In treating of many sections of mammals, it is only from the existing species that our characters and classification can be derived, and to these chiefly our observations upon the group must be directed, many of the extinct forms being so little known that they can only be referred to incidentally. With the Ungulata, however, it is quite otherwise. The history of the Artiodactyla throughout the Tertiary period is now well known, and throws great light upon the position and relations of the existing groups. The principal modifications which have taken place in the type from its earliest known and most generalised manifestation have been the following:— 1. As regards the teeth. Assumption by the grinding surfaces of the molar teeth either of a bunodont or of a selenodont form. Modification of the latter from a brachydont to a hypsodont type. Loss of upper incisors. Development of canines into projecting tusks. Loss of anterior premolars. 2. As regards the limbs. Reduction of the ulna from a complete and distinct bone to a comparatively rudimentary state, in which it coalesces more or less firmly with the radius. Reduction of the fibula till nothing but its lower extremity remains. Reduction and final loss of external pair of digits (second and fifth), with coalescence of the metapodial bones of the two middle digits. Union of the navicular and cuboid, and sometimes the ectocuneiform, bones of the tarsus. 3. Change of form of the odontoid process of the axis vertebra from a cone to a hollow half-cylinder. 4. Development of horns or antlers on the frontal bones, and gradual complication of form of antlers. 5. By inference only, increasing complication of stomach with ruminating function superadded. Modification of placenta from simple diffused to cotyledonary form. The primitive Artiodactyles, with the typical number (44) of incisor, canine, and molar teeth, brachydont molars, conical odontoid process, four distinct toes on each foot, with metapodium and all carpal bones distinct, no frontal appendages, and (in all probability) simple stomach and diffused placenta, were separated at a very early period into Bunodonts and Selenodonts, although there is evidence of intermediate forms showing a complete transition from the one modification to the other. These and other fossil forms so completely connect the four groups—Suina, Tylopoda, Tragulina, and Pecora—into which the existing members of the suborder have become divided, that in a general classification embracing both living and extinct forms these divisions cannot be maintained. In the present work, however, it will be convenient to retain them, mention being made of some of the chief annectant forms in separate sections. SUINA. The existing members of this group are characterised by their bunodont molars, and the absence of a complete fusion of the third and fourth metapodials to form a “cannon-bone.” The full Eutherian dentition is very frequently present.