XX THE VOYAGE OF H.M.S. CHALLENGER. 



included in this category. Such indifferently stable bodies are found among the 

 Spumellaria in many C o 1 1 o d a r i a and S p h se r o i d e a, as well as in the Astrolophida 

 among the Acantharia. On the contrary they are entirely wanting among the 

 Nassellaria and Ph^odaria, 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 equilil^rium 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 diplo- 

 pyramidal 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 Spumellaria 

 (especially D i s c o i d e a, P r u n o i d e a, and L a r c o i d e a), as well as in the great 

 majority of Acantharia. Perhaps the same holds good also in certain Nassellaria 

 {e.g., isopolar Tympanida) and PniEODARiA (e.g., isopolar Phseosphaeria), 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 Spumellaria (e.g., in Xiphostylus, 

 SphcBrostyhis, Lithomespilus, Lithapium) and among the Acantharia {e.g., in Zygo- 

 staurus and Amphihelone). On the contrary it is quite usual among the Nassellaria and 

 Ph^odaria (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 Nassellaria this basal 

 pole, with the porochora of the central capsule, appears always to be the lower ; as also 

 in most P h ae o g r o m i a among the Ph.-eodaria. In the peculiar bivalved P h se o- 

 c n c h i a, on the other hand, the basal pole Math the cannoj^yle is directed upwards ; as 

 also in the Challengerida and Tusearorida. The Phseosphseria and Phseocystina 

 are probably to a large extent polystatic. In general unistable equilibrium may be 

 assumed in the following categories of ground-forms : — (l) AUopolar monaxon (conical 

 and ovoid); (2) pyramidal (regular and amphithect); (3) Centroplana (amphipleura 

 and zygopleura) ; (4) Anaxouia. 



