OF MUTANT CHARACTERS. 299 



vestigial cross-over value of 11.8; that is, vestigial is 11.8 unit« to the 

 right of purple or at 18.0 to the right of l)lack. This location is hjisod 

 on a total of 13,601 flics for the jMirpIe vestigial cross-over value- 

 (2) but there are available 20,153 flics giving a black vestigial cross- 

 over value of 17.8. This distance is long enough so that donblo 

 crossing-over occurs within it, and the cross-over \-aliie nuist therefore 

 be corrected. The black purple vestigial and other back-cro.ss experi- 

 ments by which the amount of this double crossing-over has been 

 measured show that the amount of such double crossing-over is rela- 

 tively very high, the probable coincidence being about 00. The cor- 

 rected value corresponding to a given coincidence and an observjHl 

 cross-over value can be calculated closely enough for our present 

 purposes by aid of the following equation : 



2 X o 



x^ — 



C 2C 



in which C = the given coincidence, o = the observed cross-over value, 

 and 2a: = the corrected distance, all expressed a« decimal fractions 

 rather than as percentages. The correction corresponding to a 

 coincidence of 60 amounts to about 1.1 units on an observed value of 

 17.8, so that the locus of vestigial is 18.9 units to the right of black on 

 the basis of the black vestigial data. However, the precision of the 

 location based on values that must be corrected decreases rapidly with 

 the increase in the size and consequent uncertainty of the correction. 

 Although the position of vestigial at 18.9 is based on 20,168 flies, the 

 value of each fly represented in the black vestigial cross-over data is 

 not as great as the value of each fly in the purple vestigial exj)erinients, 

 where the coincidence is probably zero and no correction at all need 

 be made. Roughly, the black vestigial data should be weighted about 

 three-quarters of its face value as compared with the j)urple vestigial 

 data. By combining the two sets of approximately weighted daUi, 

 the mean position of the vestigial locus is found to be 18.5 units to the 

 right of black. 



The position of curved is reached by a combination of three sets of 

 weighted data: The most direct data, which needs no correction, is 

 that derived from the vestigial curved cross-over value of S.2 units 

 based on 1,720 flies. According to this data, the position of curved 

 is at 18.54-8.2, or 26.8 units to the right of black. The next most 

 direct method of location is by reference to purple, the purple curved 

 cross-over value of 19.9 being based on 51,136 flies. This value needs 

 correction according to the probable coincidence of 70 b}' the addition 

 of 1.5 units, which gives a locus 21.4 units to the right of iKirj)le. or 

 27.6 units to the right of black. The number of flies is to be r:i{od at 

 about 70 per cent of its face value, or at about 3S,S00 flies. The third 

 method is by means of the black curved cross-over value of 22.7 cor- 



