XVII] THE COMPARISON OF RELATED FORMS 1089 



cernible between these twin factors of expansion and compression; 

 and the very fact that the two dimensions of breadth and depth 

 tend to vary inversely assures us that, in the general process 

 of deformation, the volume and the area of cross-section are less 

 affected than are those two linear dimensions. Some years ago, 

 when I was studying the weight-length coefficient in fishes (of which 

 we have already spoken in chapter iii), that is to say the coefficient 

 k in the formula W = kL^, I was not a Httle surprised to find that k 

 (let us call it in this case ki) was all but identical in two such different 

 looking fishes as the haddock and the plaice: thus indicating that 

 these two fishes have approximately the same voluyne when they 

 are equal in length ; or, in other words, that the extent to which the 

 plaice has broadened is just about compensated for by the extent 

 to which it has also got flattened or thinned. In short, if we might 

 conceive of a haddock being transformed directly into a plaice, 

 a very large part of the change would be accounted for by supposing 

 the round fish to be "rolled out" into the flat one, as a baker rolls 

 a piece of dough. This is, as it were, an extreme case of the halance- 

 ment des organes, or "compensation of parts." 



We must not forget, while we consider the "deformation" of 

 a fish, that the fish, like the bird, is subject to certain strict limita- 

 tions of form. What we happen to have found in a particular 

 case was observed fifty yearg ago, and brought under a general rule, 

 by a naval engineer studying fishes from the shipbuilder's point of 

 view. Mr Parsons * compared the contours and the sectional areas 

 of a number of fishes and of several whales ; and he found the sec- 

 tional areas to be always very much the same at the same proportional 

 distances from the front end of the body|. Increase in depth was 

 balanced (as we also have found) by diminution of breadth; and 

 the magnitude of the "entering angle" presented to the water by 

 the advancing fish was fairly constant. Moreover, according to 

 Parsons, the position of the greatest cross-section is fixed for all 

 species, being situated at 36 per cent, of the length behind the 



* H. de B. Parsons, Displacements and area-curves of fish, Trans. Amer. Soc. 

 of Mechan. Engineers, ix, pp. 679-695, 1888. 



t That is to say, if the areas of cross-section be plotted against their distances 

 from the front end of the body, the results are very much alike for all the species 

 examined. See also Selig Hecht, Form and growth in fishes, Journ. Morph. 

 xxvn, pp. 379-400, 1916. 



