XVII] THE COMPARISON OF RELATED FORMS 775 



some which we have studied, owing to the presence of essentially 

 unimportant, but yet conspicuous differences in the position of 

 the eyes, or in the number of the fins, — that is to say in the manner 

 in which the continuous dorsal fin of the plaice appears in the 

 haddock to be cut or scolloped into a number of separate fins. 

 But 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 plaice's body, 

 as compared with the haddock's, in the dorso-ventral direction, 

 that is to say, along the y axis ; in other words, the ratio xjy 

 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 com- 

 parison 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. Ill, p. 98), that is to 

 say the coefficient k in the formula W = kL^, or k = W/L^, I 

 was not a little surprised to find that k was all but identical in 

 two such dift'erent looking fishes as our haddock and our plaice: 

 thus indicating that these two fishes, little as they resemble one 

 another externally (though they belong to two closely related 

 families), have approximately the same volume when they are 

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

 plaice's body has become expanded or broadened is just about 



