Both in its resemblances and its differences, as compared with the far longer and more complex story of the horses, the history of the †titanotheres has instructive bearings upon evolutionary theory. (1) Starting with two phyla, one of which speedily died out, the other ramified into four or five, which continued until the disastrous end, pursuing a nearly parallel course of development. (2) There was a great increase in size and especially in bulk and massiveness from species no bigger than a sheep in the Wind River stage to those which rivalled small elephants in the lower White River. (3) The teeth underwent comparatively little change; the incisors dwindled and lost functional importance and the canines were reduced, horn-like growths taking their place as weapons; the premolars grew larger and more complicated, but never attained the full size and complexity of the molars, as they did in other perissodactyl families. (4) Horn-like, bony protuberances appeared first as small humps and knobs over the eyes and steadily enlarged, at the same time shifting their position forward, until they finally attained great size and were on the nose. (5) The skull was modified so as to support these weapons and endure the shock of impact when they were put to use, (_a_) by making the upper profile strongly concave from before backward; (_b_) by greatly widening the top of the cranium, where in the older and more primitive genera the high and thin sagittal crest was placed; (_c_) by immensely increasing the thickness of the cranial bones and at the same time hollowing them by means of an intricate system of cavities; in this way sufficient strength was secured without undue increase in weight. [Illustration: FIG. 165.—Series of heads of †titanotheres in ascending geological order. _A._, _†Palæosyops_, lower Bridger. _B._, _†Manteoceras_, upper Bridger. _C._, _†Diplacodon_, Uinta. _D._, _†Titanotherium_, extreme development of horns, White River. From models in the American Museum and Princeton University.] (6) The growth of the brain did not keep pace with the increase in the size and weight of the body and head, and this deficiency may have been a factor in determining the early extinction of the family. (7) To support the huge head, stout ligaments and powerful muscles were needed in the neck and trunk and these in turn required large bony, surfaces for their attachment. To meet this need, the spines of the anterior trunk-vertebræ were very much lengthened, so as to form a hump at the shoulders, and this elongation of the spines went on in proportion to the growing weight of the head.