142 THE QUANTITATIVE METHOD IN BIOLOGY 



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

 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 Fi seeds— viz. ABC, aBC, AbC, A Be, Abe, aBc, abC, abc. 



The 6 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 6 and Die II. being 9 ). All the possible events 

 are found by working out ^ 



(ABC + aBC+AbC+ABc+Abc + aBc + abC-habc)^ 



the value (frequency) of each term being (^)^=|^. 



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

 the same as those obtained by working out 



(^+a)2x(B+&)2x(C + c)2 2 



The 27 terms are : 



A^b^C^ 

 a'BK^ 

 A^b^c^ 



o'bK^ 

 a^bH'' 



sum: ^ 



zAaBK'^ 



2A^BbC^ 



2AmKc 



2AaBH^ 



2A^Bbc^ 



2Aab^a 



2A^bKc 



2a^BbC^ 



2a^BKc 



2Aab'^c'^ 



2a^Bbc^ 



2a%Kc 



sum = 



ws 



4AaBbC^ 



^AaBKc 



4A^BbCc 



4AaBbc^ 



4Aab^Cc 



4a^BbCc 



SAaBbCc 



value : -A 



ST 



sum: If 



sum of the 27 terms = f 

 I (certitude) 



^4 



From these 27 terms (Fg 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 alluded to. Therefore I 

 limit myself to the following remarks : — 



FIRST REMARK : Since the factors ^, 5 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 {6 or $ ) in which the 8 com- 

 binations of all the factors of both parents a and j3, and thus the factors 

 themselves, coexist. In this way, instead of i6 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)^=l{A+a) (B+b) (C + c)P 



i{A+a) {B+b) {C+c)Y={ABC-\-aBC+AbC+ABc + Abc+aBc + ahC+dbcf 



