CHROMOSOME STUDIES 255 



(portion of a conjugant between the nodes) crossing over together 

 to the next segment, only one may cross (text figs. XII, XXII). 

 This he assumes to mean that a single original filament (longi- 

 tudinal half of a conjugant) of each chromosome has broken at 

 the point of their crossing (text fig. XIII) and that broken ends 

 of one filament have traded connections with the broken ends of 

 the other (text figs. XIII-XV, XXII, XXVII). That it is 

 unnecessary to assume this, is shown by the fact that we are 

 able to trace all steps in the formation of such 'cross-overs' 

 in tetrads of the ring and cross type back to the stage in which 

 the tetrad consists of a rod split in two longitudinal planes, and 

 consisting of four longitudinal filaments lying side by side 

 (figs. 150-156, 164-168, 173-178). The crossing over of fila- 

 ments results from the tendency of the four-strand rod to split 

 part of the time in the primary plane (/), and part of the time 

 in the plane at right angles to it, the secondary plane (//). If 

 the chromosome be short, but one cross-over occurs and 'a, cross' 

 results (nos. 6 and 8, fig. 150; fig. 156c); if the chromosome be 

 long, two, or, as in the compound chromosomes of Chorthippus, 

 even three cross-overs may occur (figs. 150, lO's and ll's; 155, 

 6's, 9's, lO's and ll's; 156d-156f; 174, 7-11's, 5-9's, 8-10's; 

 175, 176, and 178, 8-10's, 7-11's). This formation of the cross- 

 overs as a result of the opening-out process of the four strands 

 does away with the possibility of a "compenetration graduelle 

 de deux chromosomes au niveau d'un chiasma avec la soudure 

 des filaments qui se touchent les premiers," as Janssens has 

 supposed according to his text figures XIII-XV. 



Many investigators who have worked upon species in which 

 there occurred tetrads resulting from these long V chromo- 

 somes (Janssens, '05 among others) have misinterpreted their 

 form, representing them as two spirals twisting about each other 

 (Janssens's text fig. 1, page 391, or Davis's, '08, figure 87), 

 rather than in the way I have shown them in figures 156f, 174 

 (7-irs and 8-10's) and 176. In like manner, when dealing with 

 shorter chromosomes which give crosses (my figs. 150, 6's and 

 8's; and '08, figs. 29c, 29h) and simple rings having at one point 

 on the circle (sometimes an additional pair at the opposite point) 



