222 Prnmary and Secondarij Reduplication Series 



paper the series found when only two factors are involved will be called 

 the ' fundamental ' series for those two factors ; following Trow the 

 series observed when three factors are involved will be called the 

 secondary series ; the underlying series calculated from these secondarj^ 

 series will be called the primary series. 



The data obtained from crosses involving three factors have been 

 discussed by other writers from the point of view of the special 

 hypothesis. Owing to the great importance of the subject of coupling 

 and repulsion it seemed to me that it would be interesting to study 

 the observed phenomena by means of the general hypothesis also. 



The most complete account of such crosses is given by Punnett (3) 

 in a recent paper. The following calculations are based upon the 

 data there discussed, and reference should be made to that paper for 

 an explanation of the symbols used in the following account. 



(a) Nature of mating EBL x ebl. 



The equations from which the primary reduplication series can be 

 determined are 



Imn -\- 1 13 



m-\-n 3 

 lmn-{-m 



63, 



which give 



1 =n= 2-1, 



m = 48-3 \ 



These numbers indicate the complicated primary series 



BL : Bl : bL : bl = 21 : 10 : 10 : 21 



BE : Be : bE : be = 483 : 10 : 10 : 483 



EL : El : eL : el = 21 : 10 : 10 : 21. 



These complicated series however approach closely to the simple 

 series 



2 : 1 : 1 : 2 

 52 : 1 : 1 : 52 



2:1:1:2, 



^ It may be noted that if the two smaller observed reduplication series are equal, 

 the assumption that w = 1 cannot be true, for then I = 1. However it is impossible at present 

 to decide whether these two series are in fact equal or not owing to the relative smallness 

 of the numbers. 



