(4) The sacral vertebræ, varying from 2 to 13 in number, are fused together solidly into one piece, the combined centra forming a heavy mass and the neural canals a continuous tube, while the neural spines are united into a ridge. As a rule, only the first two vertebræ of the sacrum are in contact with the hip-bones, to support which they have developed special processes, the remainder of the mass projecting freely backward. [Illustration: FIG. 16.—Sacrum of Wolf, upper side. _I_, _II_, _III_, first, second and third sacral vertebræ. _pl._, surface for attachment to hip-bone.] [Illustration: FIG. 17.—Caudal vertebræ of Wolf, from anterior and middle parts of the tail. Letters as in Fig. 15.] (5) The caudal vertebræ vary greatly, in accordance with the length and thickness of the tail. In an animal with well-developed tail several of the anterior caudals have the parts and processes of a typical vertebra, centrum, neural arch and spine, zygapophyses and transverse processes. Posteriorly, these gradually diminish, until only the centrum is left, with low knobs or ridges, which are the remnants of the various processes. A varying number of long, cylindrical centra, diminishing backward in length and diameter, complete the caudal region and the vertebral column. In some mammals, _chevron bones_ are attached to the under side of the anterior and middle caudals; these are forked, Y-shaped bones, which form a canal for the transmission of the great blood-vessels of the tail. [Illustration: FIG. 18.—Ribs of Wolf from anterior and middle parts of the thorax. _cp._, head, _t._, tubercle.] The _ribs_, which are movably attached to the backbone, together with the dorsal vertebræ and breast-bone, compose the _thorax_, or chest. The articulation with the vertebræ is by means of a rounded head; in most cases the head has two distinct facets, the pit being formed half on the hinder border of one dorsal vertebra and half on the front border of the next succeeding one, but posteriorly the pit is often shifted, so as to be on a single vertebra. A second articulation is by means of the _tubercle_, a smooth projecting facet on the convexity of the rib’s curvature and near the head; the tubercle articulates with the transverse process of its vertebra. The ribs, in general, are curved bars of bone, which in small mammals generally and in the clawed orders are slender and rod-like, while in the hoofed mammals they are broader, thinner and more plate-like, especially the anterior ones. The number of pairs of ribs is most commonly 13, but ranges among existing mammals from 9 in certain whales to 24 in the Two-toed Sloth (_Cholœpus didactylus_). The complex curvature of the ribs, outward and backward, is such that, when they are drawn forward (in Man upward) by muscular action, the cavity of the thorax is enlarged and air is drawn into the lungs, and when they are allowed to fall back, the cavity is diminished and the air expelled.