CROSSING-OVER 553 



function of the length of the chromosome-arm. We must therefore 

 suppose that in Drosophila and in Stenobothrus the average strain is 

 also a function of the length. This can be understood in the follow- 

 ing way : if pairing begins near the centromere or near an end and 

 passes along the chromosome, the strain developed will be a function 

 of the time that the chromosomes have been paired before equili- 

 brium is reached (cf. Fig. 30) because segments that pair late will 

 partly uncoil first. Some equalisation of strain will then take place 

 after pairing between the parts of the arm. The average strain in a 

 long arm will thus be less than in a short arm which completed its 

 pairing earHer. 



The extent to which the torsion is released at the centromere can 

 probably be measured more accurately from frequencies of chias- 

 mata than of crossing-over in the progeny. Two-armed chromo- 

 somes should show a greater variance than one-armed chromosomes 

 of the same average frequency. There is no evidence of this as yet. 



There remains to be considered the effect of exceptional condi- 

 tions, especially X-ray treatment, on crossing-over. Its normal 

 occurrence in Drosophila is confined to the prophase of meiosis, 

 where it affects all pairs in the female and the sex chromosomes only 

 in the male. Exceptionally, however, it occurs. somatically (Stern, 

 1934) or in gonial nuclei before meiosis, e.g., crossing-over in the 

 male (MuUer, 1916, p. 304). This may also be inferred where groups 

 of gametes are formed having the same exceptional crossing-over, 



e.g., detachment of XX in XXY females (Kaufmann, 1933 ; Fig. 

 121). Crossing-over is increased by X-ray treatment. In the male, 

 where natural crossing-over is too rare to be traced, the induced 

 crossing-over has been shown to take place somatically (Friesen, 

 1934, 1936 ; cf. Kikkawa, 1935 b ; Patterson and Suche, 1934). 



Somatic crossing-over is probably peculiar to the Diptera, being 

 conditioned by the exceptionally strong somatic pairing of the 

 chromosomes which even leads to relational coiling. It seems that 

 this will not itself determine crossing-over, since the chromosomes 

 do not divide while coiled, but if one of their chromatids is broken 

 by X-rays at the earliest prophase the result should be the same as 

 where a breakage occurs in meiosis ; it should impose an increased 

 strain on the partner chromosome exactly opposite and thus lead to 



