ins 



THE AMERICAN NATURALIST 



[Vol. LIV 



bp (frequency between black and purple) 5.9; Sp 0.4. If 

 Castle will follow his usual procedure here, and represent 

 these frequencies by proportionate distances in a model, 

 he will disprove not only linear linkage but both Euclidean 

 and non-Euclidean geometry and plain arithmetic. The 

 trouble in the case just cited arises in the fact that the 

 first two values are those obtained under ordinary cir- 

 cumstances whereas the third is a value obtained in the 

 presence of the factor CIIL which decreases enormously 

 the amount of crossing over. Clearly it will be unfair to 

 expect a single map to represent all three values simul- 

 taneously. Nevertheless, similar although less exag- 

 gerated, disturbing influences may be, and frequently are, 

 at work causing discrepancies between the results of 

 ''ordinary" experiments, so that it should be evident 

 that the latter are not ordinarily fit to be subjected to 

 the delicate comparison which is necessary for the pur- 

 pose of determining the nature of the linkage system. 



To some critics, it might at first sight appear incon- 

 sistent for the Drosophila workers to use the above argu- 

 ment against Castle's system, in view of the fact that 

 these workers themselves also combine the results of dif- 

 ferent experiments in constructing their chromosome 

 maps. The answer to this is that the variations in link- 

 age between ordinary experiments are usually so small 

 absolutely, that, if all the data for independent linkage 

 values, like AB, BC, CD, etc.— are joined together and 

 represented in one linear map, the latter will be accurate 

 enough for the usual purpose of computing approx- 

 imately the per cents of separation: the factors will ap- 

 pear in their correct order, and with approximately the 

 correct distances between them. If, however, a study of 

 the nature of the system of linkage is to be made, much 

 more precise knowledge than this is required, for it is 

 necessary to know exactly the relative strengths of inter- 

 dependent linkages— like AB, BC and AC— as compared 

 with one another. In such a case the small absolute 

 deviations occurring in the different experiments become 



