I think that this desideratum is very nearly, if not quite, supplied by _Plagiolophus_, remains of which occur abundantly in some parts of the Upper and Middle Eocene formations. The patterns of the grinding-teeth of _Plagiolophus_ are similar to those of _Anchitherium_, and their crowns are as thinly covered with cement; but the grinders diminish in size forwards, and the last lower molar has a large hind lobe, convex outwards and concave inwards, as in _Palueotherium_. The ulna is complete and much larger than in any of the _Equidoe_, while it is more slender than in most of the true _Paloeotheria_; it is fixedly united, but not ankylosed, with the radius. There are three toes in the fore limb, the outer ones being slender, but less attenuated than in the _Equidoe_. The femur is more like that of the _Paloeotheria_ than that of the horse, and has only a small depression above its outer condyle in the place of the great fossa which is so obvious in the _Equidoe_. The fibula is distinct, but very slender, and its distal end is ankylosed with the tibia. There are three toes on the hind foot having similar proportions to those on the fore foot. The principal metacarpal and metatarsal bones are flatter than they are in any of the _Equidoe_; and the metacarpal bones are longer than the metatarsals, as in the _Paloeotheria_. In its general form, _Plagiolophus_ resembles a very small and slender horse,[4] and is totally unlike the reluctant, pig-like creature depicted in Cuvier's restoration of his _Paloeotherium minus_ in the "Ossemens Fossiles." [Footnote 4: Such, at least, is the conclusion suggested by the proportions of the skeleton figured by Cuvier and De Blainville; but perhaps something between a Horse and an Agouti would be nearest the mark.] It would be hazardous to say that _Plagiolophus_ is the exact radical form of the Equine quadrupeds; but I do not think there can be any reasonable doubt that the latter animals have resulted from the modification of some quadruped similar to _Plagiolophus_. We have thus arrived at the Middle Eocene formation, and yet have traced back the Horses only to a three-toed stock; but these three-toed forms, no less than the Equine quadrupeds themselves, present rudiments of the two other toes which appertain to what I have termed the "average" quadruped. If the expectation raised by the splints of the Horses that, in some ancestor of the Horses, these splints would be found to be complete digits, has been verified, we are furnished with very strong reasons for looking for a no less complete verification of the expectation that the three-toed _Plagiolophus_-like "avus" of the horse must have had a five-toed "atavus" at some earlier period. No such five-toed "atavus," however, has yet made its appearance among the few middle and older Eocene _Mammalia_ which are known.