No. 63G] SIIOBTER ARTICLES AND DISCUSSIOX 79 



those for long style (1), rod flower (r), and red stigma (s), 

 allelomorphie respectively to short style (L), magenta flower 

 (R) , and green stigma (S) . The order of the loci, as based upon 

 3684 individuals, was 1 r s; the per cent, of crossovers in the 

 first region (between 1 and r) was 11.62, and that in the second 

 region (between r and s) was 34.02. These relations, shown in 

 a map, are as follows: ^ ^^^^ The per cent, of 



double crossovers observed in the experiment was 2.52. Accord- 

 ing to the formula given above, the number of double crossovers 

 to be expected if crossings over were independent would be 

 11.62 per cent. X 34.02 per cent., or 4.0 per cent., which, as I 

 noted in the account of the case, exceeds the observed proportion 

 of 2.52 per cent. This difference, then, between the observed 

 and ''expected" values in Primula would indicate that inter- 

 ference existed here, but, as I further stated, the difference was 

 not significant because of the uncertainty which had attended 

 the classification of flower color in the plants with the gene for 

 green stigma. This gene caused the flower color to be lighter 

 and obliterated somewhat the distinction between red and 

 magenta. 



In the plants with red stigma, however, the flower color was 

 dark enough to render entirely certain the classification in regard 

 to red and magenta ; these plants, considered alone, would there- 

 fore furnish reliable data for determining the interference. I 

 stated that, when these reliable plants alone were taken into 

 account, no evidence of interference was to be found; but this ' 

 conclusion was due to a numerical error in the calculation of the 

 "expected" number of double crossovers, for I now find, in 

 going over the figures, that the "expected" number is consid- 

 erably higher than the number observed. Among the 1876 

 plants with red stigmas, there were 210 crossovers, or 11.2 per 

 cent., in the first region, and 688, or 36.7 per cent., in the second 

 region. The "expected" number of double crossovers is there- 

 fore 11.2 per cent. X 36.6 per cent., or 4.1 per cent. There were 

 54 double crossovers observed, or 2.9 per cent., giving a coin- 

 cidence ratio of 2.9:4.1, or .7, instead of 1.00, which would be 

 tho ratio in the al)S(Mice of interference. The difference between 

 tlic '•t'xiMrtfd" ;jiul ohserved numbers is beyond the limits of 

 random sampling, and it must therefore be concluded that in- 

 terference exists in Primula. Although no reliance can be 



