(8) The limb-bones increased in thickness until they became extremely massive, to carry the immense weight of the body, and they eventually lost the marrow-cavities, which were filled up with spongy bone, a great gain in strength. As is generally, though not universally, true of the large and heavy mammals, there was no coössification between the limb-bones and no great increase in their proportionate length. The thigh-bone, or femur, lost the cylindrical shape of the shaft, becoming flattened and very broad, and acquiring something of the appearance of the same bone in the elephants. [Illustration: FIG. 166.—Right manus of †titanotheres. _A._, _†Titanotherium_, White River (after Marsh). _B._, _†Palæosyops_, Bridger, Princeton University Museum.] (9) There was no loss or coössification of elements in wrist (carpus) or ankle (tarsus) and _no reduction of digits_ within the limits of the family. In the latest, largest and most specialized genera, as well as in the earliest, smallest and most primitive, there were four toes in the front foot and three in the hind. We have the most cogent reasons for assuming that all mammals were derived from ancestors which had five toes in each foot, neither more nor less. If this be true, then the most ancient known †titanotheres, which were small and light, had already suffered the loss of the first digit in the fore foot and of the first and fifth digits in the hind foot, but there reduction ceased. With the growing body-weight, long, narrow and slender feet would have been a detriment, whereas in swift-running animals, like horses and deer, long and very slender feet are a great advantage. The contrast is both striking and instructive, showing the importance of a short, broad, polydactyl and pillar-like foot to very large and heavy mammals, all of which have feet of this character. (10) The hoofs, as shown by the terminal bones (ungual phalanges) which formed their bony cores, were reduced in size until they became mere nail-like excrescences around the border of the massive foot. 3, 4. _Tapiridæ and †Lophiodontidæ. Tapirs and †Lophiodonts_ The history of the tapir family is not at all satisfactorily known, partly because tapirs are comparatively rare as fossils in all of the Tertiary formations, and still more for the reason that the specimens so far collected are so fragmentary, not a single half-complete skeleton among them. Had these animals actually been as rare in North America as the fossils would seem to indicate, they could not possibly have maintained themselves for so long a time, throughout nearly the whole of the Tertiary and Quaternary periods. For some reason, probably because they have always been forest-haunting animals, their habits must have kept them in places remote from the areas where the accumulation of sediments was in progress, and thus only occasional stragglers were buried and preserved.