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THE AMERICAN NATURALIST [Vol. L 



among the 712 flies obtained for group I must represent 

 Yy), or .14 per cent., of all the cases. If, then, a crossing- 

 over is found to occur somewhere between ci and v, and 

 one occurs coincidentally between s and r, the two points 

 of crossing-over may have been as far apart as Ci and r 

 (36), or as close together as v and s (8), or at any inter- 

 mediate distance. Therefore we have no right to make 

 this case stand, in the curve, for a coincidence that hap- 

 pened at a particular distance (say 10-11) and to raise 

 the ordinates for this particular distance by .14 units. 

 Each distance between 8 and 36 is consequently given 

 partial credit in our curve for the occurrence of this coinci- 

 dence, and so each of the 28 ordinates between 8 and 36 

 14 



is raised to an average height of ^ = .005 approximately. 



All the other cases are treated in a similar way, and thus 

 the curve shown by the heavy line in Fig. 12 is obtained. 



DISTANCE 



