74 



BULLETIN 16 9, UNITED STATES NATIONAL MUSEUM 



The dimensions and ratios are, from a statistical point of view, 

 continuous variates. The counts are discontinuous variates. The 

 nonniunerical observations are attributes and to these is to be added, 

 for comparison with other collections, the provenience of the speci- 



mens. 



■S3 



? Ecfypodus 



? Ecfypodus 3. 

 russelli 2 



7 a 9 10 n 5 6 7 8 9 10 11 



NUMBER OF EXTERNAL CUSPS Ml 



POSITIONS OF TYPE SPECIMENS 



"f Pa fee iy pod us J epseni 



^Ecfypodus Silberlinai 



Ptilodus graciJiS' monfanus 

 „ Ptilodus monfanus 



? Ecfypodus russelU 



„^ , ? Ptilodus 



?Ectypodu3 jyou9/ass: 

 grangen ^ 



2.0 



3.0 



Ptilodus sindain 



Y^Ectypodus 



■— ' ^'^ snbeding. 



A.O 



5.0 



6.0 7.0 



\? Ptilodus gidleyi 



8-0 9.0 



Ptilodus monfanus 



Tatecfypodus^ 



jepseni _ 



?£cfypodus ,^]}? Ecfypodus gran^en^'^Plilodus douqlassi 



russelli 

 FORT UiNIOM PTILODONTID/C. 



LENGTH P4. 



Figure 5.— Histograms of typical variates of multituberculates from the Qidley and Silberling Quarries: a. 

 Number of external cusps on Mi in four species; 6, length of Pi in the whole sample, with division of 

 species based on the study of this and all other available characters. 



The same data were recorded for the much fewer Torre j on speci- 

 mens (American Museum collection) and, from publications, for the 

 types of other known species available for comparison. 



The numerical data were then all plotted graphically in several 

 different ways, a few of which are here reproduced (figs. 5-7). Tenta- 

 tive grouping was then attempted, by taking each graphic representa- 

 tion and dividing it into as iew groups as possible. For instance, the 

 length of P4 histogram was at first divided into only three groups, 

 one from 2.45 to 3.95 mm, one from 4.85 to 5.45, and one from 5.75 

 to 8.75. (The single specimens at 4.3 and at 9.1 were left doubtful 

 and later disposed of as shown, on other data.) 



It was then found that the groupings on different characters did 

 not include the same specimens. For instance, in the grouping on 

 length of P4 the type of silberlingi (see below) is quite indistinguishable 



2» Almost all are from the Silberling or Gidley Quarries, and the few that are not from these do not differ 

 significantly. Provenience was therefore not a useful datum in sorting out the collection, but only in com- 

 paring it with other collections. 



