Dürer was acquainted with these oblique co-ordinates also, and I have copied two illustrative figures from his book[656].
In Fig. [367] I have sketched the common Copepod Oithona nana, {743} and have inscribed it in a rectangular net, with abscissae three-fifths the
| Fig. 367. Oithona nana. | Fig. 368. Sapphirina. |
length of the ordinates. Side by side (Fig. [368]) is drawn a very different Copepod, of the genus Sapphirina; and about it is drawn a network such that each co-ordinate passes (as nearly as possible) through points corresponding to those of the former figure. It will be seen that two differences are apparent. (1) The values of y in Fig. [368] are large in the upper part of the figure, and diminish rapidly towards its base. (2) The values of x are very large in the neighbourhood of the origin, but diminish rapidly as we pass towards either side, away from the median vertical axis; and it is probable that they do so according to a definite, but somewhat complicated, ratio. If, instead of seeking for an actual equation, we simply tabulate our values of x and y in the second figure as compared with the first (just as we did in comparing the feet of the Ungulates), we get the dimensions of a net in which, by simply projecting the figure of Oithona, we obtain that of Sapphirina without further trouble, e.g.:
| x (Oithona) | 0 | 3 | 6 | 9 | 12 | 15 | — |
| x′ (Sapphirina) | 0 | 8 | 10 | 12 | 13 | 14 | — |
| y (Oithona) | 0 | 5 | 10 | 15 | 20 | 25 | 30 |
| y′ (Sapphirina) | 0 | 2 | 7 | 3 | 23 | 32 | 40 |
In this manner, with a single model or type to copy from, we may record in very brief space the data requisite for the production of approximate outlines of a great number of forms. For instance the difference, at first sight immense, between the attenuated body of a Caprella and the thick-set body of a Cyamus is obviously little, and is probably nothing, more than a difference of relative magnitudes, capable of tabulation by numbers and of complete expression by means of rectilinear co-ordinates.
The Crustacea afford innumerable instances of more complex deformations. Thus we may compare various higher Crustacea with one another, even in the case of such dissimilar forms as a lobster and a crab. It is obvious that the whole body of the former is elongated as compared with the latter, and that the crab is relatively broad in the region of the carapace, while it tapers off rapidly towards its attenuated and abbreviated tail. In a general way, the elongated rectangular system of co-ordinates {744} in which we may inscribe the outline of the lobster becomes a shortened triangle in the case of the crab. In a little more detail we may compare the outline of the carapace in various crabs one with another: and the comparison will be found easy and significant, even, in many cases, down to minute details, such as the number and situation of the marginal spines, though these are in other cases subject to independent variability.
