resemble one another externally (though they belong to two closely related families), have apôÙproxôÙiôÙmateôÙly the same volume when they are equal in length; or, in other words, that the extent to which the plaiceãs body has become expanded or broadened is just about {776} compensated for by the extent to which it has also got flattened or thinned. In short, if we could permit ourselves to conceive of a haddock being directly transformed into a plaice, a very large part of the change would be simply accounted for by supposing the former fish to be ãrolled out,ã as a baker rolls a piece of dough. This is, as it were, an extreme case of the balancement des organes, or ãcompensation of parts.ã
Simple Cartesian co-ordinates will not suffice very well to compare the haddock with the plaice, for the deformation undergone by the former in comparison with the latter is more on the lines of that by which we have compared our Antigonia with our Polyprion; that is to say, the expansion is greater towards the middle of the fishãs length, and dwindles away towards either end. But again simplifying our illustration to the utmost, and being content with a rough comparison, we may assert that, when haddock and plaice are brought to the same standard of length, we can inscribe them both (apôÙproxôÙiôÙmateôÙly) in rectangular co-ordinate networks, such that Y in the plaice is about twice as great as y in the haddock. But if the volumes of the two fishes be equal, this is as much as to say that xyz in the one case (or rather the summation of all these values) is equal to XYZ in the other; and therefore (since X =ã₤ x , and Y =ã₤2 y ), it follows that Z =ã₤ z ã₤ãã₤2. When we have drawn our vertical transverse section of the haddock (or projected that fish in the yz