coordinates (as has been done by Moseley and by Blake), or in Hamiltonian vector notation. It is likewise possible (though of little interest to the naturalist) to determine the area of a conchoidal surface, or the volume of a conchoidal solid, and to find the centre of gravity of either surface or solid29. And Blake has further shewn, with considerable elaboration, how we may deal with the symmetrical distortion, due to pressure, which fossil shells are often found to have undergone, and how we may reconstitute by calculation their original undistorted form,ãa problem which, were the available methods only a little easier, would be very helpful to the palaeontologist; for, as Blake himself has shewn, it is easy to mistake a symmetrically distorted specimen of (for instance) an Ammonite, for a new and distinct species of the same genus. But it is evident that to deal fully with the mathôÙeôÙmatôÙiôÙcal problems contained in, or suggested by, the spiral shell, would require a whole treatise, rather than a single chapter of this elementary book. Let us then, leaving mathematics aside, attempt to summarise, and perhaps to extend, what has been said about the general possibilities of form in this class of organisms.
The Univalve Shell: a summary.
The surface of any shell, whether discoid or turbinate, may be imagined to be generated by the revolution about a fixed axis of a closed curve, which, remaining always geometrically similar to itself, increases continually its dimensions: and, since the rate of growth of the generating curve and its velocity of rotation follow the same law, the curve traced in space by corôÙreôÙsponôÙding points {554} in the generating curve is, in all cases, a logarithmic spiral. In discoid shells, the generating figure revolves in a plane perpendicular to the axis, as in Nautilus, the Argonaut and the Ammonite. In turbinate shells, it slides continually along the axis of revolution, and the curve