These undulating and helicoid surfaces are exactly reproduced among certain forms of spermatozoa. The tail of a spermatozoon consists normally of an axis surrounded by clearer and more fluid protoplasm, and the axis sometimes splits up into two or more slender filaments. To surface tension operating between these and the surface of the fluid protoplasm (just as in the case of the flagellum of the Trypanosome), I ascribe the formation of the undulating membrane which we find, for instance, in the spermatozoa of the newt or salamander; and of the helicoid membrane, wrapped in a far closer and more beautiful spiral than that which we saw in Spirochaeta, which is characteristic of the spermatozoa of many birds.
Before we pass from the subject of the conformation of the solitary cell we must take some account of certain other exceptional forms, less easy of explanation, and still less perfectly understood. Such is the case, for instance, with the red blood-corpuscles of man and other vertebrates; and among the sperm-cells of the decapod crustacea we find forms still more aberrant and not less perplexing. These are among the comparatively few cells or cell-like structures whose form seems to be incapable of explanation by theories of surface-tension.
In all the mammalia (save a very few) the red blood-corpuscles are flattened circular discs, dimpled in upon their two opposite sides. This configuration closely resembles that of an india-rubber ball when we pinch it tightly between finger and thumb; and we may also compare it with that experiment of Plateau’s {271} (described on p. [223]), where a flat cylindrical oil-drop, of certain relative dimensions, can, by sucking away a little of the contained oil, be made to assume the form of a biconcave disc, whose periphery is part of a nodoidal surface. From the relation of the nodoid to the “elastic curve,” we perceive that these two examples are closely akin one to the other.
Fig. 93.
The form of the corpuscle is symmetrical, and its surface is a surface of revolution; but it is obviously not a surface of constant mean curvature, nor of constant pressure. For we see at once that, in the sectional diagram (Fig. [93]), the pressure inwards due to surface tension is positive at A, and negative at C; at B there is no curvature in the plane of the paper, while perpendicular to it the curvature is negative, and the pressure therefore is also negative. Accordingly, from the point of view of surface tension alone, the blood-corpuscle is not a surface of equilibrium; or in other words, it is not a fluid drop suspended in another liquid. It is obvious therefore that some other force or forces must be at work, and the simple effect of mechanical pressure is here excluded, because the blood-corpuscle exhibits its characteristic shape while floating freely in the blood. In the lower vertebrates the blood-corpuscles have the form of a flattened oval disc, with rather sharp edges and ellipsoidal surfaces, and this again is manifestly not a surface of equilibrium.
Two facts are especially noteworthy in connection with the form of the blood-corpuscle. In the first place, its form is only maintained, that is to say it is only in equilibrium, in relation to certain properties of the medium in which it floats. If we add a little water to the blood, the corpuscle quickly loses its characteristic shape and becomes a spherical drop, that is to say a true surface of minimal area and of stable equilibrium. If on the other hand we add a strong solution of salt, or a little glycerine, the corpuscle contracts, and its surface becomes puckered and uneven. In these phenomena it is so far obeying the laws of diffusion and of surface tension. {272}
In the second place, it can be exactly imitated artificially by means of other colloid substances. Many years ago Norris made the very interesting observation that in an emulsion of glue the drops assumed a biconcave form resembling that of the mammalian corpuscles[317]. The glue was impure, and doubtless contained lecithin; and it is possible (as Professor Waymouth Reid tells me) to make a similar emulsion with cerebrosides and cholesterin oleate, in which the same conformation of the drops or particles is beautifully shewn. Now such cholesterin bodies have an important place among those in which Lehmann and others have shewn and studied the formation of fluid crystals, that is to say of bodies in which the forces of crystallisation and the forces of surface tension are battling with one another[318]; and, for want of a better explanation, we may in the meanwhile suggest that some such cause is at the bottom of the conformation the explanation of which presents so many difficulties. But we must not, perhaps, pass from this subject without adding that the case is a difficult and complex one from the physiological point of view. For the surface of a blood-corpuscle consists of a “semi-permeable membrane,” through which certain substances pass freely and not others (for the most part anions and not cations), and it may be, accordingly, that we have in life a continual state of osmotic inequilibrium, of negative osmotic tension within, to which comparatively simple cause the imperfect distension of the corpuscle may be also due[319]. The whole phenomenon would be comparatively easy to understand if we might postulate a stiffer peripheral region to the corpuscle, in the form for instance of a peripheral elastic ring. Such an annular thickening or stiffening, like the “collapse-rings” which an engineer inserts in a boiler, has been actually asserted to exist, but its presence is not authenticated.
But it is not at all improbable that we have still much to learn about the phenomena of osmosis itself, as manifested in the case of minute bodies such as a blood-corpuscle; and (as Professor Peddie suggests to me) it is by no means impossible that curvature {273} of the surface may itself modify the osmotic or perhaps the adsorptive action. If it should be found that osmotic action tended to stop, or to reverse, on change of curvature, it would follow that this phenomenon would give rise to internal currents; and the change of pressure consequent on these would tend to intensify the change of curvature when once started[320].