A. II. Tkow 287 



Let us note that with /( factors we get the following general foriiiula 

 for the series traced above : 



1 CO. 2 CO. 3 CO. (n-l)C. 0. 



(n - 2) N. C. O. ' (n - 8) N. C. O. ' (n-4) N. C. O. ' ' ' " (n-n) N. C. O. ' 



The ])ercentages of cnjss-overs iDOConie, using the formulae 



Ab X 100 Ac X 100 



AB + Ab' AC+Ac' 



1x100 2x100 3^^100 (».-l)xl00 , 



n-l ' n-1 ' n-1 ' '" n-1 ' 



a series in arithmetical progression. 



If the factors are uniform in size, the least difference between the 

 observed percentages, that between Lethal 1 ('7) and White (10), may 

 be regarded as the common difference, and the number of factors may 

 be readily determined, as approximately 300. It is however very 

 noteworthy (even critical for the crossing over hypothesis) that the 

 highest percentage recorded in No. 1 chromosome is 655, and that 

 the factors are crowded at one end of the chromosome and quite absent 

 from the other. Why should one end of a chromosome be favoured 

 more than the other ? Surely the results should be of such a nature 

 that they may be read from either end. The crowding represents high 

 reduplication. Critical study of numerous cases of high redujjlication 

 will probably prove fatal to the Morgan hypothesis. 



But a single-cross-over scheme such as this is inadequate to account 

 for all the facts. With a single cross-over taking place by chance at 

 any locus in the chromosome, we get all the combinations which appear 

 in cases of dihybridism, i.e. where two pairs of allelomorphs, such as 

 Aa, Bb, are involved, but we do not secure all the combinations which 

 are required in a case of trihybridism, where there is another pair, 

 say C'c. In order that such a combination as AbC should appear, even 

 occasionally, it is necessary that a double cross-over should take ])lace, 

 thus : 



ABC 



Hence we may deduce the rule that if there are n pahs of segregating 

 allelomorphs, the number of the loci for the crossings-over must be 



