634 
GENETICS: A. WEINSTEIN 
Proc. N. a. 
Castle, on the basis of his three dimensional theory and of Metz's data, 
arranged hairy, magenta, and forked, at the apices of a triangle, and pre- 
dicted that the hairy magenta distance (which Metz had not determined) 
would be "about 4 or 5." The data now presented (tables 3 B, 4, and 5) 
give the hairy magenta distance as 5.5 units; or — if only those cultures 
are used in which the viability is good (tables 3 B; 4 A 1539, B; 5A) — the 
hairy magenta distance is 7.03 units. 
Of course, because of the poor viability in the one case and the small num- 
bers in the other, little reliance can be placed on these determinations 
as exact values. However (and this is the point at issue) the uncer- 
tainty does not affect the arrangement of the loci, which is clearly a linear 
one; for in all the experiments where the three loci were followed simul- 
taneously, the frequency of separation of hairy and forked (0.1003) was 
the exact sum of the hairy magenta (0.0534) and the magenta forked 
(0.0469) separation frequencies. 
Now the linear order, besides disproving Castle's triangular arrangement, 
shows that the values he used were not consistent with each other; for 
the hairy forked distance, being necessarily longer than the magenta 
forked distance, cannot be 3.1 if magenta forked is 3.7. The two dis- 
tances, not being strictly comparable, should not be used to predict the 
hairy magenta distance definitely. Moreover, if the hairy magenta dis- 
tance is (as Castle predicts) 4 or 5, the hairy forked distance must be 
longer than 4 or 5 and cannot be 3.1 ; that is, if Castle's predicted value is 
correct it follows that the value on which the prediction was based is in- 
correct. Thus the fulfilment of the prediction would in itself invalidate 
the grounds on which the prediction was based. It is therefore of no 
consequence whether or not the hairy magenta value recorded in this, 
paper (5.5 for the total broods or 7.03 for those with good viability) be; 
considered in agreement with Castle's "about 4 or 5 units"; for any agree- 
ment must be accidental and the fulfilment or non-fulfilment of Castle's 
prediction can have only a dramatic and not a scientific value. ^ 
The loss of the hairy stock prevents any further determinations; but 
the data already obtained are sufficient to demonstrate that the hairy, 
magenta, and forked loci are arranged in strictly linear order. It has 
already been noted that in the cross involving simultaneously yellow, 
crossveinless and vesiculated, the yellow vesiculated separation frequency 
(20.38) is the exact sum of the yellow crossveinless (19.23) and the cross- 
veinless vesiculated (1.15) separation frequencies. Hence, in the two 
only cases in D. virilis in which (because of the absence of double crossing 
over) the linear theory can be subjected to a decisive test, the arrange- 
ment of the genes in the chromosome turns out to be precisely linear.^ 
Castle also predicted, on the basis of his theory, that rugose and glazed 
would give a crossing over value of about 4 or 5 percent.; but this pre- 
diction cannot be tested directly because rugose-glazed hybrids are 
