The Condylarthra seem to have gone out of existence before the time of the middle Eocene, but before this they had become separated into the two great divisions of odd-toed and even-toed ungulates, into which all truly hoofed beasts now living fall.

The first group (Perissodactyla) has always one or three toes functionally developed, either the third, or third, second and fourth, the two others having entirely disappeared, except for a remnant of the fifth in the forefoot of tapirs.  They have retained some at least of the upper incisor teeth, and, except in some rhinoceroses, the canines are also left; the molars and premolars are practically alike in all recent species, and in all of which we know the soft parts, the stomach has but one compartment, and there is an enormous caecum.  It is probable that they took rise earlier than their split-footed relations, and their Tertiary remains are far more numerous, but their tendency is toward disappearance, and among existing mammals they are represented only by horses, asses, rhinoceroses, and tapirs.

Contrasted with these, Artiodactyla have always an even number of functional digits, the third and fourth reaching the ground symmetrically, bearing the weight and forming the “split hoof;” the second and fifth remain, in most cases, as mere vestiges, showing externally as the accessory hoofs or dewclaws; in the hippopotamus alone they are fully developed and the animal has a four-toed foot.  In deer and bovine animals the incisors and frequently the canines have disappeared from the upper jaw, and the molars are unlike the premolars in having two lobes instead of one.  The stomach is always more or less complex; at its extreme reaching the ruminant type with four compartments, in association with which is a caecum reduced in size and simple in form.  Nearly all have horns or antlers, at least in one sex.

Most split-hoofed animals are ruminants, but there is a small remnant, probably of early types, which are not.  The present ungulates may be summed up in this way: 

Odd-toed:  (Perissodactyla)—­
  Horse,
  Ass,
  Rhinoceros,
  Tapir.

Even-toed:  (Artiodactyla)—­

Non-ruminants—­
Hippopotamus,
Swine,
Peccaries.

Ruminants—­
Camels, Llamas,
Chevrotains,
Giraffe,
Antelopes,
Sheep, Goats,
Musk-ox,
Oxen,
Deer.

The non-ruminant artiodactyls need not detain us long.  Hippopotamuses are little more than large pigs with four toes; they were never American, though many species, some very small, are found in the European Tertiary.  The two existing species are African.

In the western hemisphere swine are represented by the peccaries, differing from them chiefly in having six less teeth, one less accessory toe on the hind foot, and in a stomach of more complex character.  Peccaries also have the metapodial bones supporting the two functional digits fused together at their upper ends, forming an imperfect “cannon bone,” which is a characteristic of practically all the ruminants, but of no other hoofed beasts.  One species only enters the United States along the Mexican border.