Of the vertebral column, twenty-six vertebra are preserved (a few being represented by neural arches only). The atlas and axis are unknown. Five cervicals are present, each with a short, slightly opisthocoelus centrum, and with low weak spines. The foramena for the vertebra artery are usually large. Cervical 3 has a rather slender transverse process, projecting down—and backward. On cervicals 4, 5 and 6, these lateral processes are enlarged into broad lamellae, which reach their maximum of size on the sixth. Cervical 7 has no lamella, simply a slender transverse process. These transverse processes are strikingly like those of Nesodon. The thoracic vertebrae (of which I have complete or in parts 15) have moderately high spines, which resemble those of Adinotherium, not only in the general build, but also in the presence of a foramen for the exit of spinal nerves through each neural arch. These foramena can not be referred to as adaptations, but are special features indicating close relationship with the Nesodontidae. Six lumbar vertebra are present, each having broad depressed centra, and short wide spines. The rest of the column is unknown.
The distal portion of the humerus is preserved, showing the trochlea to be relatively narrow, with a prominent internal phlange for the ulna. The epicondyles are both small. The supratrochlear fossa is moderately deep, the anconeal fossa very deep, a large perforation connecting the two. Of the ulna, only the distal end is preserved, and it is marked by a prominent styloid process, ending in the facet for the pyramidal, this facet continuing uninterruptedly into that for the pisiform. The two ends of the radius are preserved but its length can only be conjectured. The proximal end has a large facet for the humerus; the distal end two facets, for the scaphoid and luna respectively, the two being almost continuous, except as the outline of the shallow depressions is constricted near the middle.
The carpus is preserved in toto and is decidedly weak for an animal of this size, though no more so than is the case of Nesodon and Adinotherium, with which forms the arrangement of the bones agrees in almost every detail. The scaphoid has a broad facet on the upper side for the radius, on the ulna side a narrow band-like facet for the luna, and distally facets for the trapezoid and the magnum, none for the trapezium. The luna is a larger bone with a broad radial facet on the upper side, a narrow facet for the scaphoid on the radial side, a larger one for the pyramidal on the ulnal side, and two broad facets for the magnum and unciform on the lower side. The pyramidal is a low, flattened bone, with a cup-like facet for the ulna on the upper surface, an elongated flat facet for the pisiform on the palmar surface, and below a broad facet occupying the entire lower side for the unciform. The pisiform is shaped like a tiny calcaneum, and, beside the facet for the pyramidal, has a broad contact on the styliform process of the ulna. The trapezium is a flattened nodular bone, resting against the side of the upper end of Mc. II, for which it has a flattened contact surface, but it does not properly articulate with any of the carpals. The trapezoid is a small bone, cuboidal in shape, with the proximal facet for the scaphoid rounded, and with a narrow facet for the support of Mc. II on the distal end. The magnum is a larger bone, articulating proximally with the scaphoid and luna, on the ulnal side with the unciform and distally supporting Mc. III. The unciform is the largest of the carpal bones, articulates proximally on the luna and pyramidal, on the radial side with the magnum, and distally carries Mc. IV, while on the ulnal side there is a facet for the modular vestige of Mc. V.
The metacarpals are longer than those of Adinotherium, and are much more closely pressed together, making a narrower, firmer foot. Three metacarpals are present (beside the modular vestige of Mc. V.). Mc. II and Mc. IV are slightly shorter than Mc. III, but not materially weaker, so that all three would reach the ground when the animal was standing. Though closely packed, the metacarpals are not grown together at any point. Distally each has a narrow trochlea, which carries a median crest on the palmar side only. Under the distal end of each metacarpal, there is a pair of small sesamoid bones.
All the phalanges are very short and weak, with the articular surfaces cut under obliquely, suggesting that the toes are bent upward. Distally each toe ends in a slender cleft ungual phalanx, suggesting a claw-like hoof. Rhynchippus clearly walked in a semidigitigrade manner, the weight coming principally on the metapodials, the foot as a whole resembling that of a dog.
The pelvis is unidentified. Though the bones are of about the same weight, the hind limb is longer than that of Adinotherium. The femur has a rounded head on a short but distinct neck, with the pit for the round ligament on the posterior margin of the head. The narrow digital fossa is deep. The greater trochanter is rugose and strong, but does not rise quite to the height of the head. The lesser trochanter makes a strong shelf-like process well below the head, while the third trochanter is a prominent process about the middle of the shaft, on the posterior side. The shaft is broad and flattened above, but narrows and becomes circular in section below. The condyles are relatively small, the inner being the smaller and more convex, while the outer is broader and less convex.
The tibia and fibula are a little longer than the femur, fused proximally, free distally, as in toxodonts. The proximal end of the tibia is too weathered to permit detailed description. However the upper end is wide and flattened from front to back. Distally the bone narrows until the lower part of the shaft is circular in section, the distal end enlarging again in the neighborhood of the articulation. The fibula has a broad facet for the inner side of the astragulus, and on the distal end a flattened slightly concave facet for the calcaneum.
The calcaneum is longer than in Nesodontidae. It is, however, heavy and stout, the tuber broadening slightly toward the free end, on the plantar side of which there is a tendinous sulcus as in Nesodon. The fibular facet is wide, rectangular, and convex. Of the astragular facets, the sustentacular extends well back onto the tuber, and the ectal is the usual ovoid surface. Distally there is a broad slightly concave facet for the cuboid, and external to this a narrow surface for contact on the navicular. Except in length, this bone is very like that of Adinotherium. The astragulus and rest of the tarsal bones are wanting. Parts of the metatarsals and a phalanx indicate that the hind foot is of the same tridactyl type as the front, differing only in that the median digit seems to be relatively a little heavier.
Ameghino described three species of Rhynchippus, R. equinus, R. pumulis, and R. medianus.