Though M. van Beneden’s figure (copied in Cat. Seals & Whales, p. 347. f. 69) is so unlike the figure of _Petrorhynchus capensis_ in the Cat. Seals & Whales, pp. 344 & 345. figs. 67 & 68, yet the cast of the beak of M. van Beneden’s specimen resembles the latter figure and our specimen. Family 18. ZIPHIIDÆ. Ziphiina, _Gray_, _Cat. S. & W._ pp. 327, 348. Ziphiidæ, _Gray_, _Synops. Whales & Dolph._ p. 10. Skull beaked. Maxillaries not dilated above. Intermaxillaries linear, rather swollen on the sides of the nostrils. Teeth on the sides of the lower jaw compressed. Cervical vertebræ more or less united into a consolidated mass. * _Symphysis of the lower jaw produced behind the teeth._ 1. BERARDIUS. Berardius, _Gray_, _l. c._ pp. 327, 348; _Synops. Whales. & Dolph._ p. 10. Teeth 2·2, in the front of the sides of the lower jaw, conical, compressed. Lower jaw gradually tapering in front. Symphysis moderately long, as far from the hinder tooth as from the tip. 1. Berardius arnuxi. Berardius arnuxi, _Gray_, _l. c._ p. 348, fig. 70; _Synops. Whales & Dolph._ p. 10; _Gervais_, _Ostéog. Cét._ t. 23 (skull). Inhab. New Zealand. “Skull and lower jaw, a cervical vertebra, scapula, hyoid, paddles, and pelvic bones of one individual. “Single tooth of another individual, weight 206 grains. in. “Length of head 23½ Length of nose 17 Length of dental groove 7 Length of lower jaw 19 Width at notch 5½ Width at orbits 9½ Width of intermaxillary at blow-holes 4½ Width of nose 2 Height of occiput 9½ “One small tooth imbedded close to the tip of lower jaw on left side, 1 inch high, weight 38⅘ grains, irregular triangular shape. “This is the skull of a young animal. A groove containing a strong ligament connecting the muscle of the forehead with the snout is deeply imbedded in the intermaxillary groove. The snout is described as long and flexible. Atlas and axis anchylosed. Length of cervical vertebræ 3⁷⁄₁₀ inches. Scapula, longitudinal diameter 10 inches, transverse diameter 6 inches. Paddles, length 14 inches, width 3½ inches. Hyoid arch 5½ × 4 inches high. Pelvic bones 2½ inches. “The specimen was cast on the beach on the west coast, and prepared by Dr. Knox.”—_Hector._ “Your _Berardius_ proves to be quite different from the first one we got, both in the dentition and form of the skull. We have had several good papers on it from Dr. Knox. He has made a beautiful preparation, showing that the tooth does not pass through the gum.”—_Dr. Hector_, letter dated 30th October, 1870.