| Fig. 375. Scarus sp. | Fig. 376. Pomacanthus. |
Fig. [375] is an outline diagram of a typical Scaroid fish. Let us deform its rectilinear co-ordinates into a system of (approximately) coaxial circles, as in Fig. [376], and then filling into the new system, space by space and point by point, our former diagram of Scarus, we obtain a very good outline of an allied fish, belonging to a neighbouring family, of the genus Pomacanthus. This case is all the more interesting, because upon the body of our Pomacanthus there are striking colour bands, which correspond in direction very closely to the lines of our new curved ordinates. In like manner, the still more bizarre outlines of other fishes of the same family of Chaetodonts will be found to correspond to very slight modifications of similar co-ordinates; in other words, to small variations in the values of the constants of the coaxial curves.
In Figs. [377]–380 I have represented another series of Acanthopterygian fishes, not very distantly related to the foregoing. If we start this series with the figure of Polyprion, in Fig. [377], we see that the outlines of Pseudopriacanthus (Fig. [378]) and of Sebastes or Scorpaena (Fig. [379]) are easily derived by substituting a system of triangular, or radial, co-ordinates for the rectangular ones in {750} which we had inscribed Polyprion. The very curious fish Antigonia capros, an oceanic relative of our own “boar-fish,” conforms closely to the peculiar deformation represented in Fig. [380].
| Fig. 377. Polyprion. | Fig. 378. Pseudopriacanthus altus. |
| Fig. 379. Scorpaena sp. | Fig. 380. Antigonia capros. |
Fig. [381] is a common, typical Diodon or porcupine-fish, 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, approximately and provisionally, are made to resemble a system of hyperbolas[657]. 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 mathematical sense, it is not a perfectly satisfactory or perfectly regular deformation, for the system is no longer isogonal; but
