THE LINEAR DIFFERENTIATION OF THE CHROMOSOMES IO7 



value obtained is about 12 per cent, so even at the distal end of the X 

 there has not been enough crossing-over for the chromatid segregation 

 to be on a purely chance basis). The fact that no equationals occur 

 near the centromere is a proof that we are correct in assuming that the 

 two centromeres of sister chromosomes must separate from one another 

 in the first division. 



The analysis of triploid crossing-over also shows that any of the six 

 chromatids may cross-over with any other different chromatid; but one 

 cannot determine in this way whether crossing-over may happen be- 

 tween two sister chromatids, since it would have no observable conse- 

 quences. At any one locus, however, crossing-over only occurs between 

 two chromatids; one never finds crossing-over between four chromatids 

 since that would involve two sister chromatids crossing-over in the 

 same place with chromatids belonging to two other different chromo- 

 somes, and this could only happen if all three chromosomes were 

 paired at one point in zygotene. Zygotene pairing is, however, strictly 

 in tv\'os in those organisms in which it can be cytologicaly observed. 

 Some evidence as to whether it is in twos in Drosophila can be derived 

 from a consideration of double cross-overs. The second cross-over may 

 be between the same two chromosomes as the first (recurrent double 

 cross-over), or between one of the two involved in the first cross-over 

 and the third chromosome (progressive double cross-over). There 

 should be a high proportion of progressive double cross-overs if all the 

 chromosomes were paired throughout their length, but more recurrent 

 double cross-overs if they are paired in twos with only infrequent 

 changes of partner. The evidence is not yet perfectly clear but seems to 

 be in favour of the second alternative, which fits in with the cytological 

 observations. 



The calculation of gamete ratios in experiments involving crossing- 

 over becomes progressively more compUcated in higher multiple poly- 

 ploids,^ and becomes theoretically impossible when the frequency of 

 chiasma formation, i.e. degree of metaphase association is not known. 

 In tetraploid Primula sinensis,^ the chromosomes are nearly always 

 associated in pairs at metaphase and the results obtained for the segre- 

 gation of various linked factors agree quite well with a calculation based 

 on random association of the chromosomes in pairs and an absence of 

 chromatid segregation; the latter of these hypotheses can hardly be 

 more than approximately correct. 



^ Cf. Mather 19366. ^ de Winton and Haldane 1931. 



