey Applying this 
formula we have 


ele Aan Oe I 
P”~ M—Mc * (1— 2c)m 
1 ~"M—Mc 
fab UG NG M— Mc 
~ M—Mc” M—Mc—mz+ 2mc 
mc 
VM meF ene ee ae Formula (1) 
mc 
En ==0P Mae Gnaie os Formula (2) 

