No. 592] THE MECHANISM OF CROSSING-OVER 203 



must have separated from C also, i. e., a separation has 

 occurred between A and B, and between B and C, coinci- 

 dentally. On the view above presented, a separation 

 means a crossing-over of chromosomes, and so in these 

 cases the chromosomes must be thought of as crossing- 

 over at two points coincidentally, as shown in Fig. 4. This 

 process has been named by Sturtevant * 'double crossing- 

 over.' ' As shown in the figure, where crossing-over oc- 

 curs coincidentally, both in AB and in BC, the chromosome 

 crosses and crosses back again between A and C, hence the 

 latter factors do not become separated. 



When the frequencies of separation (diagram distances) 

 between A and B, and between B and C are both small, it 

 is to be expected as a matter of pure chance, if the factors 

 are joined in line in the manner described, that such coin- 

 cidences will occur very rarely, even in proportion to the 

 small frequencies involved, and so the per cent, of separa- 

 tions between A and C will be practically as great as that 

 between A and B plus that between B and C. Hence per 

 cent. AC will be accurately represented by diagram dis- 

 tance AC. On the other hand, if separation is frequent 

 between A and B or between B and C, there should be 

 more chance of coincidence of these separations, and the 

 number of separations between A and C will fall corre- 

 spondingly short of AB + BC, which is the value of AC 

 shown on the diagram. Consequently, in predicting fre- 

 quency AC on the basis of AB and BC, allowance must be 

 made for these coincidences. But the author ventures to 

 point out that, as the number of these coincident separa- 

 tions is found to be largely determined by the frequency 

 of separation, greater frequencies being accompanied by 

 a larger proportion of coincidences, as has been shown, 

 then the amount of allowance to be made can be approxi- 

 mately calculated for any given distance on the diagram; 

 accordingly, the frequency of separation between A and C 

 can be calculated from AB + BC, t. e., from the distance 

 AC on the diagram. The precise manner in which coin- 

 cidence of separations increases with their frequency is a 



