IX] AND SPICULAR SKELETONS 461 



between. We have here three possible "interfacial contacts/' 

 each with its own specific surface-energy, per unit of surface 

 area : namely, that between our particle and the water (let us 

 call it a), that between the particle and the protoplasm (,8), and 

 that between water and protoplasm (y). 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/2)a + (aS/2)/3; 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, eqviivalent to sy, 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 Sa -f sy, or S^ -f sy, as the case may be. 

 According as a be less or greater than j8, the particle will have 

 a tendency to remain immersed in the water or in the protoplasm ; 

 but if {S/2) (a -f- j8) — sy be less than either Sa or S^, 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 equilibrium 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 magni- 

 tudes of the surface-areas concerned. It is obvious that this 

 principle may, in certain cases, help us to explain the position 

 even of a radial spicule, which is just a case where the surface of 

 the solid spicule is distributed between the fluids with a minimal 

 disturbance, or minimal replacement, of the original surface of 

 contact between the one fluid and the other. 



In like manner we may provide for the case (a common and 

 an important one) where the protoplasm "creeps up" the spicule, 

 covering it with a delicate film. In Acanthocystis we have 

 yet another special case, where the radial spicules plunge only 

 a certain distance into the protoplasm of the cell, being arrested 

 at a boundary-surface between an inner and an outer layer of 

 cytoplasm ; here we have only to assume that there is a tension 



