170 
GENETICS: STURTEVANT, BRIDGES, AND MORGAN 
Yellow white 
White bifid.. 
Yellow bifid . , 
1.2 
3.5 
4.7 
These relations, in which the sum of the smaller values is exactly equal to 
the larger one, can be represented^ only by placing the three loci in a straight 
line, in the order yellow, white, bifid. ^ 
It will be seen that this linear arrangement is necessitated by the fact 
that white never separated from yellow and bifid; i.e., no 'double crossover' 
occurred. By considering data involving only short distances (e.g., white 
bifid club, bifid club vermilion, club vermilion miniature, vermilion miniature 
sable, sable rudimentary forked, rudimentary forked bar, and forked bar 
fused; or still better, certain unpublished data including the loci ruby, cut, 
tan, garnet, etc.), it is possible to handle the whole X-chromosome of Droso- 
phila as made up of successive overlapping sections in which double crossing 
over either does not occur or is so rare as to be negligible. Since these sec- 
tions must be represented as straight lines, and since they overlap, the whole 
X-chromosome must be represented as a straight line. 
For longer sections of this same chromosome, however, double crossovers 
do occur, so that the distances apart on the straight line are no longer pro- 
portional to the crossover values. The 'map-distance' for white forked, for 
example, is 55.4, though the crossover value observed^° is 43.9. 
Castle is disturbed by such map distances greater than 50. He says: "A 
crossover value greater than fifty cannot exist. For there must be either 
linkage or no-linkage. But no-linkage means 50% crossovers, and linkage 
means less than 50% crossovers. Hence a value greater than 50% cannot 
occur." It is evident that the conclusion of this curious syllogism depends 
solely on the definition of linkage contained in the second half of the second 
premise. It is true that crossover values significantlv greater than fifty have 
never been found, but this is due to the frequency of double crossovers — to 
the fact that ' coincidence' is high for long distances. But coincidence is known 
to be a variable quantity, so that there would seem to be no a priori reason 
to suppose that crossover values greater than fifty are impossible. Further- 
more, as has been explained above, map distances greater than 50 have never 
been intended to represent observed crossover values greater than fifty. 
It is to be observed that the three dimensional figure given by Castle might 
seem capable of reduction to a curved line lying in one plane. An exami- 
nation of his figure 2 shows that the only loci far from the plane that includes 
most of the group are bifid, depressed, shifted, lethal 3, furrowed, and lethal 
sc. Let us then examine these individually. 
Bifid has already been shown to lie in the same straight line with yellow 
and white, both of which are in Castle's thickly populated plane. 
Morgan and Bridges give three crossover values for depressed, two of 
which (white depressed and depressed vermilion) are stated to be based on 59 
