Deforming fish

Among the fishes we discover a great variety of deformations, some of them of a very simple kind, while others are more striking and more unexpected.  A comparatively simple case, involving a simple shear, is illustrated [below].

The one represents, within Cartesian co-ordinates, a certain little oceanic fish known as Argyropelecus olfersi.  The other represents precisely the same outline, transferred to a system of oblique co-ordinates whose axes are inclined at an angle of 70º; but this is now (as far as can be seen on the scale of the drawing) a very good figure of an allied fish, assigned to a different genus, under the name of Sternoptyx diaphana.  The deformation illustrated by this case of Argyropelecus is precisely analogous to the simplest and commonest kind of deformation to which fossils are subject as the result of shearing-stresses in the solid rock…

[The first figure below] is a common, typical Diodon or porcupine-fish, and in [the accompanying figure] I have deformed its vertical co-ordinates into a system of concentric circles, and its horizontal co-ordinates into a system of curves which, approximately and provisionally, are made to resemble a system of hyperbolas.  The old outline, transferred 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 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 whole region of the head, the opercular orifice and the pectoral fin, practically unchanged in form, size and position; and it shows a greater and greater apparent modification of size and form as we pass from the origin towards the periphery of the system.

In a word, it is sufficient to account for the new and striking contour in all its essential details, of rounded body, exaggerated dorsal and ventral fins, and truncated tail.  In like manner, and using precisely the same co-ordinate networks, it appears to me possible to show the relations, almost bone for bone, of the skeletons of the two fishes; in other words, to reconstruct the skeleton of the one from our knowledge of the skeleton of the other, under the guidance of the same correspondence as is indicated in their external configuration…

It may also be employed for drawing hypothetical structures, on the assumption that they have varied from a known form in some definite way.  And this process may be especially useful, and will be most obviously legitimate, when we apply it to the particular case of representing intermediate stages between two forms which are actually known to exist, in other words, of reconstructing the transitional stages through which the course of evolution must have successively traveled if it has brought about the change from some ancestral type to its presumed descendant…

Our simple, or simplified, illustrations carry us but a little way, and only half prepare us for much harder things.  But interesting as the whole subject is we must meanwhile leave it alone; recognizing, however, that if the difficulties of description and representation could be overcome, it is by means of such co-ordinates in space that we should at last obtain an adequate and satisfying picture of the processes of deformation and the directions of growth.

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