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 onlv 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 l)y some linear relation of the 



