CHIASMATA AND PAIRING 129 



the three chromosomes of each kind of 6-2, 3-6 and 2-0 respectively 

 {i.e., in proportion to their length). As expected, the three types 

 have distinct frequencies of univalents — 2-8, o-i and 11-9 per cent, 

 respectively. The high frequency of univalents amongst the short 

 chromosomes is explained by the low frequency of chiasmata. The 

 fact that the long chromosomes have a slightly higher frequency 

 than the medium ones is attributed to the interference with free 

 assortment resulting from their extreme length, for they are the 

 longest chromosomes known in any organism. This may be 

 expressed by saying that they have fewer pairing blocks than the 

 shorter chromosomes, two instead of four or five. 



Thus quadrivalents are less frequent among the short chromo- 

 somes than amongst the long ones, in tetraploids not only of 

 Hyacinthus, but also of Schistocerca (White, 1933) and of Urginea 

 and Scilla (Sato, 1934). Similarly in polyploid forms with localised 

 pairing and chiasmata we must expect fewer multivalents than in 

 corresponding forms with complete pairing, since the effective 

 length for pairing is shorter. This property is possibly shown by 

 the tetraploid Allium Porrum (Levan, 1935 a). 



More direct evidence that chromosomes are held together by 

 chiasmata at metaphase will be considered in relation to pairing 

 in hybrids. For the present it must be noted that this view 

 conflicts diametrically with the old theory that chromosomes 

 are held together at metaphase by an affinity between them, and 

 adequately explains the present observations, while the old theory 

 leads one to expect in pairing uniformity, symmetry, and com- 

 pleteness, instead of variation, asymmetry and incompleteness. 



(iii) The Two Divisions. The arrangement of multiple bodies, 

 with several centromeres, in a bipolar spindle is inherently irregular. 

 The result seems to depend on three variable conditions : (i) the 

 distribution of the chiasmata in the multivalent chromosome ; 

 (ii) the spatial relationship of the centromeres of the component 

 chromosomes, as determined by their position in the chromosomes, 

 and by the position in which the chromosomes are held by the 

 chiasmata ; (iii) the relationship of the size of the chromosomes to 

 the area of the equatorial plate, i.e., whether the chromosomes are 

 crowded or not. 



R.i.. CTTOLOQY. ' 



