Fig. 328. Diagrammatic vertical outlines of various Sea-urchins: A, Palaeechinus; B, Echinus acutus; C, Cidaris; D, D′ Coelopleurus; E, E′ Genicopatagus; F, Phormosoma luculenter; G, P. tenuis; H, Asthenosoma; I, Urechinus.
of various kinds of drops, “most of which can easily be reproduced in outline by the aid of liquids of approximately equal density to water, although some of them are fugitive.” He found a difficulty in the case of the outline which represents Asthenosoma, but the reason for the anomaly is obvious; the flexible shell has flattened down until it has come in contact with the hard skeleton of the jaws, or “Aristotle’s lantern,” within, and the curvature of the outline is accordingly disturbed. The elevated, conical shells such as those of Urechinus and Coelopleurus evidently call for some further explanation; for there is here some cause at work {665} to elevate, rather than to depress the shell. Mr Darling tells me that these forms “are nearly identical in shape with globules I have frequently obtained, in which, on standing, bubbles of gas rose to the summit and pressed the skin upwards, without being able to escape.” The same condition may be at work in the sea-urchin; but a similar tendency would also be manifested by the presence in the upper part of the shell of any accumulation of substance lighter than water, such as is actually present in the masses of fatty, oily eggs.
On the Form and Branching of Blood-vessels
Passing to what may seem a very different subject, we may investigate a number of interesting points in connection with the form and structure of the blood-vessels, on the same principle and by help of the same equations as those we have used, for instance, in studying the egg-shell.
We know that the fluid pressure (P) within the vessel is balanced by (1) the tension (T) of the wall, divided by the radius of curvature, and (2) the external pressure (pn), normal to the wall: according to our formula
P = pn + T(1 ⁄ r + 1 ⁄ r′).
If we neglect the external pressure, that is to say any support which may be given to the vessel by the surrounding tissues, and if we deal only with a cylindrical vein or artery, this formula becomes simplified to the form P = T ⁄ R. That is to say, under constant pressure, the tension varies as the radius. But the tension, per unit area of the vessel, depends upon the thickness of the wall, that is to say on the amount of membranous and especially of muscular tissue of which it is composed.
Therefore, so long as the pressure is constant, the thickness of the wall should vary as the radius, or as the diameter, of the blood-vessel. But it is not the case that the pressure is constant, for it gradually falls off, by loss through friction, as we pass from the large arteries to the small; and accordingly we find that while, for a time, the cross-sections of the larger and smaller vessels are symmetrical figures, with the wall-thickness proportional to the size of the tube, this proportion is gradually lost, and the walls {666} of the small arteries, and still more of the capillaries, become exceedingly thin, and more so than in strict proportion to the narrowing of the tube.