INHERITANCE, WITH SPECIAL REFERENCE TO MENDEL'S LAWS. 63 



(i u + i^)" is at 1 + |-n, and its total frequency J\ = 4" X 4" X c n> , t ; 

 the mean of the second binomial, or 



the meaii of the third biuomial, or 



the mean of the (i + 1 )"' binomial 



The total frequency is accordingly 



= 4" X 4"c ;v ,, 3"-. 



Hence if ?>i, be the distance from the same origin of the mean of the above 

 system of binomials 



; X 3 



4. 4. 2- -"^ 



1.2.8...4 



i 4- i 4. ~ 4. 



2 / "J" 



Now 



"-' = 1 1 + 2 (n - s)x + 2 2 (!LrLH*L 



L Zi 



Multiply by ar, differentiate both sides and divide by 2, finally putting x I, and 

 we find 



3-* + (n - s) 3"-'- 1 SB 1 + 2(n - s) f 



1 . 



| 4-... 



, 



n - A- n - s 



1.2.8...* 



or 



Hence we deduce 



/! X 3"-'w f =/! (3"-' + (n - s) 8 s -'- 1 + 4i3"-'}, 







W, = 1 -f | 



