26 
GENETICS: W. E. CASTLE 
arrangement to be linear and in the group of genes most exhaustively studied, 
that of the 'sex chromosome' has represented them in a 'chromosome map, 
as shown in Diagram I. 
That the arrangement of the genes within a linkage system is strictly 
linear seems for a variety of reasons doubtful. It is doubtful, for example, 
whether an elaborate organic molecule ever has a simple string-like form. 
Let us, therefore, examine briefly the evidence for or against the idea of 
linear arrangement of the genes. It is supposed by Morgan that two genes 
lying in the same chromosome show close linkage if they lie close together, but 
less linkage if they lie farther apart, and that the farther apart they are the 
less will be their linkage. As a measure of the distance apart of two genes he 
takes the percentage of cross-overs between them. This term requires a 
word of explanation. If two genes, A and B, enter a cross in the same gamete 
and emerge from it in different gametes, one of them has evidently crossed- 
over from the chromosome in which it lay to the mate of that chromosome 
(all chromosomes being paired prior to the formation of gametes). Like- 
wise if the two genes, A and B, having entered a cross separately (being con- 
tributed by different parents), later emerge from the cross together, it is evi- 
dent that one of them has again crossed-over so as to lie in the same chromo- 
some as the other. The readiness with which cross-overs occur between 
two genes will on Morgan's hypothesis depend on their distance apart and 
the percentage of cross-overs between genes will be proportional to the dis- 
tances between them. These assumptions have abundantly proved their 
utility as a working hypothesis, for it has been found possible, knowing what 
certain cross-over values are, to predict others with a fairly good degree of 
accuracy. 
If the arrangement of the genes is strictly Hnear, so that A, B, C, etc., lie 
in a straight line, then it should be possible to infer the distance AC, if the 
distances AB and BC are known, since AC = AB -f BC. But if the distance 
AC is less than the sum of AB and BC, then the arrangement can not be 
linear, since B will lie out of line with A and C. In reality it has been found 
that the distances experimentally determined between genes remote from each 
other are in general less than the distances calculated by summation of sup- 
posedly intermediate distances, and the discrepancy increases with increase 
in the number of known intermediate genes. To account for this discrepancy 
Morgan has adopted certain subsidiary hypotheses, of 'interference,' 'double 
crossing over,' etc., in accordance with which it is supposed that cross-overs 
between nearer genes interfere with or lessen the apparent amount of cross- 
ing-over with genes more remote. He therefore bases his chromosome map 
on summation of the shorter distances. This, however, leads to results which 
can be shown to be impossible. 
Morgan's map of the sex-chromosomes places five out of twenty-nine genes 
at distances between 55 and 66 from the zero end of the chromosome, where 
yellow is located. A moment's reflection will show these to be impossible re- 
