MONOGEAPH OF THE EXISTING CKINOIDS. 9 



commonly considered their specific characters, while two others may have only a 

 small minority in common; and, as in other animals, characters perfectly reliable 

 in one group are more or less unreliable, or even perfectly worthless, in another. 

 Species may be found of all grades of differentiation, from a very small minority of 

 their characters to complete separation, but usually they fall into two classes: (1) 

 those separable from related species by a minority of their characters, the remainder 

 being held in common, and (2) those separable in all their characters. The first 

 division is in reality, of course, arbitrary, for it is undoubtedly true that any two 

 species will be found to be always separable in all their characters, provided we 

 devote a sufficient amount of study to them; it might better be worded "those 

 separable fi-om related species by a majority of the characters commonly employed 

 in specific diagnosis." 



It is usually found that a number of species differentiated according to the first 

 rule form a circumscribed unit the sum of the diversity of all the characters in which 

 does not overlap the sum of the diversity of all the characters in any other sunilar unit, 

 the assemblage of forms differentiated under the first rule thus coming as a whole under 

 the second rule. These sharply circumscribed units, as well as species falling withm 

 the limits of the second rule, I have considered as representing valid genera, while 

 forms not separated from related forms by the sum of all then- characters I have 

 regarded as species. All species agreeing in the majority of then- characters as 

 employed in systematic diagnoses I have considered as congeneric. 



Now a number of species may, according to this ruling, be strictly congeneric, 

 yet they may be united into several groups by a sharply defined single character 

 which is common to, and exactly similar in, several species, and is not found outside 

 of those species. These groups witliin the genus I have considered worthy of sub- 

 generic rank. Smiilarly, subgenera may be differentiated into distinct specific 

 groups, though usually this differentiation is, as would be expected, less apparent. 

 In the separation of the families and of the subfamilies as well as of the higher units 

 the same idea has been followed, but characters of a more fundamental nature, and 

 therefore not sufficiently plastic to be of service in the differentiation of genera and 

 species, have been employed. 



As in all other groups of annuals the various crmoid species are of very differ- 

 ent relative value. In some (mostly the more highly multibrachiate oligophreate) 

 genera if any one character whereby the species are commonly differentiated be 

 plotted on a species curve, the several species will be found to be indicated not by 

 a series of separate triangles, but by a succession of more or less marked nodes which 

 are united to the mass forming the adjacent nodes by coalesced bases in thickness 

 equal to from 10 to 60 per cent or more of the maxunum height of the neighbormg 

 nodes. Such variability and lack of absolute fixity in any one character is as a 

 rule reflected in all the characters, and thus there results a species grouji or genus 

 which may be compared to a small mountain system rising out of a plam, each 

 peak of which represents the separate species. 



In such a genus every systematic character varies between two extremes, 

 but there is often no correlation whatever between the different characters. Thus 



79140°— Bull. 82—15 2 



