FORT UNION OF CRAZY MOUNTAIN FIELD, MONT. 79 



negative fraction, while in montanus it is inclined upward to the right, 

 coefficient a significant, positive, fraction.^^ It is quite possible 

 although unprovable from these data that the distinctly different 

 type of variation in these two species characterizes difterent generic 

 groups. 



The ratio length Mi to width Mi has a standard deviation of 0.17 ± 

 0.04 in sinclairi and 0.13 ±0.03 in montanus. The means of the two, 

 2.2 and 2.0, respectively, do not differ enough to prove that they are 

 a reliable method of distinguishing these species. The character may 

 however, be taken as of taxonomic value in such cases as that of 

 silberlingi where this value, 2.6 in the unique specimen, deviates 

 significantly from the mean for sinclairi (deviation more than t"wdce 

 the standard deviation of the latter). There is a group of species 

 that seems to be characterized by a high value for tliis ratio, or 

 descriptively by a relatively long and narrow Mi, including silberlingi, 

 russelli, and grangeri in tliis fauna and Ectypodus musculus and 

 Paredypodus tardus in other Paleocene American faunas. 



There are too few specimens with M2 to provide adequate data, but 

 with its variability assumed to be about that of Mi, its length: width 

 ratio would appear to be a valuable character distinguishing Piilodus 

 mediaevus and montanus, in both of which the ratio averages 1.4 in 

 the known material, from ail other species in which it is known 

 averaging 1.7 to 1.9. 



The length of P^ in the montanus group has the very high coefficient 

 of variation 18.5 ±2.86. This is, generally, too high a coefficient for a 

 sample of one species, yet the other coefficients for the upper teeth 

 are of more reasonable size, 10.0 in the case of length M^ and con- 

 siderably smaller for the other dimensions used. It is possible that 

 some extraneous P^'s have been included, but more probable that they 

 are all of one species and that this tooth, in any event visibly reduced 

 and in process of becoming vestigial, is extreme^ variable in length. 

 In either case, its length is not a reliable specific character. The 

 number of cusps on this tooth, varying from fom' to seven in all the 

 specimens of tliis family in which it is known, seems at first sight to 

 be a helpful character and has been used in specific diagnosis, but 

 probably it is not. In specimens that, on all other data, rather 

 clearly represent one species, montanus, this cusp number shows the 

 full range of variation for the isbvnily, 4 to 7. The data, as well as 

 those for P. mediaevus, are given in table 7. 



s* The samples are inadequate for the useful exact calculation of the regression equations, but their general 

 nature is visible. 



