xiv] CROSSING-OVER 227 



which contains w, the chromosomes on the spindles of the 

 maturation divisions will contain factors m, TV, 0... and 

 M , n, o. . . ; that is to say, M and m will have crossed over 

 from their normal couplings, and will no longer be trans- 

 mitted with the characters with which they were associated 

 in the parents. Furthermore, if the factors M, TV, 0, P... 

 are arranged along the chromosome in this order, and if 

 the break in the chromosome occurs with equal frequency 

 at any point, it will evidently occur more often between 

 the widely separated factors M and P than between con- 

 tiguous factors such as M and TV or and P, and if it 

 occurs in x per cent, of cases between M and TV, and y per 

 cent, between N and 0, it will occur in x + y per cent, be- 

 tween M and 0. That is to say, the frequency with which 

 the break occurs between any two factors is proportional 

 to their distance apart in the chromosome 1 . In all these 

 respects the hypothesis corresponds closely with the facts. 

 Again, if the chromosomes are sufficiently long, or if the 

 twisting in synapsis is tight enough, it may be expected that 

 more than one break may take place, which will result in 

 an intermediate portion of chromosome A being transferred 

 to a (and of a to ^), while the portions at each end of it 

 remain in their original association (cf. Text-fig. 28). Such 

 "double crossing-over" actually occurs in experiment; if an 

 individual bearing the factors M, TV, 0, P is mated with one 

 bearing m, n, 0, ^>, it is found that a small proportion of the 

 gametes of the heterozygote have such combinations as 

 A/, n, 0, Pand m, TV, 0, p, suggesting that there have been two 

 breaks, one between M and TV and one between and P, 

 with the result that the intermediate portion of the chromo- 

 some, containing factors TV and 0, has exchanged places 



1 J. B. S. HALDANE (Journ. of 'Genetics, vm. 1919, p. 299) shows that this 

 is only approximately true. 



152 



