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

and in Fig. 382 I have deformed its vertical co-ordinates into a system of concentric circles, and its horizontal co-ordinates into a system of curves which, apôÙproxôÙiôÙmateôÙly and provisionally, are made to resemble a system of hyperbolas16. The old outline, transferred {751} in its integrity to the new network, appears as a manifest representation of the closely allied, but very different looking, sunfish, Orthagoriscus mola. This is a particularly instructive case of deformation or transformation. It is true that, in a mathôÙeôÙmatôÙiôÙcal sense, it is not a perfectly satisfactory or perfectly regular deformation, for the system is no longer isogonal; but

A D'Arcy Thompson transformation grid showing how a rectangular coordinate system maps to a curved one to relate fish shapes.

Fig. 381. Diodon. Fig. 382. Orthagoriscus.

nevertheless, it is symmetrical to the eye, and obviously approaches to an isogonal system under certain conditions of friction or constraint. And as such it accounts, by one single integral transformation, for all the apparently separate and distinct external differences between the two fishes. It leaves the parts near to the origin of the system, the

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