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THE AMERICAN NATURALIST [Vol. XLIX 



YWN g YEAb YEN 



In this and in the following tables the order of the cross- 

 over gametes is always given the same, viz.: the first 

 factor to the left above (Y) joins the two following below, 

 R and Ab, (taking the switch as it were at the first cross- 

 over). Then follows the cross-over that is the converse 

 of the preceding (the first factor to the left below switch- 

 ing over to join W and N) . The second crossing is taken 

 in the same way, thus Y and "W switch over to Ab, and 

 conversely G and R switch over to N. The double cross- 

 over takes the switch twice ; thus Y to R and then to N ; 

 and conversely G to W and then to Ab. The F 2 flies 

 should correspond to these gametic classes (since the F x 

 male was a triple recessive) except in so far as the ab- 

 normal classes change to phenotypic normal types. Thus 

 the non-cross-over class GRAb will, in this sense, con- 

 tribute to the single cross-over class GRN ; and the single 

 cross-over class YRAb to the double cross-over class 

 YRN. The last-named class can not, therefore, be used as 

 a measure of the double crossing over, since it is more 

 probable that any flies of this kind that appear will be 

 only phenotypic YRN, than that they should belong to 

 the YBN class genetically. Only the GWAb class may 

 be used as a measure of double crossing over, and, as will 

 be shown below, much caution must be used even in this 

 case. 



It will be seen in the table that only relatively few of 

 the GRAb type have changed to the normal type, because 

 the conditions were favorable for abnormal although the 

 cultures ran in most cases for ten days, but during this 

 time they still contained plenty of wet food. It will be 

 noticed that the changed class GRN corresponds to one 

 of the single cross-over classes, consequently GRN is a 

 mixed class, and can not be used to base any calculation 

 on. It is true, one may roughly determine how many 



