252 CHROMOSOMES IN HEREDITY: MECHANICAL 



and this can be verified where two factors are Hnked with a third, 

 as Sturtevant showed in 1914. The amount of crossing-over between 

 the two should, when small, approximate to either the sum or the 

 difference between the amounts of their crossing-over with the 

 third. This is always the case in organisms with simple pairing of 

 chromosomes. But the exact relation is not a simple one as might 

 be supposed, i.e., the resultant crossing-over is not equal to the sum 

 of the two smaller proportions minus twice their product (to allow 

 for double crossing-over which would cancel itself out), but minus 

 something less than this. It follows that double crossing-over 

 between factors fairly close to one another is not so frequent as 

 randomness requires ; the occurrence of one cross-over may there- 

 fore be said to " interfere " with the occurrence of another in its 

 neighbourhood, and the property is known as " interference " 

 (Muller, 1916). 



These principles must be understood in order to follow the 

 cytological evidence. The conditions of crossing-over will be 

 examined in detail at a later stage in relation to this evidence. 



(iii) The Cytological Theory. The observation that the 

 chromosomes paired at diplotene came together at various points 

 along their length — points which we now recognise as chiasmata — • 

 suggested to Riickert in 1892 that the chromosomes exchanged 

 material at these points. The view was ignored in the following 

 years, being naturally overshadowed by the idea of permanence in 

 the structure of the chromosomes. The four chromatids of the 

 bivalent were usually supposed to be derived without change, 

 two from one parental chromosome and two from its mate. The 

 question then was merely whether the two chromatids which passed 

 to the pole together at the first division were derived from the same 

 parental chromosome or from the two partners. In the first case 

 the first division would be " reductional " in respect of differences 

 between the partners, in the second case it would be " equational.*' 



The controversy was confused owing to a lack of distinction 

 between numerical reduction and qualitative reduction. We now 

 know that reduction in number does not occur at either division, 

 but simply through the two divisions following one another so 

 rapidly that no division of chromosomes takes place in the interphase 



