No. 632] CHIASMATTPE AND CROSSING OVER 203 



two threads that are connected by a chiasma and two that 

 are not thus connected; but if the model be rotated 

 through an angle of 90° the appearance is reversed, the 

 "chiasma" now appearing between the two threads that 

 previously seemed unconnected, and vice versa. 



The same appearance, due to the same cause, is given 

 in early stages of the lateral arm-formation in the single 

 rings (5 I, B, C), and is shown with even greater clear- 

 ness in early stages of the double crosses. The latter 

 arise by separation of the free ends of the four threads 

 from each end towards the middle point, but along dif- 

 ferent planes (Fig. 5 III, B-D), i. e., from one end along 

 the equation-cleft, from the other along the reduction- 

 cleft— a process that is continued until all four threads 

 come to lie in a single plane in the form of a double cross. 

 Here, too, a "chiasma" {ch) is very clearly seen; but as 

 in the foregoing cases it is an optical illusion ; the models 

 in three dimensions show at once that a straight split 

 through the tetrad involves no transverse break in the 

 chiasma, and that its two strands merely draw apart as 

 the division proceeds. In themselves these figures give 

 no reason whatever to assume that such a break (cross- 

 ing-over) has taken place at an earlier period or that the 

 synaptic mates have been twisted about each other, as 

 Janssens assumes. 



Such an origin of the double or multiple rings seems at 

 first sight wholly inconsistent with Janssens 's interpre- 

 tation; for if it be correctly determined the relation of 

 the synaptic mates to the ring-formation is wholly dif- 

 ferent in successive rings, as is shown in Figs. 3 D, E, 

 and 4- A. Specifically, in case of any two successive 

 rings one always shows the synaptic mates, lying on op- 

 posite sides of the ring-opening, and each longitudinally 

 split, while in the adjoining ring half of each synaptic 

 mate surrounds the entire ring-opening, lying in close 

 contact with the corresponding half of its mate. Only in 

 the first case, accordingly, does the longitudinal cleft of 

 the ring correspond to the equation-division. In the sec- 



