LINKAGE RELATIONS IN MENDELISM 117 
matin threads which twist about each other and these elements are held 
to occupy invariable loci in the chromatin thread, then the percentage of 
crossing-over between any two loci may be taken as an indication of the 
distance between the factors. For obviously if the chromatin thread is 
as likely to break between any two chromomeres as between any other 
two, then the farther apart two factors lie in the chromatin threads repre- 
senting homologous chromosomes, the greater is the chance that crossing- 
over will occur between them. 
The results of the application of this idea to the linkage relations 
existing in Drosophila are shown in Fig. 54. In this chromosome map of 
Drosophila the factors have been plotted in a linear series according to 
their relative position in the chromosomes as determined by linkage rela- 
tions. The evidence as yet is not sufficient to give an accurate picture of 
the arrangement of all the factors, but the number of factors plotted and 
the relations which they display provide further evidence of the corre- 
spondence between the chromosomes and the factor groups. Morgan 
has taken 1 per cent. of crossing-over as the unit for expressing linkage 
relations. Expressed in such units the first chromosome, which contains 
all the sex-linked factors, has a length of 66.2. The second and third 
groups, as far as determined, have lengths of 91.9 and 85.0, respectively. 
These lengths in general correspond fairly well to the known relative 
sizes of the two large pairs of autosomes when compared with each 
other and with the X-chromosomes. In the fourth group but two 
factors are known and their loci are so close together that thus far no 
crossing-over has been observed between them. Accordingly no definite 
value can be fixed for their linkage relations. From a knowledge of 
the small relative size of the third autosome Muller, at the time he an- 
nounced the discovery of the first factor in the fourth group, predicted 
that factors in this group would show very close linkage values. This 
prediction has been upheld satisfactorily and it is further evidence that 
the chromosome theory of heredity works. 
The demonstration that factors lie in a linear series in each group 
provides a unique method of predicting the results of factor behavior. 
Obviously if a factor is known to belong to a particular group, it is 
possible to predict confidently that it will display independent segre- 
gation with factors belonging to other groups. But further than this 
when the loci of a number of factors in a given group have been plotted 
accurately, with a new factor it is only necessary to determine the linkage 
relations with two of the plotted loci in order to determine its locus. 
When its locus has been determined, its linkage values with any other 
members in the group may be predicted from its distance in units from 
those factors. To illustrate, in Group I, if the position of miniature 
were unknown, it might be tested with vermilion and sable. It would 
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