The Behavior of the Chromosomes as Studied through Linkage. 243 



next smallest expectation was that for YWM, and this combination gave 

 the strongest interference. The longest distances involved were in the 

 combination YVE, and this gave the weakest interference. The signific- 

 ance of this relation for the chromosome view is very great, for it 

 means that one cross-over tends to prevent the occuiTence of another 

 one close to it, but that this tendency decreases as we get further away 

 from the locus of the first cross-over. If crossing over depends upon 

 a twisting of the chromosomes so that genes in the same chromosome 

 may come to lie on opposite sides of the lireak, then it is evident that 

 the twist must be tighter in order to bring about double crossing over 

 in short distances than when longer distances are involved. Further 

 study of the phenomena of interference should throw much light on the 

 nature of the chiasmatype and on the whole question of linkage. For 

 the present, however, the matter must be left until we have obtained 

 more reliable and extensive data. 



The reason that in table TI, we found observed percentage of 

 cross-overs to be less than calculated distance is now apparent. For 

 when two cross-overs occur in the same chromosome pair the effect 

 upon genes lying on opposite sides of the interchanged segments will 

 be to leave them in the same relation to each other as before. There- 

 fore a double cross -over between two loci will be classed as a non- 

 cross-over unless we can follow the behavior of an intermediate locus 

 at the same time. This will tend to make the observed percent of cross- 

 overs too small. Moi'cover, since double crossing over is much less likely 

 to occur in short distances than in longer ones, this effect will become 

 more marked when longer distances are involved. These are exactly the 

 relations which we found to exist in table II. It was these consider- 

 ations which led me always to use the cross-overs between adjacent loci 

 as a basis for calculations, since these are less likely to be complicated 

 by double crossing over. But even so this difficulty is not entirely 

 overcome, since certain unpublished data involving intermediate loci show 

 that double crossing over occurs witMn the distance WV. 



Triple Crossing Over. 

 There is one case reported at the end of this paper (table X^TI) 

 in which four pairs of sex-linked genes are involved. Such a cross 

 gives an opportunity for triple crossing over — i.e., the occurrence of 

 three cross-overs in the same chromosome pair. This did not occur, as 

 is shown in table Y, and was scarcely to be expected in the numbers 



