GENETICS: W. E. CASTLE 
31 
it is evident that this rearrangement can have come about only as a result of 
two breaks in the linkage chain, viz., one between A and B, and another be- 
tween B and C. But if the arrangement is not linear, double-crossing-over 
need not be assumed as an explanation of the observed regroupings. For if 
A, B, and C are Hnked in a triangle, not in a straight line, then B may be 
freed from its connections with A and C without necessarily disturbing the con- 
nection of A and C with each other. Freeing of B will involve no greater num- 
ber of breaks than the freeing of either A or C. It will still be true, however, 
as indicated by the experimental data, that certain groupings of three par- 
ticular genes are easier to obtain than others. Thus in the case of the three 
genes white, bifid and vermilion, it is hardest to obtain the regrouping which 
involves detaching bifid from the other two. Morgan assumes that this is 
because bifid lies between the other two in a single linkage chain and so could 
be detached only by two breaks; it is possible, however, that the reason may 
be that bifid lies peripherally in the linkage system and could be detached 
only by an oblique longitudinal break, whereas either of the others could be 
detached by a simple transverse break. Similarly in the trio, white- vermilion- 
sable, it is vermilion which is difficult to detach; and in the group, vermilion- 
sable-bar, it is sable. Always it is the middle one considered with reference to 
the long axis of the system. This may be because, as Morgan supposes, only 
transverse breaks occur, of which two taking place simultaneously are re- 
quired to produce the difficult regrouping, or it may be because transverse 
breaks are more frequent than oblique longitudinal ones, of which a single 
one would suffice to accomplish the regrouping, if the genes are not strictly 
linear in arrangement. 
The phenomenon of 'coincidence' as described by Weinstein' is this. If 
crossing-over occurs toward one end of a chromosome, it is less likely to occur 
simultaneously elsewhere in the same chromosome. Crossing-over in one 
part of a chromosome is thus supposed to 'interfere with' crossing-over else- 
where in the same chromosome. If we adopt the hypothesis of linear ar- 
rangement, interference must be assumed to occur. Observed facts require 
this. But if we do not adopt this h3^othesis but suppose that what have 
been called 'double cross-overs' are really the result of single oblique or single 
longitudinal breaks, then the supposed phenomenon of interference may mean 
only this, that transverse breaks are more likely to occur than longitudinal 
ones. 
Finally, if the genes are not arranged in a single linear chain, the chiasma- 
type theory will need to be reexamined. Such a purely mechanical theory 
seems inadequate to account for interchange of equivalent parts between twin 
organic molecules, such as the duplex linkage systems of a germ-cell at the 
reduction division must be. It seems more probable that preceding the 
reduction division a period of instability within the chromosome molecule 
comes on. Twin molecules are now closely approximated and parts of one 
may leave their former connections and acquire new connections with the 
