Genus BERARDIUS Duvernoy. Of this genus the National Museum has three skulls and three skeletons representing the species _bairdii_, and a skull representing the species _arnuxii_. The latter, Cat. No. 21511, U.S.N.M., is without exact locality, but is catalogued as having been obtained in New Zealand. As the species _arnuxii_ has been well described and figured by Flower[48] and others, no detailed account of this skull is given here. Measurements of it, however, are included with those of _B. bairdii_ in the table on p. 68. BERARDIUS BAIRDII Stejneger. _Berardius bairdii_ Stejneger, Proc. U. S. Nat. Mus., vol. 6, p. 75, June 22, 1883. _Berardius vegæ_ Malm, Bihang K. Svenska Vet. Akad. Handl., vol. 8, 1883, No. 4, p. 109.[49] This species was based by Dr. L. Stejneger on a skull obtained by Mr. N. Grebnitzki in Stare Gavan, on the eastern shore of Bering Island, Commander Group, Bering Sea, in the autumn of 1881. In 1879 a portion of a skull of the same species was found on Bering Island by the _Vega_ expedition, and was made the basis of a new species, _B. vegæ_, by A. W. Malm, the description of which was published a few months after that of Doctor Stejneger. The National Museum subsequently received another skull from Bering Island, through Mr. N. Grebnitzki, but, so far as I am aware, nothing further was heard of the species until 1903 and 1904, when the National Museum received three nearly complete skeletons, two of them from St. George Island, Pribilof Group, Bering Sea, and one from the coast of California. The material now in the National Museum is as follows:[50] (1) _Cat. No. 20992_.—Skull and mandible of an immature individual collected by Dr. L. Stejneger in Bering Island. Original number 1520. Catalogued November 24, 1883. Type. (2) _Cat. No._ (lacking).—Skull and mandible of an immature individual. Collected by Mr. N. Grebnitzki in Bering Island (?). Mounted. (3) _Cat. No. 142118_.—Skull, mandible, and cervical vertebræ of a very young individual. Collected by Dr. L. Stejneger, June 5, 1883, on North Rookery, Bering Island. Original number 2191. This specimen is accompanied by notes and measurements. (4) _Cat. No. 49726_.—Skeleton and measurements of an adult female. Near East Rookery, St. George Island, Pribilof Group. Collected by James Judge, in June, 1903. Length, 40 feet 2 inches. (5) _Cat. No. 49727_.—Skeleton and measurements of an immature male. Same locality and date as the preceding. Length, 25 feet 5 inches. The two skeletons (4) and (5) are somewhat incomplete. The Museum received a photograph of the female from Maj. Ezra W. Clark. (6) _Cat. No. 49725_.—Skeleton and two photographs of an adult male (?) stranded on Centerville beach near Ferndale, Humboldt County, California, October, 1904. Length, about 41 feet.