LINKAGE 65 
the per cent. of crossing over between it and the 
factor nearest to it. For shorter distances it may be 
said that the number of units on the map between any 
two factors (A and C), will equal the per cent. of 
crossing over that will actually be observed between 
them in an experiment involving these two pairs of 
factors, even although their distance on the map may 
not have been obtained directly from their linkage 
with each other, their positions having, instead, been 
determined by their linkage with other factors. On 
account of double crossing over, however, this would 
not be expected to hold for the longer distances; and, 
as has been explained, we do actually find that, if 
long distances are involved, the distance between A 
and C determined as on the map, by adding the inter- 
mediate distances A-B and B-C, is longer than the 
distance AC as directly determined in an experiment 
involving only these two pairs of factors. It never- 
theless remains true that, given the distance between 
any two factors on the map, the per cent. of crossing 
over between them can always be calculated from this 
distance (since the amount of discrepancy due to 
double crossing over also depends on the distance) ; 
this shows that the amount of crossing over between 
‘them is an expression of their position in a linear 
series. This striking fact, that the mathematical 
relations between the various linkage values conforms 
to a linear series, is a strong argument that the factors 
are actually arranged in line in the chromosomes. 
If the relations between the various linkage values 
were not determined by some linear relation of the 
5 
