which I have represented in Fig. [396]. In this case it will perhaps be noticed that the correspondence is not always quite accurate in small details. It could easily have been made much more accurate by giving a slightly sinuous curvature to certain of the co-ordinates. But as they stand, the correspondence indicated is very close, and the simplicity of the figures illustrates all the better the general character of the transformation.
By similar and not more violent changes we pass easily to such allied forms as the Titanotheres (Fig. [397]); and the well-known series of species of Titanotherium, by which Professor Osborn has {763} illustrated the evolution of this genus, constitutes a simple and suitable case for the application of our method.
But our method enables us to pass over greater gaps than these, and to discern the general, and to a very large extent even the detailed, resemblances between the skull of the rhinoceros and those of the tapir or the horse. From the Cartesian co-ordinates in which we have begun by inscribing the skull of a primitive rhinoceros, we pass to the tapir’s skull (Fig. [398]), firstly, by converting the rectangular into a triangular network, by which we represent the depression of the anterior and the progressively increasing elevation of the posterior part of the skull; and secondly, by giving to the vertical ordinates a curvature such as to bring about a certain longitudinal compression, or condensation, in the forepart of the skull, especially in the nasal and orbital regions.
| Fig. 397. Titanotherium robustum. | Fig. 398. Tapir’s skull. |
The conformation of the horse’s skull departs from that of our primitive Perissodactyle (that is to say our early type of rhinoceros, Hyrachyus) in a direction that is nearly the opposite of that taken by Titanotherium and by the recent species of rhinoceros. For we perceive, by Fig. [399], that the horizontal co-ordinates, which in these latter cases became transformed into curves with the concavity upwards, are curved, in the case of the horse, in the opposite direction. And the vertical ordinates, which are also curved, somewhat in the same fashion as in the tapir, are very nearly equidistant, instead of being, as in that animal, crowded together anteriorly. Ordinates and abscissae form an oblique {764} system, as is shown in the figure. In this case I have attempted to produce the network beyond the region which is actually required to include the diagram of the horse’s skull, in order to show better the form of the general transformation, with a part only of which we have actually to deal.
Fig. 399. Horse’s skull.
Fig. 400. Rabbit’s skull.