142 THE QUANTITATIVE METHOD IN BIOLOGY 



the value (frequency) of each letter (simple event) being |. 

 this way 27 terms (sorts of seeds) are obtained (see below). 



In 



Remark (compare Remark, p. 138) : According to the principle of segrega- 

 tion, 8 sorts of germ cells of each sex are produced by the plants raised from 

 the Fj seeds — viz. ABC, aBC, AbC, ABc, Abe, aBc, abC, abc. 



The (5 germ cells being united at random with the 9 germ cells, the result is 

 the same as if two dice I. and II. with eight faces each (for instance, two regular 

 octahedra) were cast successively, the 8 sorts of germ cells being marked on the 

 faces of each die (Die I. being S and Die II. being 9 ). All the possible events 

 are found by working out 1 



(ABC + aBC+AbC+ABc+Abc + aBc + abC + abc)^ 



the value (frequency) of each term being (i)'=J. 



We obtain in this way 64 terms, which are reduced to 27. The latter are 

 the same as those obtained by working out 



(A +0]" xiB+byxiC + c)" ■■ 



The 27 terms are : 



A^b^C^ 

 a^B^C^ 

 AWc^ 

 a^B^c^ 



sum: 



■FT 



2AaB^C^ 



zA^BbC^ 



2A^B^Cc 



2AaB^c^ 



zA^Bbc^ 



2Aab^C^ 



2A^bKc 



2amba 



2a^BKc 



2Aab^c^ 



2a^Bbc^ 



2a%^Cc 



sum = If 



4AaBbO 



4AaB^Cc 



4A^BbCc 



4AaBbc^ 



4Aab^Cc 



4a^BbCc 



SAaBbCc 



value : -A 



■rr 



sum: If 



sum of the 27 terms = |f = 

 I (certitude) 



From these 27 terms (Fj seeds) we may draw the same in- 

 formation as from the 3 terms in the first experiment ((i)-(7), 

 p. 120) and from the 9 terms in the second experiment (p. 138) . 

 By analysing the 27 terms successively the reader may easily 

 find in each of them the information aUuded to. Therefore I 

 Umit myself to the following remarks : — 



FIRST REMARK : Since the factors A, B and C are domi- 

 nant, in all the terms in which one of them coexists with the 

 recessive of the same pair, the recessive property is latent. 



1 Each octahedral die represents a germ cell (S or 9 ) in which the 8 com- 

 binations of all the factors of both parents a and p, and thus the factors 

 themselves, coexist. In this way, instead of 16 sorts of germ cells (8 of each 

 sex), only 2 sorts (i sort of each sex) are needed. Compare the tetrahedra, 

 p. 138, Remark. 



2 This may be easily demonstrated in the following way : — 



(A+a)''x{B+b)'x(C+c)^=UA+a)(B + b){C + c)Y ,^ , ,, 



[(A+a) {B + b) {C+c)Y={ABC + aBC+AbC+ABc+Abc + aBc + abC + ai!cf 



