894 THE VOYAGE OF H.M.S. CHALLENGEE. 



be derived easily from such a tripod ; but the groups A, C, and E only by means of 

 the hypothesis that the original tripod may be completely reduced and finally lost. 

 This hypothesis was employed in 1881 in my Prodromus, since I had convinced myself 

 that the " triradial structure " is prevalent in the great majority of Nassellakia, and 

 is perhaps more important than the sagittal ring. 



3. Monophyletic hypothesis, deriving all Nassellaeia from a latticed cephalis, 

 a simple ovate or subspherical fenestrated shell without ring and trij)od [Cyrtocalpis, 

 Archicapsa, &c.). The groujjs C, E, F, and G may be derived easily from such a cephalis, 

 but the groups A, B, and D only by means of the hypothesis that the sagittal ring as 

 well as the basal trijiod may remain as the last remnants of a reduced cephalis. This 

 hypothesis was given in 1862 in my Monograph, where I constructed the' first pedigree 

 of Eadiolaria (j). 234). I there derived all the Cyrtida from the Sphseroidea 

 {Cyrtidosphccra), supposing that Cyrtocalpis and some other Monocyrtida may form a 

 dii'ect phylogenetical passage from the Sphseroidea to the Cyrtoidea. 



4. Polyphyletic hypotheses, deriving the different groups of Nassellakia from 

 different skeletonless Nassellida, by development of simple siliceous skeletons in different 

 ways. Among the numerous polyphyletic hypotheses which are possible, one of the 

 simplest would be the supposition that three different fundamental forms of skeleton may 

 have arisen independently one from another : (l) a simple sagittal ring as original form 

 of the Stephoidea and Spyroidea (A) ; (2) a simple basal tripod as original form 

 of the Plectoidea (B) ; (3) a simple latticed cephalis as original form of the 

 Botryodea and Cy rt oidea (C). This triphyletic hypothesis is supported by R. 

 Hertwig (1879, loc. cit, p. 136) ; he assumes that the original skeletonless Nassellida 

 (Ci/stidium) have produced three different branches, his " Acanthodesmida " 

 ( = Stephoidea and Spyroidea) with a primary ring, his " Plagiacanthida " 

 ( = Plectoidea) with a primary tripod, and his Cyrtida (=:Botryodea and 

 Cyrtoidea) with a primary cephalis. This hypothesis seems rather probable on the 

 first view ; but it meets with the greatest difficulties in view of the fact that these 

 three original elements of the skeleton are more or less evidently combined in the great 

 majority of Nassellakia. The greatest difficulty arises from the fact that often among 

 very similar and closely allied forms the first exhibits all three elements (A, B, C) com- 

 bined, whilst the second has a combination of A and B, the third of B and C, the 

 fourth of A and C ; and there are other forms, very similar to the former, in which one 

 element only is recognisable. Another difficulty arises from the fact that the intimate 

 structure of the cephalis in the majority of C y r t e 1 1 a r i a is not perfectly known, and 

 often exhibits structures which are difficult to explain with regard to the three elements 

 A, B, C. Under these cii'cumstances further researches on the numerous imperfectly 

 known Nassellakia are required, and chiefly accurate observations on their more minute 

 structure and on their important ontogeny. 



