REPORT ON THE RADIOLARJA. 1691 



scnts the regular octahedron, with eight congruent triangular faces and six corners. 

 It has the same form as the well-known antheridia of Chara (Gener. Morphol., 

 vol. i. p. 412). Circogonia (PL 115, figs. 8-10; PL 117, fig. 1) exhibits twelve 

 radial- spines, opposite in pairs in six equidistant diameters. The surface of the shell 

 is divided into twenty equal and equilateral triangles, and agrees therefore with the 

 regular icosahedron. The same form appears also in some forms of Aulosphcera, and 

 in several Astrosphserida (Gener. Morphol., vol. i. p. 41 1). Circorrhegma (PL 117, 

 fig. 2) possesses a regular shell with twelve equal pentagonal faces and twenty 

 equidistant corners, from which arise twenty regularly disposed radial spines. It 

 represents therefore the regular " pentagonal dodecahedron," the same remarkable form 

 which is found in some Astrosphserida, and in the pollen -grains of some plants, e.g., 

 Bucholzia maritima, Fumaria spicata, Polygonum amphibium, &c. (Gener. Morphol., 

 vol. i. p. 412, Taf. ii. fig. 18 . 



The three genera of Circoporida mentioned therefore represent three different forms 

 of regular polyhedrons, in the exact mathematical sense, viz., Circoporus, the regular 

 octahedron, Circogonia, the regular icosahedron, and Circorrhegma, the regular dodeca- 

 hedron. In each of these three regular forms all the faces, edges, and corners are 

 equal. The remaining three genera of Circoporida represent, however, three forms of 

 subregular or irregular endospherical polyhedra, which are not perfectly regular. 

 Circospathis (PL 115, figs. 4-7; PL 117, fig. 3) is a rather common form, and 

 constantly possesses nine symmetrically disposed radial spines ; the shell is either 

 spherical or polyhedral, with fourteen triangular faces and thirty edges ; the nine spines 

 lie in three meridional planes, which are crossed at equal angles (three equidistant spines 

 in each plane). We call this remarkable form the tetradecahedron ; it appears also in 

 some Astrosphserida (e.g., in Haliomma echinaster, figured in my Monograph, Taf. 

 xxiv. fig. 1). Circostephanus (PL 116, fig. 3) exhibits a subregular polyhedral shell 

 with a variable number of triangular faces and of radial spines (twenty-four to forty or 

 more). Circostephanus sexagenarius possesses sixty triangular equilateral faces, which 

 are disposed in twelve pentagonal groups (each with five faces), so that the shell seems 

 to be derived from a regular pentagonal dodecahedron, the twelve regular faces of 

 which are divided each into five congruent triangles. From its corners arise thirty -two 

 radial spines (twelve from the central points of the pentagons, twenty from the meeting 

 corners of every three pentagons). In other cases the number of faces and radial spines 

 seems to be larger and their arrangement more irregular. The same may be said of 

 Haeckeliana, in which the dimpled shell is constantly spherical, and possesses a variable 

 number of radial spines, from sixteen to fifty -five (usually between thirty and forty). 



The structure of the shell in the Circoporida is the same as in the Tuscarorida, of 

 a peculiar porcellanous nature. The shell-wall is very thick, more or less opaque,, and in 

 direct light whitish or yellowish. Its surface is dimpled, with numerous small, circular, 



