of _Palaeomastodon_. The fusion of the post-tympanic portion of the squamosum is, in _Palaeomastodon_, much further advanced than in _Pyrotherium_, so that the passage to the ear is not apparent in the basal view of the former, but makes a considerable notch on the under side of the skull of _Pyrotherium_. The mandibles are excessively thick and heavy, being united at the symphysis, which extends back to the front of the second molar. The ascending rami are prolonged backward, but do not rise above the level of the articulation. The atlas is a massive vertebra with the anterior cotyles deeply excavated, especially on the upper side, so that, as Gaudry suggested, the head must have been carried low. The flat posterior cotyles face obliquely downward. The neural arch is light and without a spine or an opening for the vertebral artery. The basal portion of the bone, however, is excessively heavy and thick; the socket for the odontoid process not reaching to the middle of the basal bar. The neural canal is oval in section, being a good deal wider than high, and of small size. The transverse processes are short, heavy projections, adapted to receive heavy muscles. On the ventral surface there projects from the posterior margin a strong hypophysis, which, as Gaudry has pointed out, is unusual, but which is a character of the atlas of the _Palaeomastodon_. The axis is a short, heavy bone, with the anterior cotyles facing obliquely upward, a small neural arch, no spine, and with a thick odontoid process, which has the form of a quarter of a hemisphere set onto the front of the centrum. Cervicals 3 and 4 are very short vertebrae with light neural arches and no spines. The neural canal is fully three times as high as wide. Thus it is entirely evident that the neck of _Pyrotherium_ was extremely short, as is the case with elephants, which alone would not be significant, but coincides with many other elephant features. Gaudry described a lumbar vertebra which is also a short, heavy bone. Otherwise the vertebral column of _Pyrotherium_ is unknown. The distal end of the scapula is described by Gaudry as indicating a short, heavy bone, with the glenoid cavity compressed so as to be about twice as long as it is wide. The coracoid is a short, blunt process. The spine was broken off, but enough remained to indicate a moderately high spine, prolonged toward the humerus, and bent somewhat forward.