No. 631] FACTORS OF HEREDITY 



105 



small values but not of the large ones. If the validity of 

 the evenly curved figure were accepted, it would in no 

 way disagree with the finding of a linear arrangement of 

 the genes, but would merely substitute a curved line for 

 a straight one. In a really non-linear figure, such as 

 shown in Fig. 2, the relations between the smaller dis- 

 tances would be (if anything) less of a linear type than 

 the relations between the larger distances,— factors 

 further apart in a thick rod, for example, would have to 

 be more in line than those near together. The fact that 

 the opposite relation holds in the actual data shows con- 

 clusively that the factors are in some sort of a line. 

 There is an a priori objection, however, to accepting a 

 curved line as an explanation of the linkage relations, in 

 that it is very difficult to imagine a plausible set of con- 

 ditions in the chromosome which would hold the factors 

 rigidly in this curved' line but which would at the same 

 time determine the number of separations between the 

 factors according to their direct (straight) t distances 

 from each other, instead of according to their distances 

 along this line. But, quite aside from a priori reasons, 

 there is an experimental result absolutely fatal to the 

 curved line " explanation"; this consists in the finding of 

 those classes which are termed by the Drosophila work- 

 ers " triple crossovers." In the case of these classes the 

 separations are of such a type as to require the assump- 

 tion of a break in the curved line at three points simul- 

 taneously. As it is obvious that a break in only one plane 

 could not cut the curve at more than two points, the triple 

 crossovers therefore would have to be due to a break in 

 more than one plane. The occurrence of breaks m more 



