Shell tuberculate, with slight sagittal and sharp collar strictures. Pores subregular, circular. Cephalis nut-shaped, larger than the short truncate thorax. Coronet with fifteen to twenty short conical, parallel and vertical feet, about as long as the thorax. _Dimensions._--Cephalis 0.06 long, 0.09 broad; thorax 0.02 long, 0.07 broad. _Habitat._--Fossil in Barbados. 4. _Desmospyris carpocanium_, n. sp. Shell smooth, with slight sagittal and slight collar strictures. Pores subregular, circular, small and numerous. Cephalis campanulate, smaller than the ovate thorax. Coronet with fifteen to twenty irregular lamellar feet, which are longer than the thorax, pointed, nearly vertical and parallel. _Dimensions._--Cephalis 0.05 long, 0.08 broad; thorax 0.07 long, 0.1 broad. _Habitat._--South Pacific, Station 298, depth 2225 fathoms. Family LV. #ANDROSPYRIDA#, n. fam. (Pl. 88-90). _Definition._--#Spyroidea# with galea and thorax; the shell composed of a bilocular cephalis and of two secondary joints, a galea arising from its upper face, and a thorax arising from its lower face. {1091}The family #Androspyrida# differs from the three preceding families of #Spyroidea# in the three-jointed shell, in which the galea of the Tholospyrida and the thorax of the Phormospyrida are combined; it may therefore be derived from the latter by development of a galea, or from the former by formation of a thorax. The common ancestral group of these three families is probably the Zygospyrida. But it may be that a part of the Androspyrida has originated directly from the #Stephoidea#. Two species only of this family were hitherto known, _Amphispyris reticulata_ (figured, in 1872, by Ehrenberg, as _Dictyospyris_) and _Sphærospyris sphæra_ (described, in 1882, by Bütschli, as _Dictyospyris_). Thirty new species were found in the collection of the Challenger, and are here disposed in seven genera. But perhaps these may represent three different families, which we here enumerate as subfamilies; the Lamprospyrida, Perispyrida, and Nephrospyrida. The Lamprospyrida, the first subfamily, are tripodal #Spyroidea# with galea and thorax; they may therefore be regarded as a combination of _Tholospyris_ and _Acrospyris_. In the simpler form, _Androspyris_ (Pl. 83, fig. 8), the network of the shell is simple, and allows a very clear recognition of the internal structure. In the splendid _Lamprospyris_, derived from it (Pl. 89, figs. 13, 14) the delicate network is more or less spongy. The large apical horn is branched and fenestrated in the latter and simple in the former.