Page:Scientific results HMS Challenger vol 18 part 1.djvu/40

xx included in this category. Such indifferently stable bodies are found among the in many  and, as well as in the Astrolophida among the. On the contrary they are entirely wanting among the and, since their central capsule constantly presents a main axis with a differentiated basal pole, and determines the position of stable equilibrium.

42. Polystatic Ground-Forms.—Those ground forms are defined as polystatic or multistable in which the body is in equilibrium in several different positions (though not in an infinite number). The number of these positions is usually twice as many as that of the constant equal isopolar axes exhibited by the form. Hence the regular polyhedra have as many positions of equilibrium as they have angles or sides, the icosahedron twenty, dodecahedron twelve, octahedron eight, cube six, tetrahedron four. The isopolar monaxon ground-forms (lens, ellipsoid, cylinder) and the diplopyramidal ground forms (quadrilonchial and lentelliptical) have two positions of stable equilibrium, since the two poles of the vertical axis are equal and similar and the body is divided into equal halves by the equatorial plane. This is the case in many (especially, , and ), as well as in the great majority of. Perhaps the same holds good also in certain (e.g., isopolar Tympanida) and  (e.g., isopolar ), though here unistable equilibrium appears to be necessitated by the constant main axis of the central capsule and the differentiated basal pole of the main axis.

43. Monostatic Ground-Forms.—Those ground-forms are classed as monostatic or unistable in which the body is in equilibrium only in one position, since the centre of gravity of the body lies in a constant vertical axis below its centre. This fixed position is only rarely and exceptionally found among the (e.g., in Xiphostylus, Sphærostylus, Lithomespilus, Lithapium) and among the  (e.g., in Zygostaurus and Amphibelone). On the contrary it is quite usual among the and  (with but few exceptions); for here a vertical main axis, with a differentiated basal pole, is determined even by the formation of the central capsule, and usually also by the corresponding structure of the skeleton. Among the this basal pole, with the porochora of the central capsule, appears always to be the lower; as also in most  among the. In the peculiar bivalved, on the other hand, the basal pole with the cannopyle is directed upwards; as also in the Challengerida and Tuscarorida. The and  are probably to a large extent polystatic. In general unistable equilibrium may be assumed in the following categories of ground-forms:—(1) Allopolar monaxon (conical and ovoid); (2) pyramidal (regular and amphithect); (3) Centroplana (amphipleura and zygopleura); (4) Anaxonia.