formed, this long and comparatively rigid filament is separated by a distinct surface from the neighbouring protoplasm, that is to say from the more fluid surface-protoplasm of the cell; and the latter begins to creep up the filament, just as water would creep up the interior of a glass tube, or the sides of a glass rod immersed in the liquid. It is the simple case of a balance between three separate tensions: (1) that between the filament and the adjacent protoplasm, (2) that between the filament and the adjacent water, and (3) that between the water and the protoplasm. Calling these tensions respectively Tÿ£¢ fp , Tÿ£¢ fw , and Tÿ£¢ wp , equiôÙlibôÙrium will be attained when the angle of contact between the fluid protoplasm and the filament is such that cosã₤öÝ =ã₤( Tÿ£¢ fw ã₤ãã₤ Tÿ£¢ wp )ã₤ãã₤ Tÿ£¢ fp . It is evident in this case that the angle is a very small one. The precise form of the curve is somewhat different from that which, under ordinary circumstances, is assumed by a liquid which creeps up a solid surface, as water in contact with air creeps up a surface of glass; the difference being due to the fact that here, owing to the density of the protoplasm being practically identical with that of the surrounding medium, the whole system is practically immune from gravity. Under normal circumstances the curve is part of the ãelastic curveã by which that surface of revolution is generated which we have called, after Plateau, the nodoid; but in the present case it is apparently a catenary. Whatever curve it be, it obviously forms a surface of revolution around the filament.
Since the attraction exercised by this surface tension is symmetrical around the filament, the latter will be pulled equally {266} in all directions; in other words it will tend to be set normally to the surface of the sphere, that is to say radiating directly outwards from the centre. If the distance between two adjacent filaments be considerable, the curve will simply meet the filament at the angle öÝ already referred to; but if they be sufficiently near together, we shall have a continuous catenary curve forming a hanging loop between one filament and the other. And when this is so, and the radial filaments are more or less symmetrically interspaced, we may have a beautiful system of honeycomb-like depressions over the surface of the organism, each cell of the honeycomb having a strictly defined geometric configuration.
In the simpler Radiolaria, the spherical form of the entire organism is equally well-marked; and here, as also in the more complicated Heliozoa (such as Actinosphaerium), the organism is differentiated into several distinct layers, each boundary surface tending to be spherical, and so constituting sphere within sphere. One of these layers at least is close packed with vacuoles, forming an ãalveolar meshwork,ã with the conôÙfiôÙgurôÙaôÙtions of which we shall attempt in another chapter to correlate the charôÙacôÙterôÙisôÙtic structure of certain complex types of skeleton.
An exceptional form of cell, but a beautiful manifestation of