700 ON CONCRETIONS, SPICULES, ETC. [ch. 



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, equi- 

 valent 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 Sol + sy, or 

 S^ + sy, as the case may be. Accordingly as a be less or greater 

 than ^, the particle will have a tendency to remain immersed in 

 the water or in the protoplasm ; but if (aS/2) (a + ^) - sy be less 

 than either Sol or 8/3, 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 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 

 magnitudes of the surface-areas concerned. 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 sohd spicule is dis- 

 tributed 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 dehcate film, and forming catenary curves or 

 festoons between one spicule and another; and a less fluid or more 

 tenacious thread of protoplasm may serve, like a solid spicule, to 

 extend the more fluid film, as we see, for instance, in Chlamydomyxa 

 or in Gromia. When the spicules are numerous and close-set, the 

 surface-film of protoplasm stretching between them will tend to look 

 like a layer of concave or inverted bubbles ; and this honeycombed 

 bubbly surface is sometimes beautifully regular, to judge from a 

 well-known figure of the living Globigerina* . 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 



* See H. B. Brady's Challenger Monograph, pi. Ixxvii; and see the figure of 

 Chlamydomyxa in Doflein's Protozoenkunde, p. 374. 



