Let us begin by choosing as our type the skull of Hyrachyus agrarius, Cope, from the Middle Eocene of North America, as figured by Osborn in his Monograph of the Extinct Rhinoceroses[659] (Fig. [394]).
The many other forms of primitive rhinoceros described in the monograph differ from Hyrachyus in various details—in the characters of the teeth, sometimes in the number of the toes, and so forth; and they also differ very considerably in the general {761} appearance of the skull. But these differences in the conformation of the skull, conspicuous as they are at first sight, will be found easy to bring under the conception of a simple and homogeneous transformation, such as would result from the application of some not very complicated stress. For instance, the corresponding
Fig. 394. Skull of Hyrachyus agrarius. (After Osborn.)
Fig. 395. Skull of Aceratherium tridactylum. (After Osborn.)
co-ordinates of Aceratherium tridactylum, as shown in Fig. [395], indicate that the essential difference between this skull and the former one may be summed up by saying that the long axis of the skull of Aceratherium has undergone a slight double curvature, while the upper parts of the skull have at the same time been {762} subject to a vertical expansion, or to growth in somewhat greater proportion than the lower parts. Precisely the same changes, on a somewhat greater scale, give us the skull of an existing rhinoceros.
Among the species of Aceratherium, the posterior, or occipital, view of the skull presents specific differences which are perhaps more conspicuous than those furnished by the side view; and these differences are very strikingly brought out by the series of conformal transformations
Fig. 396. Occipital view of the skulls of various extinct rhinoceroses (Aceratherium spp.). (After Osborn.)