of surface-energy at the boundary, which cause the spicules to be retained there, and to take up their position in its plane. The case is somewhat, though not directly, analogous to that of a cirrus cloud, which marks the place of a surface of discontinuity in a stratified atmosphere.
We have, then, to enquire what are the conditions which shall, apart from gravity, confine an extraneous body to a surface-film; and we may do this very simply, by considering the surface-energy of the entire system. In Fig. 218 we have two fluids in contact with one another (let us call them water and protoplasm), and a body ( b ) which may be immersed in either, or may be restricted to the boundary {461} between. We have here three possible ãinterfacial contactsã each with its own specific surface-energy, per unit of surface area: namely, that between our particle and the water (let us call it öÝ), that between the particle and the protoplasm (öý), and that between water and protoplasm (ö°). When the body lies in the boundary of the two fluids, let us say half in one and half in the other, the surface-energies concerned are equivalent to ( S ã₤ãã₤2)öÝã₤+ã₤( S ã₤ãã₤2)öý; but we must also remember that, by the presence of the particle, a small portion (equal to its sectional area s ) of the original contact-surface between water and protoplasm has been obliterated, and with it a proportionate quantity of energy, equivalent to s ö°, has been set free. When, on the other hand, the body lies entirely within one or other fluid, the surface-energies of the system (so far as we are concerned) are equivalent to S öÝã₤+ã₤ s ö°, or S öýã₤+ã₤ s ö°, as the case may be. According as öÝ be less or greater than öý, the particle will have a tendency to remain immersed in the water or in the protoplasm; but if ( S ã₤ãã₤2)(öÝã₤+ã₤öý)ã₤ãã₤ s ö° be less than either S öÝ or S öý, then the condition of minimal potential will be found when the particle lies, as we have said, in the boundary zone, half in one fluid and half in the other; and, if we were to attempt a more general solution of the problem, we should evidently have to deal with possible conditions of equiôÙlibôÙrium under which the necessary balance of energies would be attained by the particle rising or sinking in the boundary zone, so as to adjust the relative