constitute a symmetrical system of forces, with one resultant downwards, in the direction of gravity, and another outwards in a radial direction; and if we look upon the shell as originally spherical, both will tend to depress the sphere into a flattened cake. We need not consider the radial component, but may treat the case as that of a spherical shell symmetrically depressed under the influence of gravity. This is precisely the condition which we have to deal with in a drop of liquid lying on a plate; the form of which is determined by its own uniform surface-tension, plus gravity, acting against the uniform internal hydrostatic pressure. Simple as this system is, the full mathôÙeôÙmatôÙiôÙcal inôÙvesôÙtiôÙgaôÙtion of the form of a drop is not easy, and we can scarcely hope that the systematic study of the Echinodermata will ever be conducted by methods based on Laplaceãs differential equation14; but we have no difficulty in seeing that the various forms represented in a series of sea-urchin shells are no other than those which we may easily and perfectly imitate in drops.
In the case of the drop of water (or of any other particular liquid) the specific surface-tension is always constant, and the pressure varies inversely as the radius of curvature; therefore the smaller the drop the more nearly is it able to conserve the spherical form, and the larger the drop the more does it become flattened under gravity. We can represent the phenomenon by using india-rubber balls filled with water, of different sizes; the little ones will remain very nearly spherical, but the larger will fall down ãof their own weight,ã into the form of more and more flattened cakes; and we see the same thing when we let drops of heavy oil (such as the orthotoluidene spoken of on p. 219), fall through a tall column of water, the little ones remaining round, and the big ones getting more and more flattened as they sink. In the case of the sea-urchin, the same series of forms may be assumed to occur, irrespective of size, through variations in T, the specific tension, or ãstrength,ã of the enveloping shell. Accordingly we may study, entirely from this point of view, such a series as the following (Fig. 328). In a very few cases, such as the fossil Palaeechinus, we have an apôÙproxôÙiôÙmateôÙly spherical {664} shell, that is to say a shell so strong that the influence of gravity becomes negligible as a cause of deformation. The ordinary species of Echinus begin to display a pronounced depression, and this reaches its maximum in such soft-shelled flexible forms as Phormosoma. On the general question I took the opportunity of consulting Mr C. R. Darling, who is an acknowledged expert in drops, and he at once agreed with me that such forms as are represented in Fig. 328 are no other than diagrammatic illustrations