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nydus/On Growth and FormPublic
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Table of Contents

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

of this skull we select a number of points obviously corôÙreôÙsponôÙding {754} to points where our rectangular co-ordinates intersect particular bones or other recognisable features in our typical crocodile, we shall easily discover that the lines joining these points in Notosuchus fall into such a co-ordinate network as that which is represented in Fig. 383, c. To all intents and purposes, then, this not very complex system, representing one harmonious 〜deformation,〝 accounts for all the differences between the two figures, and is sufficient to enable one at any time to reconstruct a detailed drawing, bone for bone, of the skull of Notosuchus from the model furnished by the common crocodile.

D'Arcy Thompson's transformation grids showing the deformation of a fish pelvis shape from rectangular (A) to curved (B).

The many diverse forms of Dinosaurian reptiles, all of which manifest a strong family likeness underlying much superficial diversity, furnish us with plentiful material for comparison by the method of transôÙforôÙmaôÙtions. As an instance, I have figured the pelvic bones of Stegosaurus and of Camptosaurus (Fig. 384, a, b) to show that, when the former is taken as our Cartesian type, a slight curvature and an apôÙproxôÙiôÙmateôÙly logarithmic extension of the x-axis brings us easily to the configuration of the other. In the original specimen of Camptosaurus described by Marsh17, the anterior portion of the iliac bone is missing; and in Marsh〙s restoration this part of the bone is drawn as though it came somewhat abruptly to a sharp point. In my figure I {755} have completed this missing part of the bone in harmony with the general co-ordinate network which is suggested by our comparison of the two entire pelves; and I venture to think that the result is more natural in appearance, and more likely to be correct than was Marsh〙s conjectural restoration. It would seem, in fact, that there is an obvious field for the employment of the method of co-ordinates in this task of reproducing missing portions of a structure to the proper scale and in harmony

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