A. H. Trow 315 



In these experiments there is reduplication between M and S of the 

 form 7:1:1:7; but M and D and S and D show no reduplication and 

 give each the normal ratio 1:1:1:1. 



We may now consider the more important case, where there are 

 three factors A, B and C and reduplication between A and B in the 

 form n : 1 : 1 : 71, and between A and C in the form m : I : I : m. 



The gametic series when A and B are alone considered would be 



nABC + nABc + lAbC + 1 Abe + laBC + laBc + wabC + nabc. 



To secure reduplication between A and C as well, and of the form 

 m : 1 : 1 : w, the terms involving AC and ac must be multiplied by m ; 

 the series thus becomes 



w/nABC 4- nABc + /?iAbC + 1 Abe + laBC + maBe + nabC + wmabc. 



Extracting the three pairs separately from this series, we get 



AB : Ab : aB : ab :: nm 4 n : m + 1 : 1 + m : m + rnn 



AC : Ae : aC : ac 



BC : Be : bC : be 



From this procedure, it is clear that reduplication between A and B 

 and betw^een A and C involves reduplication between B and C. It is 

 worthy of note that this derived or secondary type of reduplication has 

 apparently been entirely overlooked, especially as there is good reason 

 to suppose that it has already been observed experimentally. Moreover, 

 it belongs to a fundamentally different series, — of the form p • q ' g '■ p. 



Gregory's interesting results on Primula sinensis illustrate this case. 

 In the MSG group of experiments, where M and S have the same 

 significance as above, G represents green stigma, dominant over g — red 

 stigma. The best numerical results are given by the crosses in which 

 the Fi — MSGmsg was crossed by the triple recessive msgmsg. In 

 such cases it is clear that the ratios of the zygotic series coincide with 

 those of the Fi gametic series. The results may be grouped as 



follows : — 



MS Ms mS ms 



Nob. found 53 3 6 40 



Expectation on ratio of 7:1:1:7 45 6 6 45 



