I think it necessary to distinguish between the former and the latter classes of intermediate forms, as intercalary types and linear types. When I apply the former term, I merely mean to say that as a matter of fact, the form B, so named, is intermediate between the others, in the sense in which the Anoplotherium is intermediate between the Pigs and the Ruminants—without either affirming, or denying, any direct genetic relation between the three forms involved. When I apply the latter term, on the other hand, I mean to express the opinion that the forms A, B, and C constitute a line of descent, and that B is thus part of the lineage of C.

From the time when Cuvier's wonderful researches upon the extinct Mammals of the Paris gypsum first made intercalary types known, and caused them to be recognized as such, the number of such forms has steadily increased among the higher Mammalia. Not only do we now know numerous intercalary forms of Ungulata, but M. Gaudry's great monograph upon the fossils of Pikermi (which strikes me as one of the most perfect pieces of palaeontological work I have seen for a long time) shows us, among the Primates, Mesopithecus as an intercalary form between the Semnopitheci and the Macaci; and among the Carnivora, Hyaenictis and Ictitherium as intercalary, or, perhaps, linear types between the Viverridae and the Hyaenidae.

Hardly any order of the higher Mammalia stands so apparently separate and isolated from the rest as that of the Cetacea; though a careful consideration of the structure of the pinnipede Carnivora, or Seals, shows, in them, many an approximation towards the still more completely marine mammals. The extinct Zeuglodon, however, presents us with an intercalary form between the type of the Seals and that of the Whales. The skull of this great Eocene sea-monster, in fact, shows by the narrow and prolonged interorbital region; the extensive union of the parietal bones in a sagittal suture; the well-developed nasal bones; the distinct and large incisors implanted in premaxillary bones, which take a full share in bounding the fore part of the gape; the two-fanged molar teeth with triangular and serrated crowns, not exceeding five on each side in each jaw; and the existence of a deciduous dentition—its close relation with the Seals. While, on the other hand, the produced rostral form of the snout, the long symphysis, and the low coronary process of the mandible are approximations to the cetacean form of those parts.

The scapula resembles that of the cetacean Hyperoodon, but the supra-spinous fossa is larger and more seal-like; as is the humerus, which differs from that of the Cetacea in presenting true articular surfaces for the free jointing of the bones of the fore-arm. In the apparently complete absence of hinder limbs, and in the characters of the vertebral column, the Zeuglodon lies on the cetacean side of the boundary line; so that, upon the whole, the Zeuglodonts, transitional as they are, are conveniently retained in the cetacean order. And the publication, in 1864, of M. Van Beneden's memoir on the Miocene and Pliocene Squalodon, furnished much better means than anatomists previously possessed of fitting in another link of the chain which connects the existing Cetacea with Zeuglodon. The teeth are much more numerous, although the molars exhibit the zeuglodont double fang; the nasal bones are very short, and the upper surface of the rostrum presents the groove, filled up during life by the prolongation of the ethmoidal cartilage, which is so characteristic of the majority of the Cetacea.

It appears to me that, just as among the existing Carnivora, the walruses and the eared seals are intercalary forms between the fissipede Carnivora and the ordinary seals, so the Zeuglodonts are intercalary between the Carnivora, as a whole, and the Cetacea. Whether the Zeuglodonts are also linear types in their relation to these two groups cannot be ascertained, until we have more definite knowledge than we possess at present, respecting the relations in time of the Carnivora and Cetacea.

Thus far we have been concerned with the intercalary types which occupy the intervals between Families or Orders of the same class; but the investigations which have been carried on by Professor Gegenbaur, Professor Cope, and myself into the structure and relations of the extinct reptilian forms of the Ornithoscelida (or Dinosauria and Compsognatha) have brought to light the existence of intercalary forms between what have hitherto been always regarded as very distinct classes of the vertebrate sub-kingdom, namely Reptilia and Aves. Whatever inferences may, or may not, be drawn from the fact, it is now an established truth that, in many of these Ornithoscelida, the hind limbs and the pelvis are much more similar to those of Birds than they are to those of Reptiles, and that these Bird-reptiles, or Reptile-birds, were more or less completely bipedal.

When I addressed you in 1862, I should have been bold indeed had I suggested that palaeontology would before long show us the possibility of a direct transition from the type of the lizard to that of the ostrich. At the present moment we have, in the Ornithoscelida, the intercalary type, which proves that transition to be something more than a possibility; but it is very doubtful whether any of the genera of Ornithoscelida with which we are at present acquainted are the actual linear types by which the transition from the lizard to the bird was effected. These, very probably, are still hidden from us in the older formations.

Let us now endeavour to find some cases of true linear types, or forms which are intermediate between others because they stand in a direct genetic relation to them. It is no easy matter to find clear and unmistakable evidence of filiation among fossil animals; for, in order that such evidence should be quite satisfactory, it is necessary that we should be acquainted with all the most important features of the organization of the animals which are supposed to be thus related, and not merely with the fragments upon which the genera and species of the palaeontologist are so often based. M. Gaudry has arranged the species of Hyaenidae, Proboscidea, Rhinocerotidae, and Equidae in their order of filiation from their earliest appearance in the Miocene epoch to the present time, and Professor Rütimeyer has drawn up similar schemes for the Oxen and other Ungulata—with what, I am disposed to think, is a fair and probable approximation to the order of nature. But, as no one is better aware than these two learned, acute, and philosophical biologists, all such arrangements must be regarded as provisional, except in those cases in which, by a fortunate accident, large series of remains are obtainable from a thick and wide-spread series of deposits. It is easy to accumulate probabilities—hard to make out some particular case in such a way that it will stand rigorous criticism.

After much search, however, I think that such a case is to be made out in favour of the pedigree of the Horses.

The genus Equus is represented as far back as the latter part of the Miocene epoch; but in deposits belonging to the middle of that epoch its place is taken by two other genera, Hipparion and Anchitherium[1]; and, in the lowest Miocene and upper Eocene, only the last genus occurs. A species of Anchitherium was referred by Cuvier to the Palaeotheria under the name of P. aurelianense. The grinding-teeth are in fact very similar in shape and in pattern, and in the absence of any thick layer of cement, to those of some species of Palaeotherium, especially Cuvier's Palaeotherium minus, which has been formed into a separate genus, Plagiolophus, by Pomel. But in the fact that there are only six full-sized grinders in the lower jaw, the first premolar being very small; that the anterior grinders are as large as, or rather larger than, the posterior ones; that the second premolar has an anterior prolongation; and that the posterior molar of the lower jaw has, as Cuvier pointed out, a posterior lobe of much smaller size and different form, the dentition of Anchitherium departs from the type of the Palaeotherium, and approaches that of the Horse.