Head beaked. Nostrils two, united into a single transverse or crescent-like blower on the centre of the back of the crown. Teeth only in the front or sides of the lower jaw, fitting into pits in the upper one. Dorsal fin falcate. Pectoral fin ovate, small, low down on the side of the body: fingers short, 4- or 5-jointed; second and third the longest; fourth rather shorter; first and fifth rather short. Cervical vertebræ more or less united into one mass. Family 16. HYPEROODONTIDÆ. Hyperoodontina, _Gray_, _l. c._ p. 327. Hyperoodontidæ, _Gray_, _Synops. Whales & Dolph._ p. 9. Blower lunate. Beak of the skull with a high crest on each side above, formed by the elevation of the maxillary bones in front of the blower. Teeth 2 or 4, in front of the lower jaw, conical. Cervical vertebræ united into one mass. 1. HYPEROODON. Hyperoodon, _Gray_, _l. c._ pp. 327, 328; _Synops. Whales & Dolph._ p. 9. Beak of the skull bent downwards: crest of the back of the beak sharp-edged, above as high as the occiput. Vertebræ 44 or 45:—C. 7 (all united into one solid mass). D. 9. L. 10. C. 18 or 19. 1. Hyperoodon butzkopf. B.M. Hyperoodon butzkopf, _Gray_, _l. c._ p. 330; _Synops. Whales & Dolph._ p. 9, t. 3. Hyperoodon rostratum, _Reinhardt_, _in Eschricht’s Vid. Selsk._ v. t. 7 (male fœtus and skeleton); _Gray_, _Synops. Whales & Dolph._ t. 3. f. 1-4. Inhab. North Sea. 1. Hyperoodon semijunctus, _Cope_, _Proc. Acad. Nat. Sci. Philad._ 1865, p. 15 (280), 1869, p. 21. Inhab. Charlestown Harbour. Most likely a variety of _H. butzkopf_. 2. LAGENOCETUS. Lagenocetus, _Gray_, _l. c._ pp. 327, 336; _Synops. Whales & Dolph._ p. 9. Beak of the skull straight, erect, very large, flattened, higher than the occiput. 1. Lagenocetus latifrons. B.M. Lagenocetus latifrons, _Gray_, _l. c._ p. 339; _Synops. Whales & Dolph._ p. 9. Hyperoodon latifrons, _Gray_, _Zool. Ereb. & Ter._ t. 24; _Reinhardt_, _in Eschricht’s Vidensk. Selsk. Skr._ v. t. 6 (skull). Inhab. North Sea. “Plate 6 represents the skull of a male of _Hyperoodon latifrons_ (Gray), from the Färöer, of which the complete skeleton, 25 feet long, is preserved in the University’s Museum. “Eschricht believed, as is known, that _H. latifrons_ was established on a very old male of the common Dögling, _Hyperoodon rostratus_; but Gray’s species must now be regarded as well grounded. “Plate 7 represents the male (fœtus) of the common _H. rostratus_. All figures of half the natural size.”—_Reinhardt._ Family 17. EPIODONTIDÆ. Epiodontina, _Gray_, _Cat. S. & W._ p. 327. Epiodontidæ, _Gray_, _Synops. Whales & Dolph._ p. 9.