again we may at pleasure reconstruct the curve.
But it is the next step in the employment of co-ordinates which is of special interest and use to the morphologist; and this step consists in the alteration, or ãtransformation,ã of our system of co-ordinates and in the study of the corôÙreôÙsponôÙding transformation of the curve or figure inscribed in the co-ordinate network.
Let us inscribe in a system of Cartesian co-ordinates the outline of an organism, however complicated, or a part thereof: such as a fish, a crab, or a mammalian skull. We may now treat this complicated figure, in general terms, as a function of x, y. If we submit our rectangular system to ãdeformation,ã on simple and recognised lines, altering, for instance, the direction of the axes, the ratio of xã₤ãã₤y, or substituting for x and y some more complicated expressions, then we shall obtain a new system of co-ordinates, whose deformation from the original type the inscribed figure will precisely follow. In other words, we obtain a new figure, which represents the old figure under strain, and is a function of the new co-ordinates in precisely the same way as the old figure was of the original co-ordinates x and y.
The problem is closely akin to that of the cartographer who transfers identical data to one projection or another; and whose object is to secure (if it be possible) a complete corôÙreôÙsponôÙdence, in each small unit of area, between the one representation and the other. The morphologist will not seek to draw his organic forms in a new and artificial projection; but, in the converse aspect of the problem, he will inquire whether two different but more or less obviously related forms can be so analysed and interpreted that each may be shown to be a transformed representation of the other. This once demonstrated, it will be a comparatively easy task (in all probability) to postulate the direction and magnitude of the