THE MECHANICS OF THE CHROMOSOMES 121 



them. The general necessity of some such hypothesis is shown by the 

 faa that the chromosomes are not always associated in threes in tri- 

 ploids, fours in tetraploids, etc., as they would be if the association was 

 due to a general attraction between homologues, DarUngton^ points out 

 that the attraction between homologues (in pairs) is responsible for 

 zygotene pairing, and that this pairing must be distinguished from 

 metaphase association (which he unfortunately also refers to as "pair- 

 ing"; in this work the word pairing is kept for zygotene pairing and 

 pairing in saUvary glands, etc., while the formation of metaphase 

 bivalents is spoken of as association). The suggestion that association 

 is a result of chiasma formation allowed Darlington to use the chiasma- 

 length relation to predict the frequency of association in short chromo- 

 some fragments in Fritillaria; the long chromosomes form 2-58 chias- 

 mata per bivalent, fragments one-ninth as long should form 0-29 

 chiasmata and should be associated in 29 per cent of nuclei; the actual 

 association found was 22 per cent, which is as good an agreement as 

 can be expected. 



3. The Theory of Crossing-Over 



The earliest speculations on the breakage theory of crossing-over 

 related the phenomenon to chiasma formation : Morgan^ pointed to the 

 observation of Janssens^ as providing a material basis for the theory, 

 but did not attempt to distinguish between "total" chiasmatypy, in 

 which breakage and rejoining was supposed to occur between whole 

 chromosomes, and "partial" chiasmatypy, in which it occurs between 

 chromatids. Recent genetic (p. 103) and cytological evidence shows 

 that only the second of these mechanisms need be considered: crossing- 

 over takes place in the four-strand stage. The partial chiasmatype 

 hypothesis, as it is at present put forward (Belling, Darlington),^ states 

 that the occurrence of a cross-over is the cause of the change of partner 

 among four chromatids associated in pairs which is made apparent as 

 a chiasma. Its only rival for serious consideration is the hypothesis, at 

 one time suggested by Darlington but more recentiy upheld mainly by 

 Sax,5 that crossing-over takes place by the breakage of interstitial 

 chiasmata during the reduction in number between diplotene and 

 metaphase. 



The partial chiasmatype hypothesis supposes that all chiasmata are 

 the results of previous crossing-over. This cannot be proved directly, 



^ Darlington 19306, 1937. ^ Qf Morgan 1926. ' Janssens 1909, 1924. 

 * Cf. Belling 1931, 1933, Darlington 1937. ^ Sax 1930, 1931. 



