NO. IO PHYLOGENETIC STUDY OF RECENT CRINOIDS CLARK 63 



This, however, is not a strictly correct presentation of the case. 



In dealing with the families we considered in each the same number 

 of contrasted characters and, with a few exceptions, each pair was 

 represented in each family, so that the totals were directly comparable. 



But the number of the contrasted pairs considered in the various 

 structural units varies very greatly, running from 1 to 10. As there 

 are six families, the actual number of pairs and the actual number of 

 characters for each structural unit is as follows : 



Total number Total number 



of pairs in all of characters 



umt trasted characters the families considered 



Structural Pairs of con- f irs . „ f characters 



trasted characters ;.„ <„„:i;.„„ „„„„;j~,<./i 



Calyx 10 60 120 



Arms 9 54 108 



Column 7 42 84 



Disk 5 30 60 



Pinnules 5 30 60 



General Structure.... 1 .6 12 



Thus in order to raise the figures for all the structural units in 

 all the families to the same relative value it is necessary to multiply 

 each by the following numbers : 



Calyx 10 x 63 x 6—3780 Disk 5 x 126 x 6 — 3780 



Arms 9 x 70 x 6 — 3780 Pinnules S x 126 x 6 — 3780 



Column 7 x 90 x 6 — 3780 General 1 x 630 x 6 — 3780 



Applying these multiples to the table (the figures of which already 

 include the multiple 6) we have: 



General 630 (1) 3780 (2) difference 3150 (2) 



Calyx 1890 (1) 2205 (2) 3*5 (2) 



Disk 1764 (1) 1512 (2) 252 (1) 



Arms 2310 ( 1 ) i960 (2) 350 ( 1 ) 



Column 2070 (1) 1710 (2) 360 (1) 



Pinnules 3402 (1) 1008 (2) 2394 (1) 



In terms of the least specialized structural unit (the pinnules) this 

 gives us the following ratios of specialization: 



General 

 Calyx . . 

 Disk 

 Arms . . . 

 Column 

 Pinnules 



