The order, Tillodontia, established by Professor O. C. Marsh, would seem to bear more striking evidence still in the same direction, coming as it does from the earliest geological formation, the lower Eocene, in which Rodents are found; and combining some of the characters of Carnivores with those of both Ungulates and Rodents, as though they were survivors of some still earlier type unrepresented, as indeed are all Mammals, in any as yet explored strata of the Cretaceous age. Similar affinity has often been spoken of as existing between the Toxodontia of the Post-Tertiary South American deposits and the Rodents; but as this much later date might have led us to expect, the similarities between the two orders are by no means so clearly made out.

As regards existing Ungulata, the affinities of the Rodentia are distributed pretty evenly between the two divisions of Ungulata Artiodactyla, the non-Ruminantia s. Bunodonta and the Ruminantia s. Selenodonta (for which see W. Kowalewsky, .Ph. Tr. vol. 163, pp. 69-74, 1873) and the Perissodactyla; but it must be borne in mind that though the differences between the now existing Hoofed animals thus named are very sharply defined, geological researches, especially in the American Tertiaries, have revealed to us forms in which these lines of demarcation tend to become obscured, or at least approximated. It would be easy to say, for example, that the imperfection of the orbital ring was a point of considerable importance, and united the Rodentia with the Perissodactyla; but Professor O. C. Marsh (see Introduction and Succession of Vertebrate Life in America, 1879, p. 161) states that several species of Cervidae from the lower Pliocene of the west of America fail to have the orbit closed behind.

A simple way of expressing the known facts may perhaps be furnished by saying that though the Rodentia with reference merely to their claws would be ranged with the Unguiculata rather than with the Ungulata of Linnaeus (see Systerna Naturae, ed. xiii. vol. i. p. 17), they nevertheless present both in their skeleton and in their internal organs more marked points of essential affinity to the latter than to the former of these two sets of Mammalia, and that even as regards the particular difference, such as it is, which exists between claws and hoofs, the subungulate character of certain South American Rodents (Dasyprocta, Caelogenys, Dinomys, Cavia, Dolichotis, and, notably, Hydrochaerus) very much reduces its value. The fact pointed out in the Description of Preparation, p. 27, note, to the effect that the microscopic character of the ultimate radicles or spon-gioles of the lacteal system in the Rabbit resembles that of the Ruminants rather than that of the Unguiculata, illustrates this position. On the other hand, however, Krause, Hdbk. der Menschlichen Anatomie, p. 234, 1876, has pointed out that the Rabbit, unlike the Ungulata, Horse, Pig, Ox, and Sheep, has capillary veins in the spleen instead of wide funnel-shaped orifices for the commencement of those vessels.

The semi-pedunculate fashion in which the deciduous serotina is in the Guinea Pig, Agouti, and some other Rodents, attached to the wall of the uterus, and the fact that in the former at least of the animals named this structure is sometimes retained within the uterus at parturition, may appear to point to the existence of some approximation to the character of the non-deciduate cotyledonary placentation of typical Ruminants. But the springing up in later foetal life of a zone of villi, supplied by omphalo-mesenteric vessels around and exteriorly to the placental area in Rodents, though of physiological interest, as was pointed out in the Zoological Transactions for 1863, vol. v, still does not constitute, as seems to have been more recently stated, any but a physiological approximation of the Rodent to the Ruminant type of placentation.

The peculiarity of the placentae of the Guinea Pig and Agouti just alluded to, the comparative simplicity of their caecum, and the great development of the spirally-coiled portion of their colon, and the presence in them of but a single superior cava, the small number of their mammae and of their young, and the early attainment by them of the faculty of self-help, are points in which they resemble the Artiodactyla and differ from the Lagomorpht; but, as the Descriptions of the Preparations (Nos. 3 and 4) show, Brandt is entirely justified in pointing, l.c. p. 291, to numerous connecting links, characteribus nonnullis generis Leporini cum Ruminantium ordine.

The apparent paradox of an affinity connecting the Proboscidea (the Elephant and Mastodon) with the living Rodents, has already been alluded to, p. 8. One of the most striking of these resemblances lies in the facts that in both sets of animals the intermaxillary interposes itself between the maxillary and the nasal bones and joins the frontal without however touching upon the lacrymal bone, relations which do not exist either in the Aye-aye, or in the Hyrax, or in the Dugong, animals with incisors of somewhat similar relative proportions. But this remarkable peculiarity had not been attained to by the Pliocene genus and suborder Glires hebetidentati of Alston, represented by the Mesotherium, in which animal the intermaxillary's nasal process is too short to prevent the maxillary from abutting upon the nasal, and fails, as in Hyrax alone of the animals just mentioned, to reach the frontal.

The absence of enamel from the incisor teeth or tusks of the adult Elephant, otherwise so exactly homologous with the incisors of the Rodents, might appear to constitute a difference between them and those of the Rodents, did we not know that these teeth when first cut in the Elephant have a cap of enamel, and that a serially homologous fact is presented to us in the possession by the American Pliocene Mastodons of a band of enamel on their tusks (see Marsh, l. c. p. 41).

The naked-eye structure of the molars of many Rodents, such as the Capybara, is strikingly like that of the Elephants, and the microscopic arrangement of the enamel in the same teeth in the Elephant and the Mastodon has been shown to be of the same type as that observable in all Rodents except the Leporidae and the Hystricidae. The coronoid processes of the lower jaw are small, and the relations of the malars to the malar processes of the maxillaries and of the squamous bones are the same in both orders, both the latter bones entering into the composition of the arch.