104 



THE AMERICAN X ATT' BALI ST 



[Vol. LIV 



modifications due to specific correlations between cross- 

 ings over in different regions. But since, as has been 

 stated, the differences between the larger per cents of 

 crossing over and the linear distances are not unregu- 

 lated, but do give clear evidence of being themselves a 

 function of the map distances, these larger per cents of 

 separation as well as the smaller ones can be used in 

 proof of the linear system of linkage. The systematic 

 differences between the frequencies and the map are 

 hence due to double and other multiple cross overs, which 

 vary in frequency in accordance with the distance in- 

 volved. 



It is true that a certain amount of the differences actu- 

 ally found between the larger frequencies and their corre- 



sponding distances on a straight linear map might be 

 thought of as due to the cumulation of minor discrep- 

 ancies which existed between the small frequencies and 

 distances but each one of which was by itself too small 

 to be detected in the data for the smaller distances, being 

 within the limits of experimental error. As the small 

 discrepancies in such a case would, to be always cumu- 

 lative, all have to have a bias in the same direction, this 

 would amount to saying that the line along which the 

 points were really disposed had a slow, even curve, too 

 slight to be detected except when large distances were 

 considered. The straight line would then be sufficiently 

 accurate as a proportionate representation of all the 



