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THE AMERICAN NATURALIST [Vol. L 



Sturtevant found that there is indeed a linear relation in 

 the frequencies of separation (14, 16). In the case of 

 smaller per cents, of separation, per cent. AC always is 

 precisely equal to the sum or difference of per cents. AB 

 and BC (within the limits of probable error), so that the 

 per cents, of separation for all combinations of these fac- 

 tors is accurately represented by a linear diagram. In the 

 case of higher per cents, of separation (long distances), the 

 highest of the three frequencies (let us call it AC) falls 

 short of the sum of the other two (AB + BC), and so it is 

 a smaller number than the distance representing it on the 

 diagram, but it nevertheless (within the normal limits of 

 error) can be calculated from this diagram distance AC, 

 for a constant relation was discoverable between this hy- 

 pothetical distance and the actual frequency. Thus the 

 different frequencies do not bear any random relation 

 to each other that is mathematically possible, but bear 

 relations that disclose a linear connection between the 

 factors. 



It remains to consider the meaning of the fact that in 

 cases where there is a high per cent, of separations, the 

 highest per cent.— that between A and C, let us say— is 

 not as great as the value of the distance AC representing 

 it on the diagram. /. p., it is less than the sum of the per 



cents shown between A and B, and B and C, respectively. 

 If, whenever A and B or B and C separate, A and C sep- 

 arate also, as shown in Fig. 2, (a) and (b), then per cent. 

 AC would be equal to per cent. AB plus per cent. BC, but 

 since per cent. AC is lower than this, there must be cases 

 in which, although A and B or B and C separate, A and C 



separates from A but A does not separate from C, that B 



fail to separate. It is obvious that in these 



3, where B 



