As regards size, the largest specimen of _B. arnuxii_ of which I find record is the type specimen. This was 32 feet long, and the skull 1,400 mm., or about 55 inches long. This appears to have been an adult male. The Centerville specimen of _bairdii_, which was an adult male, was about 41 feet long, and the skull 1,532 mm., or about 60 inches long, while the adult female from St. George Island was 40 feet 2 inches long and the skull 56 inches. Although the total length of the specimens of _bairdii_ is so much greater, it will be observed that the length of the skull, while a little greater, absolutely fails to measure up to the proportions found in _arnuxii_. It might be suspected on this account that the external measurements of _bairdii_ were exaggerated, but that such is not the case will appear from an examination of the measurements of vertebræ given on page 75. It is evident that the specimens of _bairdii_ are far more massive in all parts of the skeleton than the specimen of _arnuxii_ there cited. The same relations will be found upon comparing measurements of the specimen of _arnuxii_ figured by Van Beneden and Gervais.[57] The truth appears to be that _bairdii_ is a much larger species, but that the skull is considerably smaller relatively. SKULL. The skull of _Berardius bairdii_ presents many characters by which it may be distinguished from that of _arnuxii_, whether adult or young. As compared with the latter, the rostrum is less massive at the base. The pterygoid has a rounded extension posteriorly and superiorly, so that the posterior portion of the upper border of the pterygoid sinus is convex, rather than nearly straight, as in _arnuxii_. The exoccipital is larger and broader distally below, and its external surface is plane or concave, rather than convex, as in _arnuxii_. The distal end of the zygomatic process is much more incurved. The nasal bones instead of presenting lateral extensions have nearly straight sides. The vomer is deeply emarginate at the base of the skull posteriorly where it rests against the presphenoid. The palatines extend scarcely or not at all in front of the pterygoids. The foregoing differences will readily be seen by comparing the figures on Pls. 26-29 with those of the type of _B. arnuxii_ given in Van Beneden and Gervais’s Osteography, plate 23. The following are dimensions of skulls of both species: _Dimensions of five skulls of Berardius bairdii (including the type) and of three skulls of B. arnuxii._