118 GENETICS IN RELATION TO AGRICULTURE 
give about 3 per cent. of crossing-over with vermilion and about 7 per 
cent. with sable. Knowing the position of the vermilion locus at 33.0 
and the sable locus at 43.0, we would be able from these data to fix the 
locus position of miniature at about 36.0. With this value determined 
we could confidently predict for example that miniature and white 
would show somewhat less than 35 per cent. of crossing-over or miniature 
and bar about 21 per cent. The ability to make such predictions is a 
unique product of recent investigations in heredity. 
How experimental results support the hypothesis of linear arrange- 
ment of factors may be illustrated by what Morgan calls a three-point 
experiment, 7.¢., an experiment involving three different factors in the 
same chromosome. We may take three factors which are in widely 
separated loci in the chromosome, white at locus about 1.0, miniature 
at about 36.0, and bar at about 57.0. The summaries which Morgan 
and Bridges have given of the data involving these three loci are in- 
cluded in Table XXIV. White and miniature give directly 33.2 per cent. 
of crossing-over, and miniature and bar 20.5 per cent. Since the distance 
between white and miniature plus that between miniature and bar is 
equal to 53.7, this latter value should represent the distance between 
white and bar. But direct experimental determinations of the per- 
centage of crossing-over between white and bar give a value of 43.6 per 
cent., which is 10.1 per cent. short of the calculated value. 
TaBLe XXIV.—Crossinc-ovpeR FoR THE Loct W, M, and B’ In Drosoputua. 
Data OstTainep BY Matina FEMALES OF THE CONSTITUTION 
(wmB'X)(WMb'X) With Tripte Recesstves Mares (wmb!X)Y. 
Number | Number Per cent. 
Character combinations| of flies. | of cross- |of crossing- 
| classified overs over 
White miniature....| 110,701 | 31,071 33.2 
Miniature bar...... 3,112 636 20.5 
Whiteibar. 3.5 s.45 5,955 2,601 43.6 
The reason for this should be plain from a consideration of Fig. 55 
which shows diagrammatically how the chromosomes behave in a three- 
point experiment. On the left in the two upper groups are represented 
the two chromosomes with the factors in the original positions in which 
they were derived from the parents. On the right the homologus chromo- 
somes are shown twisted about each other, and at A, B, C, and D the 
types of chromosomes which are obtained after chromatin interchange in 
synapsis. The numbers below refer to the relative frequency of pro- 
duction of the four types of chromosome pairs in this three-point experi- 
ment based on the data of Table XXIV. In A (Fig. 55) no exchanges 
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