STUDIES ON THE GENETICS OF FLOWER-COLOURS, ETC. 
115 
theoretical. 1 So it is clear that we have here to deal with a case of linkage 
belonging to either one of the two above series or at least to some series 
similar to it. 
To sum up : the cross magenta X orange has segregated in F, in the 
ratio of 3 magentas and 1 orange, because It and 7> are completely linked 
together.; in the linkage became partial in some magentas, and consequently 
their i'bofispring contain reds besides magentas and oranges. 
If we will adopt the chromosome theory of Morgan we have, for instance, 
the gametes CJRP, CUb, Crli, Crb in the ratio 5‘5 :1:1: 5"5 (5'5 being 
the average of 5 and 6 in the two series of linkage above cited', and 
consequently 15-4% cross-overs and 84 '6% non-cross-overs respectively. 2 3 The 
following consideration may then be made. The factors It and 7> are 
located very near in the same chromosome, and consequently closely linked 
together as the rule. But sometimes the crossing-over takes place, so that 
they come to lie in two different, though homologous, chromosomes, the ratio 
of cross-overs against non-cross-overs being found to be 15*4 : 84*6. 
The facts which point out towards the variation of the linkage ratio of 
certain factors have been sometimes observed till now. To cite some instances, 
Gregory in his researches on Primula sinensis, has found in the .TVofspring 
ex ills x tilS (magenta and long-styled by red and short-styled) the complete 
linkage between 3L and S, whereas in those ex 31 S X ms (magenta and short 
by red and long) the partial one belonging to the series 7 : 1: 1: 7 has been 
observed between the same factors. 1 Baue, in his experiments in Antirrhinum 
mo jus, has found in the 7i-oflspring ex FFGG xffgg (red and piduratum 
flower by non-red and non-piduraturn ) that the linkage ratio between F (red) 
and G ( piduratum ) is variable in different cases (3 : 1: 1: 3, 4 : 1: 1: 4, 
7 :1:1: 7, or even 1: 1:1: 1, i. e. normal). 4 In Lathyrus odoratus Bateson 
1 S. Pearson, Tables for Statisticians and Biometricians, Cambridge, 1914, Table Nil. 
2 If we calculate the linkage ratio according to the formulas of Emerson (Amer. Natur¬ 
alist, Vol. 50, 1916, pp. 1411-1429) we have from the corrected phænotypic ratios CUB : 
CUb : CrB : Crb = 178-75 :20 : 20 :46-25 (from the actual 181: 20 : 20 : 64-20 = 181:20 : 20 : 44) 
r = 6-80 and .S' = 1-34 and consequently the linkage ratio =r/s = 5-0 :1. 
3 Journ. of Genetics, Vol. 1, 1911, p. 129. 
4 Zeitsch. f but. Abstamm, u. Vererbungslehre, Bd. 6, 1912, p. 204 ff ; and Einleitung in die 
