speaking broadly, and apart from such minor differences as these, it is manifest that the chief factor in the case (so far as we at present see) is simply the broadening out of the plaiceãs body, as compared with the haddockãs, in the dorso-ventral direction, that is to say, along the y axis; in other words, the ratio xã₤ãã₤y is much less, (and indeed little more than half as great), in the haddock than in the plaice. But we also recognise at once that while the plaice (as compared with the haddock) is expanded in one direction, it is also flattened, or thinned out, in the other: y increases, but z diminishes, relatively to x. And furthermore, we soon see that this is a common or even a general phenomenon. The high, expanded body in our Antigonia or in our sun-fish is at the same time flattened or compressed from side to side, in comparison with the related fishes which we have chosen as standards of reference or comparison; and conversely, such a fish as the skate, while it is expanded from side to side in comparison with a shark or dogfish, is at the same time flattened or depressed in its vertical section. We proceed then, to enquire whether there be any simple relation of magnitude discernible between these twin factors of expansion and compression; and the very fact that the two dimensions tend to vary inversely already assures us that, in the general process of deformation, the volume is less affected than are the linear dimensions. Some years ago, when I was studying the length-weight co-efficient in fishes (of which we have already spoken in Chap. III, p. 98), that is to say the coefficient k in the formula W =ã₤kÿ£¢Lÿ£¢3ã₤, or k =ã₤Wã₤ãã₤Lÿ£¢3ã₤, I was not a little surprised to find that k was all but identical in two such different looking fishes as our haddock and our plaice: thus indicating that these two fishes, little as they
Table of Contents
CHAPTER XVII ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON OF RELATED FORMS
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