70 



winged, vermilion-eyed female by 

 rudimentary winged, red-eyed male. 

 The analysis and results are seen in 

 Table 1. 



It is of course obvious from the 

 figures that there is something peculiar 

 about the rudimentary winged flies, 

 since they appear in far too small num- 

 bers. This point need not detain us 

 here, as it always comes up in connec- 

 tion with rudimentary crosses, and is 



Table 1 



Long vermilion 

 Rudimentary red 



9— MpX MpX 

 ^— mPX 



MpX mPX— long red 9 



MpX — long vermilion $ 



Gametes F^ 



Eggs —MPX mPX MpX mpX 

 Spenn— MpX 



MPXMpXl , J o^L<i 



mPXMpXJ-^^^g^^'i ^^^^ 



mpXMpxH°"g^^™'l'«" 5-417 

 MPX —long red 5—105 



mPX — rudimentary red S — 33 



MpX — long vermilion $ — 316 



mpX — rudimentary vermilion $ — 4 



being investigated by Morgan. The 

 point of interest at present is the link- 

 age. In the F2 generation the original 

 combinations, red rudimentary and 

 vermilion long, are much more fre- 

 quent in the males (allowing for the 

 low viability of rudimentary) than 

 are the two new or cross-over com- 

 binations, red long and vermihon rudi- 

 mentary. It is obvious from the anal- 

 ysis that no evidence of association can 

 be found in the females, since the M 

 present in all female-producing sperm 

 masks m when it occurs. But the ratio 

 of cross-overs in the gametes is given 



o 

 B c 



-1-1 



0.0 1.0 



STURTEVANT 



without complication by the F2 males, 

 since the male-producing sperm of the 

 Fi male bore no sex-linked genes. 

 There are in this case 349 males in the 

 non-cross-over classes and 109 in the 

 cross-overs. The method which has 

 seemed most satisfactory for express- 

 ing the relative position of factors, on 

 the theory proposed in the beginning 

 of this paper, is as follows. The unit 

 of 'distance' is taken as a portion of the 

 chromosome of such length that, on 

 the average, one cross-over will occur 

 in it out of every 100 gametes formed. 

 That is, per cent of cross-overs, is used 

 as an index of distance. In the case of 

 P and M there occurred 109 cross- 

 overs in 405 gametes, a ratio of 26.9 in 

 100; 26.9, the per cent of cross-overs, 

 is considered as the 'distance' between 

 P and M. 



THE LINEAR ARRANGEMENT 

 OF THE FACTORS 



Table 2 shows the proportion of 

 cross-overs in those cases which have 

 been worked out. The detailed re- 

 sults of the crosses involved are given 

 at the end of this paper. The 16287 

 cases for B and CO are from Dexter 

 ('12). Inasmuch as C and O are com- 

 pletely linked I have added the num- 

 bers for C, for O, and for C and O 

 taken together, giving the total re- 

 sults in the lines beginning (C, O) P, 

 B (C, O), etc., and have used these 

 figures, instead of the individual C, O, 

 or CO results, in my calculations. The 

 fractions in the column marked 'pro- 

 portion of cross-overs' represent the 

 number of cross-overs (numerator) to 

 total available gametes (denominator). 



As will be explained later, one is 

 more likely to obtain accurate figures 

 for distances if those distances are 

 short, i.e., if the association is strong. 



P R 



1 — I 



30.7 33.7 



M 



1 — 



57.6 



