10 THE AMERICAN NATURALIST [Vol. L 



possible, by adding together the frequencies of separation 

 between all adjoining factors, to obtain the total frequency 

 of crossing-over in the chromosome. This total frequency 

 would be represented in the diagrams by the total length 

 of the latter, since it is always the per cent, of separations 

 between the most closely adjoining factors which is chosen 

 to determine the number of units of length in any region 

 of the diagram. Now, the total frequency of crossing- 

 over in a chromosome ought, we should expect, to be de- 

 termined by the length of that chromosome. Accordingly, 

 we should expect to find differences between the total fre- 

 quencies of interchange (or the diagram lengths) of the 

 different groups of factors exactly paralleling the size 

 differences existing between the chromosomes themselves. 

 It will be seen, however, that such an expectation assumes 

 also (1) that crossing-over occurs with equal frequency 

 in all parts of a chromosome, and in equal parts of dif- 

 ferent chromosomes, and (2) that the factors available 

 for working out the total frequency of interchange do not 

 lie in any one limited region of the chromosome, but are 

 more or less scattered, some of them lying near each end. 

 A negative result from our test, then, might merely mean 

 that one of these two assumptions was incorrect, and this 

 would not disprove any essential point in the theory of 

 crossing-over previously outlined. On the other hand, a 

 positive result would seem to be too much of a coincidence 

 to happen by mere chance, and so would seem to prove the 

 correctness both of our main theory and of the two latter 

 points. 



In regard to the size relations existing among the chro- 

 mosomes themselves, as determined by cytological ob- 

 servations, the work of Stevens (13), taken in connection 

 with the later work of Metz (5), and of Bridges (2), shows 

 that there are four pairs of chromosomes in Drosophila: 

 a pair of moderately long sex chromosomes, two pairs of 

 very long < < autosome s," and one pair of minute ' ' auto- 

 somes.' ' 



We may next consider the lengths of the genetic groups, 



