Order VI. CYRTELLARIA, Haeckel, 1881. _Definition_.--NASSELLARIA with a complete lattice-shell enveloping the central capsule. Suborder I. SPYROIDEA, Haeckel. _Spyridina_, Ehrenberg (_pro parte_), 1847, Monatsber. d. k. preuss. Akad. d. Wiss. Berlin, p. 54. _Zygocyrtida_, Haeckel, 1862, Monogr. d. Radiol., p. 291. _Zygocyrtida_, Bütschli, 1882, Zeitschr. f. wiss. Zool., vol. xxxvi. p. 501. _Acanthodesmida_, R. Hertwig, 1879, Organismus der Radiol., p. 68. _Spyrida_ vel _Spyroidea_, Haeckel, 1881, Prodromus, p. 440. _Definition._--NASSELLARIA with a complete lattice-shell, exhibiting constantly a bilocular cephalis with a sagittal constriction. The suborder #Spyroidea#, and the two following closely allied suborders, #Botryodea# and #Cyrtoidea#, represent together that large group of Radiolaria which I first described in my Monograph (1862, pp. 272, 280) as the family Cyrtida, but afterwards as a separate order (or sublegion) under the name #Cyrtellaria# (1883, Jena. Sitzungsber., Feb. 16, p. 18). This group comprises all those MONOPYLEA or NASSELLARIA which possess a complete lattice-shell, whilst the preceding #Plectellaria# never develop a perfect fenestrated shell enveloping the central capsule. The #Spyroidea# differ from the other #Cyrtellaria# (#Botryodea# and #Cyrtoidea#) in the bilocular shape of the cephalis, which is bisected by the sagittal ring and a corresponding longitudinal constriction into two symmetrical halves. The #Spyroidea# appear in the first system of Polycystina of Ehrenberg (1847, _loc. cit._, pp. 53, 54) as the fourth of his seven families, under the name Spyridina, with the following definition:--"Testæ nucleo destitutæ (associatæ et coalitæ); cellulæ binæ clathratæ, nucis forma amplæ, strictura longitudinali levius discretæ." Ehrenberg united them with his "Polycystina composita or SPUMELLARIA" and separated them from the closely allied "Polycystina solitaria or NASSELLARIA." He distinguished among them five genera, two of which have no external appendages (_Dictyospyris_ and _Pleurospyris_), whilst the other three possess spiny or lamellar appendages (_Ceratospyris_, _Cladospyris_, and _Petalospyris_). These five genera and the accompanying definitions were also repeated in the same terms in the last system of Ehrenberg (1875, _loc. cit._, p. 157). In my Monograph (1862, pp. 280, 291) the #Spyroidea# are enumerated as a {1016}subfamily of the Cyrtida, under the name Zygocyrtida, with the following definition:--"Lattice-shell divided by an annular sagittal longitudinal constriction into two neighbouring equal joints or chambers." I adopted at that time the above five genera of Ehrenberg, only eight species of which were known.