_Definition._--#Spyroidea# with a galea, but without thorax; the shell being composed of the bilocular cephalis and of an aboral cupola or galea arising from its coryphal face. The family #Tholospyrida# differs from the preceding Zygospyrida, its ancestral group, in the development of a galea, _i.e._, a fenestrated hemispherical or dome-shaped cupola, which covers the upper face of the cephalis like a cap. Only three species of this family have been hitherto described: _Pylospyris_ (or _Spyridobotrys_) _trinacria_, figured in my Monograph (1862), _Pylospyris_ (or _Lithopera_) _denticulata_, figured by Ehrenberg (1872), and _Lophospyris_ (or _Ceratospyris_) _acuminata_, figured by Hertwig (1879). Fourteen new species have been found in the collection of the Challenger, which we dispose here among five genera. These may be derived from corresponding genera of Zygospyrida by the development of a galea. {1078}The number and disposition of the terminal feet around the basal plate do not vary so much in the Tholospyrida as in the Zygospyrida. We find here only one genus with three feet, _Tholospyris_ (corresponding to _Tripospyris_); one genus with two lateral feet, _Lophospyris_ (corresponding to _Dipospyris_); and two genera with numerous feet, the horned _Sepalospyris_ and the hornless _Tiarospyris_ (the former corresponding to _Petalospyris_, the latter to _Gorgospyris_). The fifth genus (_Pylospyris_) has no feet at all, and may be derived from _Circospyris_ among the Zygospyrida. The cephalis exhibits in the Tholospyrida the same typical structure which we have described above of all #Spyroidea# (compare p. 1017). The cupola or galea, arising from its upper face, seems to be a secondary production, perhaps caused by an apical growth of the central capsule, or in other cases by descending branches of the apical horn, which cover the apical face of the calymma with protecting network. _Synopsis of the Genera of Tholospyrida._ {Three basal feet (two I. Subfamily Lophospyrida. { paired pectoral and Two or three basal (cortinar{ an odd caudal), 469. _Tholospyris_. feet). Galea with a horn. { {Two paired basal { (pectoral) feet, 470. _Lophospyris_. II. Subfamily Tiarospyrida. }Galea with a horn, 471. _Sepalospyris_. Numerous basal feet in a } corona (six to nine }Galea without a horn, 472. _Tiarospyris_. or more). } III. Subfamily Pylospyrida. }Galea with a horn, 473. _Pylospyris_. No basal feet. } Genus 469. _Tholospyris_,[87] Haeckel, 1881, Prodromus, p. 441. _Definition._--#Tholospyrida# with three basal feet and an apical horn.