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CHAPTER XVII ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON OF RELATED FORMS

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.

Two side-by-side D'Arcy Thompson transformation grids illustrating the morphological change between a horse and a donkey skull.

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

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