No. 592] THE MECHANISM OF CROSSING-OVER 201 



difference of their distances from any third factor (B) of 

 the same group, i. e., length AC = length AB ± length BC, 

 the + or — depending on whether the third factor is be- 

 tween or beyond the other two (see Fig. 3). Accordingly, 

 if, as Morgan suggested, the frequencies of separation 

 (linkage values) between factors depend on their distances 

 apart, then the frequency of separation (degree of link- 

 age) between the two factors, A and C, should be predict- 

 able, given the frequency of separation of each from the 

 third factor, B. To put the matter diagrammatically, A, 

 B and C have been represented in figure 3 as points along 

 a line; A and B, we will suppose, separate from each other 

 in heredity in 20 per cent, of cases, to correspond with 

 which they have been placed the same number of units (20) 

 apart in the diagram ; similarly, B and C, which we will 

 suppose to separate 10 per cent, of the time, have been 

 placed 10 units apart. (As above pointed out, there are 

 obviously two possible diagrams to choose between, de- 

 pending on whether C is beyond A and B or between 

 them.) Then, if it be true that the frequency of separa- 

 tion between any factors is always precisely proportional 

 to their distance apart, it will follow that the per cent, of 

 separations between A and C will be equal to the number 

 of units of distance on our diagrammatic chromosome be- 

 tween A and C ; this in turn equals AB ± BC = 30 or 10. 

 If separation frequency bears a less simple relation to dis- 

 tance, but is nevertheless determined by it (see below), 

 frequency AC will not equal distance AC (t. e., AB ± BC) 

 but can be calculated from the latter. On the other hand, 

 if our premises are false, and there is no linear relation at 

 all between the factors that determine their frequency of 

 separation, then frequency AC will not be equal to dia- 

 gram distance AC (*. e., to AB ± BC), nor even, in the 

 case of different sets of factors, will it bear any constant 

 relation to diagram distance AC ; that is, it would not be 

 possible to discover any constant rules for calculating the 

 third frequency from the two others which will hold, even 

 approximately, for various sets of factors (BCD, LMN, 

 etc.). 



