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THE AMERICAN NATURALIST [Vol. LIV 



It would have been inconvenient to represent the ob- 

 served linkage results for this factor by proportionate 

 lines in the model, for, according to the results, lethal 2 

 would have to be placed at 9.6 from w and 17.7 from v, 

 thus making the distance between w and v not greater 

 than 27.3, whereas the established distance between w 

 and v themselves is as much as 30.5 ; similarly, although 

 only 9.6 from w, lethal 2 must be placed only 15.5 from 

 m, although w and m are known to be at least 33.2 units 

 from each other. Either the wv and wm lines would 

 have to be considerably curved, therefore, or the lines 

 between lethal 2 and the other factors would have to be 

 stretched in some way— perhaps dotted lines would meet 

 the difficulty! 



Although any scheme of representing linkage results 

 by exactly proportionate distances encounters the con- 

 tradictions discussed above, it is noticeable that nearly 

 all the most extreme departures from a plane curved 

 figure (that figure which comes nearest to representing, 

 by strictly proportionate distances, the ratios resulting 

 from that type of linear linkage which actually exists) 

 occur in the case of factors whose linkage ratios are dis- 

 torted by differential viability or difficult classification. 

 This is why the factors A, fr, sh, cl, bi, and the lethals 

 stand out from the fairly regular curved line which 

 Castle's models would otherwise conform to. The first 

 two of the above factors are uncertain of classification, 

 the others mentioned affect viability markedly. In the 

 case of nearly all the remaining factors of the model, 

 even though the results were taken from different exper- 

 iments, it was nevertheless found, when the data were 

 plotted, that they agreed pretty well with the expecta- 

 tions based on linear linkage. Moreover, the better the 

 experimental conditions are in regard to viability, cer- 

 tainty of classification, and size of counts,— the more 

 closely are these synthesized results of individual ex- 

 periments found to coincide with the linear findings of 

 experiments involving three or more points simulta- 



