4. Polyphyletic hypothesis, deriving the different groups of NASSELLARIA 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: (1) 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 #Cyrtoidea# (C). This triphyletic hypothesis is supported by R. Hertwig (1879, _loc. cit._, p. 136); he assumes that the original skeletonless Nassellida (_Cystidium_) 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 NASSELLARIA. 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) combined, 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 #Cyrtellaria# is not perfectly known, and often exhibits structures which are difficult to explain with regard to the three elements A, B, C. Under these circumstances further researches on the numerous imperfectly known NASSELLARIA are required, and chiefly accurate observations on their more minute structure and on their important ontogeny. {895}We divide the immense legion of NASSELLARIA into two large orders, the #Plectellaria# without complete lattice-shell, and the #Cyrtellaria# with a complete lattice-shell or a "cephalis," including the central capsule; the latter, of course, have arisen from the former. The #Plectellaria# comprise three different suborders, the #Nassoidea# (without skeleton), the #Plectoidea# (with a tripodal skeleton, without ring), and the #Stephoidea# (with a primary sagittal ring, with or without tripod). The #Cyrtellaria# again also comprise three different suborders, the #Spyroidea# (with bilocular cephalis and a sagittal constriction), the #Botryodea# (with multilocular and lobate cephalis, exhibiting two or more constrictions and three or more lobes), and the #Cyrtoidea# (with simple, unilocular cephalis, without constriction). _Synopsis of the Orders and Suborders of_ NASSELLARIA.