MancJiester Memoirs, Vol. xlviii. (1904), No. 34- 5 



imac^ine for the sake of simplicity that each plant produces 

 4 seeds), we see that the proportions of Z^'s, DR's, and R's 

 in successive generations are as follows : — 



Generation. 



D. DR. R. 



D. 



Ratios. 

 DR. 



.ff. 



I. 



I 2 I 



(4 +2 4 2 + 4) = 



I 



2 



I 



2. 



646 



(24 + 4 8 4 + 24) = 



3 



2 



3 



3- 



28 8 28 

 (112 + 8 16 8+112) = 



7 



2 



7 



4- 



120 16 120 



(480+16 32 16 + 480) = 



15 



2 



15 



5- 



496 32 496 



3T 



2 



31 



The ratio of Z?'s, jDR's, and i^'s can be foretold in any 

 generation n, by this formula : 



n : DR : R 

 2"- I : 2 : 2"— I 



" In the loth generation, for instance, 2"— i = 1,023. There 

 result, therefore, in each 2,048 plants which arise in this 

 generation J, 023 with constant dominant character, 1,023 

 with the recessive character, and only two hybrids." 

 (Bateson '94, p. 59). 



(4) Mendel's theory to account for his results. 

 Mendel knew that green-seeded peas bred true, when 

 self-fertilized or cross-fertilized by other green peas ; and 



