FORT UNIOX OF CRAZY MOUNTAIN" FIELD, MONT. 179 



The onl}^ deflection in the frequency curve is in the 12.05-12.55 group, 

 and this is not significant. By actual calculation, which need not be 

 given here, a deflection at this point would have to be of at least 3 to 

 have any probable significance, and tliis deflection is in fact only of 1. 

 The mean, the median, and the mode almost exactly coincide. 



The distribution thus indicates a unimodal, unskewed curve, and 

 provides no warrant for splitting into two groups, or species, on the 

 basis of size (or of this dimension, which is sufficiently closely cor- 

 related with size). 



The actual positions of the types are indicated on the histogram. 

 The neotype of C. corrugatus, although not elsewhere formally so 

 designated, is such essentially as Matthew (Pale. Mem.) largely bases 

 his redefinition of the species on it. The type of C. corrugatus has no 

 Ma, but it must have measured about 12.0 mm in this dim^ension, calcu- 

 lated from the ratios of associated M^ and M2 in surely conspecific 

 individuals of about the same size. M2 of the neotype of C. cor- 

 rugatus is 12.4 mm in length and of the type of C. ferox 13.4 mm.^* 

 The deviations of these three specimens are: C.jerox, type, +0.72; 

 C. corrugatus, plesiotype, —0.28; C. corrugatus, type, calculated, 

 — 0.68. All these deviations are considerably less than the standard 

 deviation. There is no reason or warrant for placing these individuals 

 in different species on the basis of size.^^ 



The coefficient of variation, 8.34, is high and indicates a species of 

 considerable variability in size, but there are many cases of dimen- 

 sions of single species, and even of subspecies or pure races, with 

 equally high variabiUty, or higher, and this figure does not in itself 

 suggest that two species, inseparable on these data, may be present. 



These data do not prove that two species are not present: Such 

 proof of a negative is practically impossible, and the burden of proof 

 is always to be considered as rec^uired from the positive side. They 

 do show that in this sample it is impossible to distinguish two size 

 groups (and hence two species distinguished by size differences), that 

 the distribution is not inconsistent in modality, variability, etc., with 

 a single species, and adding considerations somewhat beyond purely 

 statistical treatment, that if two species were present they would very 

 probably not correspond with those now recognized. 



There are no other variates or attributes, so far as I can observe, 

 that do permit any differentiation of this group into two or more 

 species. The supposed species occur together, at the same horizon 

 and localities, and in approximately eciual numbers."^ 



'6 It ii crushed and spread a little, but this can be exactly allowed for. 



" It may also be noted that on the purely hypothetical and extremely improbable supposition that two 

 species were present and that their size limit corresponded with the deflection in the frequency curve given, 

 the neotype of C. corrugatus would belong with C. ferox and the type of C. corrugatus would be on the bound- 

 ary between the two groups. 



" This, of course, depends on individual identifications, but if these were to be based on any rational 

 size distinction the grouping would have to be into two approximately equal groups. 



