THROUGH CUMULATIVE SEGEEGATION. 



263 



Table VIII. 



Simplified Formulas, giving the Froportions 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— 2c)my \ 



When the numerator, {l—2c)7nv, is less than the denominator, MV-MVc, 

 the sum of the whole series within the brackets may be obtained in accordance 



with the formula 8=^-^, in which S = the sum of the series, a=the first 



term, and g' = the constant multiplier. 



II_ mvc 1 

 P^MY-MVc^ {\-2^v 

 MV-MVc 



_ mvc MV— MY g 



~MV-MYc^MV-MYc-mi;+2wyc 



=M.Y-mvr{2mv-MN)c (Formula 1) 

 Applying the same method to the formula in Table VII,, we find that 



T_H m'v'c 



p- p X ^ X MV-7WV + (2/?i'y' - MVK 



T_H 2m'v'c 



•'• P~P^MV-wV+(2mV-MV)c' 



and 



T _ 2m'v'c 



U"^M.Y-m'v'-\- {2m' v' -M.Y)c ^ ^ 



If M=10, m=5, m'=5, Y=l, v = j^j;, v'=:yV» c=tV> 



^ Toff T§ff T^ff_ 4 50 _ 9 _ 1 . 



then p = — I p5_io>> 1 =ioo_45_ 1 =-^-s?oo-iSff-T7 , 



J- '9-— lO-rUo -90 90 9ff 



and (as m—m\ and v—v') 



T „H , ^T H T , , , 



g=2p=2rVi=^ ; and-p^p XJJ = AX^=TV 

 If M = 10, w=10, w'=10, Y = \, v=^\, i;' = 9V, c=to. 



HI 1 



tufin ^ ^ = 1 • 



l/llDll p 10l/'20 10^ 1 TOO 101 2 10 ^2' 



^ 9' 9ffiV9o '9VTff -^O" 9DT^9 90 



T TUT 



and g = B\=7V; and -=pXg = 77'8^. 



In this latter case, where the Vigour of Hybrids is tV t^iat of Pure-breeds, 



while their Fecundity is equal to that of Pure-breeds, we find p =§-2, 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 that of Pure-breeds, 

 while their Vigour is equal. 



