THROUGH CUMULATIVE SEGREGATION. 
263 
Table VIII. 
Simplified Formulas , giving the Proportions in which Half-breeds 
and Three-quarter-breeds stand to Fure-breeds when we have 
both Segregate Fecundity and Segregate Vigour. 
From Table VI. we learn that 
H_ mvc ( (1—2 c)mv \ 
p-MV— MV^ X i 1+ MV^MVc + ■ ■ ■ )■ 
When the numerator, (1—2 c)mv, is less than the denominator, MV— MVc, 
the sum of the whole series within the brackets may be obtained in accordance 
with the formula S=^ — — , in which S = the sum of the series, a=the first 
term, and q = the constant multiplier. 
H mvc 1 
P MV— MVc X (1— 2c)mv 
_ MV — MVc 
mvc MV — MVc 
MV — MVc X MV — MVc — mv-\-2mvc 
mvc 
"“MV— mv-\-(2mv — MV)c ^ oimua ) 
Applying the same method to the formula in Table VII., we find that 
T H _ m'v'c 
y 9v 
P P MV— m'v' + (2m'v' — MV)c' 
T H 2 m'v'c 
P — P X MV— m'v'+(2m'v' — MV)c ’ 
( 2 ) 
and 
T 
2 m'v'c 
H MV— m'v'+(2m'v'— MV)c 
If M=10, m= 5, m'= 5, V=|, v = T V, v ' = T V> c= ts, 
TT -Sl _s_ -A 
then — — LAS UL° IAS- 
P 10 _5__J_/'iO 10\1 100 4 3 1_ .5 4 
■*- lFTuo ^9 - J 1 O "9 O" 9 0 Oo 9 0 
and (as m—m\ and v=v') 
T H T H T 
g=2|=2 T V=| ; and^=gxg=Axi=* 
( 3 ) 
then 
10 1 01/20 1 0\J_ 1 00 1012 10 
9 V9 0 "9 710 9 O M 9 0 0 0 
H T 
P — P X H~ 
TUT 
tt 5 and 5 = b Xs = jtW 
In this latter case, where the Vigour of Hybrids is T V that of Pure-breeds, 
while their Fecundity is equal to that of Pure-breeds, we find p = f, > which is 
the same result as that given in the 8th line of the last column of Table V., 
where the Fecundity of cross unions and of Hybrids is T V that of Pure-breeds, 
while their Vigour is equal. 
