Only a few of the ribs accompany the skeleton of the adult female from St. George Island, Alaska (Cat. No. 49726), but there are eleven thoracic vertebræ, the transverse processes of the eleventh being short and thick, like those of the tenth, with a distinct facet for the rib at the free end. This facet, however, is directed obliquely backward and occupies only the posterior half of the free margin. There is no doubt in my mind that the number of thoracic vertebræ in _B. bairdii_ is normally 11 and in _B. arnuxii_, 10. This would ordinarily be of little importance, as in nearly all kinds of cetaceans a variation of one, or even two, in the number of thoracic and lumbar vertebræ in different individuals of the same species is commonly met with. In the present family, however, the number of thoracic vertebræ shows little variation, and as all known skeletons of _B. bairdii_ have eleven thoracics and all known skeletons of _arnuxii_ appear to have ten thoracics, it seems probable that this difference is specific. At all events, it is correlated with a difference in the form of the vertebræ themselves. As is well known, the transverse processes of the thoracics in this family undergo a sudden change of form and position near the end of the series, the elevated processes on the anterior thoracics being replaced on the posterior vertebræ by others at a lower level on the sides of the centra. This change takes place differently and on different vertebræ in the two species under consideration. VERTEBRÆ. In _B. arnuxii_ the eighth thoracic has no facet at the posterior end of the centrum for the articulation of the head of a ninth rib and no distinct transverse process, the tubercle of the rib articulating with a facet on the side of the metapophysis. In _B. bairdii_ the eighth thoracic is similar, but there is a distinct facet at the posterior end of the centrum. (Pl. 32, fig. 1.) In _B. arnuxii_ the ninth thoracic has a very distinct transverse process on the side of the centrum, while in _B. bairdii_ the ninth thoracic has a short, slender process attached to the side of the metapophysis and no facet at the posterior end of the centrum. (Pl. 32, fig. 1.) In _B. arnuxii_ the tenth thoracic is the second one having a distinct transverse process, and the latter is broad distally and has the articular facet on the posterior portion of the free margin. In _B. bairdii_ the tenth thoracic is the first having a distinct transverse process on the side of the centrum. (Pl. 32, fig. 1.) There are only ten thoracics in _B. arnuxii_, as already mentioned, but in _B. bairdii_ there are eleven, and the eleventh is that which bears the second transverse process on the side of the centrum.