50 



one suborder, Desmosticha Haeckel. In the „CliallengeV'-Echini the same course is 

 followed, and it is here (p. 18) even attempted in a mathematical way „to show 

 once for all how futile it must be to carry on the attempts of tracing the gene- 

 alogy of this or that group of animals", in case the Echinoidea. There are about 

 twenty variable terms in Echini, „which may be, of course, combined in all pos- 

 sible ways one with the other, and which are capable in their most restricted 

 limits of at least 2'" combinations; and when we remember that in the 225 genera 

 which we have thus far recognised, we may imagine any one or all the twenty 

 variables affecting the relationship of each of the genera, it seems somewhat hazar- 

 dous, to say the least, to attempt anything beyond the broadest indications of the 

 outlines of the relationship". This may be theoretically true, but in pratice there 

 remain only some few characters to be taken into consideration when trying to 

 trace the relationship of the forms, and the matter is not so difficult as it looks 

 from the mathematical problem as put up by Agassiz. 



More elaborate classifications have been given especially by Pomel, Duncan, 

 Lambert and Gregory ') ; they are represented above in a tabular view. 



Also the system of Bell-) ought to be mentioned, viz. 



Entobranchiata. 



Fam. 1. Cidaridæ. 

 Ectobranchiata. 



Ser. a. (Palæoproctous.) 



Fam. 2. Salenidæ. 

 Ser. ß. (Neoproctous.) 

 Subser. I. (polylepid.) 



Fam. 3. Echinothuridæ. 

 Subser. II. (decalepid.) 

 Fam. 4. Arbaciadæ. 



— 5. Diadematidæ. 



— 6. Echinidæ. 



As seen by these tabular views there is very little accordance among 

 authors on the classification of the regular Echini. Leaving aside here the question, 

 as to the propriety of subdividing the whole class into Regularia and Irregularia, 

 or into Gnathostomata and Atelostomata, I shall here deal only with the Regularia. 



The Palœechinoidea have hitherto been regarded as a separate subclass, 

 differing from all the other Echinids (Euechinoidea) in having more than two series 

 or (Bothriocidaris) only one series of interambulacral plates and two or more ambu- 



') A review of the different classifications of the Ecliinoidea has l)een given by Meissner in 

 Bronn's Classen u. Ordn. Echinodennen. p. 1321. 



') The Kcliinometrldæ, tlieir affinities and systematic position. Proc. Zool Soc. 1881. p 41U. 



