256 
REV. J. T. GULICK ON DIVERGENT EVOLUTION 
degrees of Segregation. If we make c = yl-y or yyYo, we 
find that Half-breeds = Pure-breeds, wliile tbe latter are con- 
stantly decreasing, wbicb shows that imperfect Positive Segre- 
gation, without tbe aid of some quality like Segregate Pecundity, 
cannot prevent a species being finally fused with other species, as 
long as the whole number of each successive generation does not 
increase. 
Let us now consider cases in which the Segregation is incom- 
plete but Segregate Pecundity comes in to modify the result. 
Let M = 2, m— 1, c= T 1 0 -. Substituting these values in our 
formula, we shall find that the sum of the infinite progression is 
§=y§. And M — Mc = -J o, which makes the half-breeds = the 
pure forms Xm; and cm = T Y- Let M=2, m— 1, c= T y-o; 
then Half-breeds = Pure forms Xy-Jy-. Let M = 2, m— 1, c—\\ 
then the infinite progression = 1, M — Mc=l, and the pure forms 
in each generation will equal A, aud the half-breeds A x y. 
Therefore Half-breeds = Pure-breeds x 
Let M=3, m= 2, c = \ ; theu the sum of the infinite pro- 
gression^, and the Half-breeds = £ x 2 x A(M — and 
the Pure-breeds = 1 x A(M— Me)' 1-1 ; therefore Half-breeds = 
Pure-breeds x f . 
Let M=3, ni= 2, c— § ; then Half-breeds = Pure-breeds x f . 
Let M = 3, m — 2, c=\ ; then Half-breeds — Pure-breeds x f. 
Let M=3, m= 2, c = i; then Half-breeds = Pure-breeds x 
Let M=3, m= 2, c= T Y; then Half-breeds = Pure-breeds x-^-. 
Let M=3, m= 2, c = yjyo 5 then Half-breeds = Pure-breeds 
Simplified Formulas for the Proportions in ivliich Half-breeds 
and Three-quarter-breeds stand to Pure-breeds ivhen all are 
equally vigorous. 
From Table III. we learn that 
Wliem (1— 2c)?;i is less than M — Me, the series within the brackets is a de- 
creasing geometrical progression, and we may obtain the value of the whole 
Table IV. 
H me 
1 
P~M— Mc X 
(1 —2 c)m 
H-Me 
