1. Monophyletic hypothesis, deriving all NASSELLARIA from a simple sagittal ring (_Archicircus_, _Lithocircus_, &c., Pl. 81). The groups A, D, E, and G may be derived easily from such a ring, but the groups B, C, and F only by means of the hypothesis that the original ring may be completely reduced and finally lost. This hypothesis was stated by me in the years 1877 to 1879, when I had got the first general survey of the astonishing number of new NASSELLARIA in the Challenger collection, and as I had found the sagittal ring in the majority of them. This, my former hypothesis, is mentioned by Richard Hertwig (1879, _loc. cit._, pp. 68, 126). It was afterwards supported with particular energy by O. Bütschli (1882, Zeitschr. für wiss. Zool., Bd. XXXVI.). 2. Monophyletic hypothesis, deriving all NASSELLARIA from a basal tripod (_Triplagia_, _Plagoniscus_, &c., Pl. 91). The groups B, D, F, and G, all triradiate, may {894}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 NASSELLARIA, and is perhaps more important than the sagittal ring. 3. Monophyletic hypothesis, deriving all NASSELLARIA from a latticed cephalis, a simple ovate or subspherical fenestrated shell without ring and tripod (_Cyrtocalpis_, _Archicapsa_, &_c._). The groups 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 tripod 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 Radiolaria (p. 234). I there derived all the Cyrtida from the #Sphæroidea# (_Cyrtidosphæra_), supposing that _Cyrtocalpis_ and some other Monocyrtida may form a direct phylogenetical passage from the #Sphæroidea# to the #Cyrtoidea#.