DIVERGENT EVOLUTION THROUGH SEGREGATION. 327 
with this number in the nth generation, and pursuing the same method as was used 
in constructing Table III, we obtain the following series: 
Three-quarter-breeds— 
n—1H 
nth generation =A (MV—MVe) p2e m'v!, 
I— 1 
(n+-1)th generation —A(MV—MVe) p 26 m'v'> (1—2c)m’v' + 4 (MV—MVe)" 26 m!v'. 
= aap iH 
(n+2)th generation =A(MV—MVe) — 552¢ m'ni( (I —2e)m 0) 4 -A(MV—MVe)- pzem'r s< 
n+1H 
(( 1—2c) m'v') + A(MV—MVe) pe m'v!. 
iH n 2, '\ it 
(n+n)th 2 eee sp 2c m'»'(MV—M Ve) ( ae mtUae ) eee 
Pp 
(1—2ce)m! ae (& (1—2e)m ss) oe 
MV—MvVe MV ave) MV—MVe ). 
: Sag uv H 2c m'v! 
In the (n+7)th generation, P=A(MV—M Ve) ; and therefore ——f Be < 
os (emeyee YC eC DY). : 
TABLE VIII.—Simplified formulas, giving the proportions in which Half-breeds and 
Three-quarter-breeds stand to Pure-breeds when we have both Segregate Fecundity and 
Segregate Vigor. 
From Table VI we learn that 
H_ __mve 2e)mv 
= =< , : 
P MV—MVe ( te MVe ) 
When the numerator, (1—2c)mv, is less than the denominator, MV —MVe, the sum 
of the whole series within the brackets may be obtained in accordance with the 
(Tae : : : : : 
formula $ Sm in which S=the sum of the series, a= the first term, and ¢= the 
constant multiplier. 
EAS. mve il 
“PP” MV—MVc*%._(1— 2c) mv 
~MV—MVe 
mve MV—MVe mve 
MV —MVe* MV —MVe— mo+2mre MV — mv--Qmv—MvVje °°) 
Applying the same method to the formula in Table VII, we find that 
TIGEL m'v'c 
PP X2XMVv— mv Om MV)e. 
‘ T H 2m’! v ‘ec 
“Pp PXMV — mo’+@m’—MV)c? = ° (2) 
and 
At: Da Uy ee a. ; 
Hea Magan Om'v— MV )e ae (3) 
: = ~ ov SE op ee 
If M=10, m=5, m’=5, V4, v=, V'= 1s, c= 1, 
H Tho 180 TRO 150 ’ 1 
then : — 3 400——108—12 9 
— l —J 0 5 M 5 4 = 
P — 1,0 —y+43— she TO Ska 45—a0 on 
and (as m—=m/’, and v=’) 
1 al ia bl — 
oe =2;5—}; and — x See 
If M—10, m—=10, m’—10, V=3, v=, V' =, C= 10, 
1 ci 
then = = ou a 5 ss} 
2¢ el ee Cas 
P yy aot (s§—4 2) ro 0 as Cee ag ar d 
a 4b Vee <TH 
° Es | 
and HH y= i); and a =p x Sed 
