MEASUREMENT OF VARIABLE PROPERTIES 135 



and the $ germ cells also 500 D + 500 R in number,^ the 500 D 

 $ being united at random with 500 $ , 250 D $ meet 250 D ? 

 and 250 D $ meet 250 R $ , and in a similar way 250 R $ meet 

 250 D $ and 250 R $ meet 250 7^ $ . Four sorts of com- 

 pound events are equally possible, and therefore four sorts of 

 seedsKFg generation) are produced in equal numbers — viz. 



250 Z) ^ X 250 Z) ? = 250 seeds DD 



(250 Z) ^ X 250 iR ¥ = 250 „ DR) 



1250 i? ^ X 250 Z) ¥ = 250 „ RD\ 



250 i? ^ X 250 i^ ¥ = 250 „ RR 



All the events under consideration are the same as if a very 

 large number of white balls D and an equal number of black 

 balls R were brought into an urn and taken one by one in 1000 

 series of two, the first ball of each series being $ and the second 

 ball ¥ . All the possible events are expressed by the trinomial 

 obtained by working out {D-\-RY, in which D = R = \ (see § 98) 

 — viz. 



(Z) + ie)2 = Z)2 + 2Z)ie + i?2 



This trinomial gives us complete information about the 

 hereditary possibilities and visible properties of the 1000 seeds 

 of the F2 generation and about the frequency of each sort of 

 seeds (compare § 94, (i)-(7), p. 120) : 



(i) Each letter represents a simple event ; in other words, a 

 germ cell (J or ¥ ) containing a factor D or R. 



(2) The numerical value of each letter is the expression of the 

 frequency of the corresponding simple event ; in other words, 

 of the relative number of existing germ cells of each sort 

 (D = R = o'^o of the total number). 



(3) From the number of terms we know how many sorts of 

 compoimd events are possible (the order of succession of the 

 simple events being neglected) '^ ; in other words, how many 

 sorts of seeds are produced. Three sorts exist, but as often as 

 a germ cell D meets a germ cell R the coexisting simple events 

 (factors) produce a resultant by which the primordium D becomes 

 visible and R latent. Therefore it is impossible to distinguish 

 Z)2 from DR (or RD) and (with regard to the visible properties) 

 only two sorts of seeds (round or wrinkled) exist. (Compare 

 examples (C) and (D) in § 102, p. 130.) 



(4) The numerical value of each term represents the fre- 

 quency of the corresponding compound event ; in other 

 words, the relative number of seeds of the corresponding sort. 



1 The figure 500 is taken arbitrarily instead of x. 



' This means the sexual difference being overlooked : the first simple event 

 of each pair (first ball or germ cell) is supposed to be 6 , the second 9 . 



