No. 632] CI11ASMATYPE AND CROSSING OVER '205 



duced, however, to show that such torsion leads to double 

 ring-formation by a process of chiasmatypy. On the con- 

 trary, the evidence thus far indicates that the torsion is 

 undone as the prophases advance ; and it is a significant 

 fact that in these same twisted rings the free ends of the 

 chromatids (forming the lateral arms) show the typical 

 relation as described above, giving the appearance of a 

 chiasma at each end (as in Fig. 3 E, F, or 5 II). 4 Such 

 "chiasmas" (like those seen at the junction of two rings) 

 are not for a moment to be confused with the appearance 

 of crossed threads given in side views of actually twisted 

 rings. 



Such is the contradiction— at first sight it seems ir- 

 reconcilable — between Janssens's conclusions and those 

 of other investigators of these tetrads. These latter re- 

 sults, in particular those of Kobertson and of Wenrich, 

 are supported by very detailed and precise studies ; and 

 my own observations, particularly on the double crosses, 

 are altogether in favor of their conclusions. Until J ans- 

 sens's evidence is before us in greater detail it remains 

 to be seen whether the contradiction really is as great as 

 it now appears. In the meantime we may briefly con- 

 sider certain possibilities which may help to define the 

 issue more clearly. 



The conflict of results has not, I think, grown out of 

 the fact that Janssens has worked with a different type 

 of compound ring, though this is possible, nor can we 

 assume that he has not reckoned with the results of other 

 observers. I incline to think that the contradiction may 

 be in the main one of theoretical interpretation rather 

 than of known fact ; for in theory all the observed facts 

 may quite logically be interpreted as the result of achias- 

 matype that has been completed at a stage prior to the 

 ring-formation. Specifically we might assume that a 

 cross-over has earlier been completed at each node in the 

 series, causing an exchange of two longitudinal halves in 



4 See for instance Granata ('10, Fig. 29), Robertson ('16, Tigs. 1506, 

 175), Wenrich ( '17, PI. I, Figs. 8, 9), and Mohr ('16, Fig/ 131). The same 



