256 RET. J. T. GULICK ON DIVERGENT ETOLrTION 



degrees of Segregation. If we make c=j^ or xitVoj "^^ ^^i^^ 

 find that Half-breeds = Pure-breeds, while the latter are con- 

 stantly decreasing, which shows that imperfect Positive Segre- 

 gation, without the 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, 7n = l, c^-^^-. Substituting these values in our 

 formula, we shall find that the sum of the infinite progression is 

 f =|-§. And M— Mc = -Jf, which makes the half-breeds = the 

 pure iovmsX cm; and cm=^^. Let M=2, m=l, c=y^ ; 

 then Half-breeds =Pure forms Xy-J-g-. Let M = 2, m = l, c=^ ; 

 then the infinite progression = 1, M — Mc = l, and the pure forms 

 in each generation will equal A, and the half-breeds Ax-|-. 

 Therefore Half-breeds = Pure-breeds x 



Let M=3, m=2, c= ^ ; then the sum of the infinite pro- 

 gression = l, and the Half-breeds= i~ x 2 x A(M — Mc)?i-i, and 

 the Pure-breeds=lix A(M— Mc)'^-i ; therefore Half-breeds = 

 Pure-breeds x f . 



Let M=3, m=2, c=^', then Half-breeds = Pure-breeds x |. 



Let M = 3, m = 2, c=J ; then Half-breeds= Pure-breeds X f. 



Let M=3, w=2, c = J ; then Half-breeds = Pure-breeds X f. 



Let M=3, m=2, c=po ; then Half-breeds = Pure-breedsX-i^. 



Let M=3, m=2, c=j^ ; then Half-breeds = Pure-breeds 



Table IV. 



Simplified Formulas for the 'Pro]^ or lions in which Half-hreeds 

 and Three-quarter-breeds stand to Fure-hreeds when all are 

 equally vigorous. 



From Table III. we learn that 



Whem (1 — 2c)m is less than M-Mc, the series within the brackets is a de- 

 creasing geometrical progression, and we may obtain the value of the whole 



series by the formula 8=^^^. Applying this formula we have 

 H mc 1 



