plane), we have reason accordingly to anticipate that we can draw a similar projection (or section) of the plaice by simply doubling the y ãs and halving the z ãs: and, very apôÙproxôÙiôÙmateôÙly, this turns out to be the case. The plaice is (in round numbers) just about twice as broad and also just about half as thick as the haddock; and therefore the ratio of breadth to thickness (or y to z ) is just about four times as great in the one case as in the other.
It is true that this simple, or simplified, illustration carries us but a very little way, and only half prepares us for much greater complications. For instance, we have no right or reason to presume that the equality of weights, or volumes, is a common, much less a general rule. And again, in all cases of more complex deformation, such as that by which we have compared Diodon with the sunfish, we must be prepared for very much more {777} recondite methods of comparison and analysis, leading doubtless to very much more complicated results. In this last case, of Diodon and the sunfish, we have seen that the vertical expansion of the latter as compared with the former fish, increases rapidly as we go backwards towards the tail; but we can by no means say that the lateral compression increases in like proportion. If anything, it would seem that the said expansion and compression tend to vary inversely; for the Diodon is very thick in front and greatly thinned away behind, while the flattened sunfish is more nearly of the same thickness all the way along. Interesting as the whole subject is we must meanwhile leave it alone; recognising, however, that if the difficulties of description and representation could be overcome, it is by means of such co-ordinates in space that we should at last obtain an adequate and satisfying picture of the processes of deformation and of the directions of growth22.