92 Rediqilieatioii Series in Sweet Peas 



BEL X be I cross. Also there is evidence for supposing that the 

 "repulsion" reduplication is of the same value as the "coupling" re- 

 duplication between two given factors. We shall assume then for 

 argument that the reduplication between B and E is of the value 

 1 : 63 : 63 : 1. For B and L (p. 84) the experimental data are closely 

 approached by a series 10 : 1 : 1 : 10. We have therefore the 3 series : 



(c() B and E— 1 : 63 : 63 : 1, 

 (/3) E and L^ 1 : 12 : 12 : 1, 

 (7) B and L— 10 : 1 : 1 : 10. 



If we treat (a) and (/S) as the primary series the value of (7) 

 deduced theoretically should be 



(63 X 12) + 1 : 63 + 12 : 63 + 12 : (63 x 12) + 1 



i.e. 1001 : 1 : 1 : lO'Ol, 



which is a remarkably close approximation to the experimental pro- 

 portions. 



It will be noticed that in each of the above cases we have chosen 

 as our two primary .series those in which the reduplication values are 

 highest. This was also done by Trow in his analysis of Gregory's 

 primulas. It is only in this way that the hypothesis will work, for, as 

 can be readily shewn, the value of the redujjlication in the secondary 

 series must always be less than in either of the two primary series 

 from which it is derived. 



Let A, B, and C be the three factors concerned, and let the redupli- 

 cation series for 



A and B = p : 1 : 1 : p (a), 



A and C=p-\-x:\ -.1 : p + .c (/S), 



where /; > 1 and x is positive. 



Then the series for 



B and C=p{p+ x) -1-1 : 2p 4- .r : 'Ip + ,/• : p (p + ./) 4-1 (7)- 



It is required to shew that 



2)jj} + x)j^l p 



2p + .v r 



i.e. p" + px -i- I < 2/r +j)x, 



i.e. 1 < p". 



which is evident since on hypothesis /) > 1. 



