VARIATION IN THE GENUS EREBIA, 71 



object is to discover whether those data give any evidence as 

 regards the hypothesis, that inequahty in the numerical propor- 

 tions of the sexes, when coupled with variability in the pre- 

 ponderating sex, tends towards continued fluctuation of the 

 variable character. Of what nature, then, will the data be that 

 will lend support to this hypothesis? It is a matter of very 

 general observation that when the ordinary individual variations 

 of a species are thrown into a scheme of distribution, the curve 

 derived from them is normal. The essential property of a 

 normal curve is that it falls away symmetrically on either side of 

 M by regular gradations, the numbers becoming gradually less 

 below, and more above the mean. Curves A and B in Fig. 1 

 are therefore not truly normal, but curve C is. [See Entom. 

 Oct. 1901, p. 278.] 



Now, on the theory under discussion, we would not expect the 

 individual variations to fall into a normal curve, if the sexes are 

 disproportional, &c. ; there should be breaks in the continuity of 

 the slope, if the principle in question has come into play. If, of 

 course, we take individuals from many different areas, or from 

 one very large continuous area, we might obtain a normal curve, 

 owing to the whirligig of chance having brought in his revenges, 

 and filled up the breaks of continuity in one area with individuals 

 from another ; but if we take individuals from one somewhat 

 confined area, we should expect to find these breaks. By breaks 

 in the continuity of the slope, breaks in the actual series of 

 variations are not necessarily implied. The latter breaks, 

 namely, when some variations are omitted altogether, might be 

 accounted for by natural selection ; but when in some confined 

 area all the variations do occur, but not in such numerical pro- 

 portions as to fall into a normal scheme, then the facts are most 

 easily accounted for by the hypothesis that has been framed. A 

 confirmatory test besides this of abnormality of slope would be 

 in the M of individuals of some confined area not corresponding 

 to M of other areas, taken separately or combined. The method 

 then will be to fix on some species with numerical disproportion 

 of sexes, to select some character of that species which is variable 

 in the preponderating sex, then to determine if that character 

 falls into a normal scheme or not when a group of individuals is 

 considered that has been derived from some one confined area, 

 and also if the M of those from the confined area is the same as 

 the M of other areas taken separately or combined. The con- 

 clusions arrived at from the following data must be accepted 

 tentatively, as my material is not large enough to ensure any- 

 thing like accuracy. 



(To be continued.) 



