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



the other fourteen spines appear rudimentary ; and in some of them the two equatorial 

 spines of the hydrotomical plane are much larger than the four polar spines of the same 

 plane. This curious relation reaches its maximum in the Diploconida (PL 140). 



The different development of the two equatorial axes (of the larger hydrotomical and 

 the smaller geotomical axis) is the first and most important cause of the peculiar forms, 

 which are produced in the four cited families. We derive these terms also from the 

 metaphor of the terrestrial glolie. The hydrotomical plane is that meridian plane of the 

 globe which intersects almost only the water-hemisphere (the island of Ferro in the Atlantic, 

 the island of Pandora in the Pacific). Perpendicular to this is the geotomical plane, the 

 meridian of which intersects great land-masses in both hemispheres (Bombay in India, 

 Athabasca in Canada). Both poles of the smaller geotomical axis are everywhere equal 

 (the East Indian and the Western American). However, both poles of the larger 

 hydrotomical axis (the eastern Atlantic and the western Pacific) are in some genera very 

 diff'erent, e.g., in Amphihclone among the Amphilonchida, and in Zygostaurus among the 

 Quadrilonchida. In this case we call the anterior (commonly more developed) pole of 

 the hydrotomical axis the frontal pole, the o^jposite posterior (commonly smaller) the 

 caudal pole (PI. 131, figs. 7, 8; PI. 132. figs. 9, 10). On both sides of these (right 

 and left) lie symmetrically the two equal poles of the geotomical lateral axis. 



The promorphology of the Acantharia demonstrates that the geometrical funda- 

 mental form in those groups is diflerent. In the majority of the Acantharia, where the 

 two equatorial axes are equal, that form is a double square-pyramid or a " quadrate 

 octahedron " ; the four equal equatorial spines indicate the two diagonals of the square, 

 which is the common base of the united regular four-sided pyramids ; their common axis 

 is the spineless axis of the body ; the ends of the polar spines fall on the edges of the 

 pyramids, while the ends of the tropical spines fall on the halving lines of their faces. 

 However, in those Acantharia in which the two equatorial axes become diflerent, the 

 square double pyramid becomes changed into a rhombic double pyramid ; the common 

 base of the united pyramids is thus a rhombus ; the hydrotomical axis is the larger, 

 the geotomical axis the smaller diagonal of the rhombus. 



Opposed to the Icosacantha, under the name "Adelacantha," is the small group of Actin- 

 elida, in which the number and disposition of the radial spines is variable, not determined 

 by the MiiUerian law. Probably this group is the common ancestral stock, from which 

 the Icosacantha have been derived by gradual development of their peculiar disposition. 

 Probably the oldest and most primitive form of all Acantharia is Actinelius, in which 

 a variable and undetermined (often very large) number of radial spines is united in 

 one common central point, and therefore forms a needle-sphere. AVhilst here all spines 

 (often more than a hundred) are of equal size and form, in the nearly allied Astrolo2'>hufi 

 large and small spines are intermingled. Both genera together form the small ancestral 

 family of Astrolophida. In the strange family of Litholophida the radial spines do not 



