Definition.—Larcoidea with regular, incompletely latticed cortical shell, distinguished by two to four or more symmetrically disposed gates or large fissures remaining between one to three latticed dimensive girdles (perpendicular one to another). One, two, or three concentric systems of such girdles (each system with three girdles) may be developed.

The family Pylonida is the most important and interesting among all the Larcoidea, not only because it is much richer in different and peculiar forms than the other families of this section, but also because it has direct and very complex relations to all the other families of Larcoidea. It is even possible that the Pylonida represent the original ancestral group of the whole section, and that the apparently simpler group of the Larcarida must be derived from the former by retrogressive metamorphosis.

Till the year 1881 the family Pylonida, which here now exhibits ten genera with eighty-six species, was only represented by one single species, accurately described and extensively illustrated by Johannes Müller in 1858, the well known and widely distributed cosmopolitan Tetrapyle octacantha (Abhandl. d. k. Akad. d. Wiss. Berlin, p. 33, Taf. iii.). A slight modification of it was afterwards described by Ehrenberg as Schizomma quadrilobum (Abhandl. d. k. Akad. d. Wiss. Berlin, 1872, Taf. ii. fig. 12). A more accurate description of it, with a good explanation of its characteristic growth, was given in 1879 by Richard Hertwig in his Organismus der Radiolarien (pp. 52-54, Taf. iv. figs. 7, 8; Taf. vi. figs. 2, 5). In my Prodromus (1881, p. 463) I constituted for a large number of allied species, detected in the Challenger collection, the special family Pylonida, and distinguished among it twelve different genera. However, I think it now better to restrict the definition of the family as given in the above definition, and to remove from it a number of genera formerly with it united, as the genera Triopyle and Hexapyle, appertaining to the Discoidea.

The characteristic type of all true Pylonida is clearly demonstrated by their peculiar mode of growth, the consequence of which is the imperfect lattice-work of the fenestrated larcoid shell. This remarkable growth is effected by the development of elliptical latticed girdles (or rings), which enclose a quite simple, spherical, subspherical, or lentelliptical primordial shell. The girdles lie in three different planes, perpendicular to one another, and are of different sizes; each girdle being somewhat larger than the foregoing and somewhat smaller than the following girdle. Between these latticed girdles remain on the surface of the shell large openings or "gates," which are not closed by network, and it is just the symmetrical disposition and form of these open "gates," separated and enclosed by the fenestrated girdles, which give to the Pylonida their characteristic appearance.

To understand clearly this peculiar constitution of the Pylonida-shell by a system of alternating girdles, developing one after the other it is indispensable to pay careful attention to the three different elliptical dimensive planes, which characterise all Larcoidea, and to the three different dimensive axes, which bisect those planes. The girdle which first develops around simple primordial shell or central chamber is the transverse girdle, lying in the equatorial plane; then comes, secondly, the lateral girdle, lying in the lateral plane; and thirdly follows the sagittal girdle, lying in the sagittal or median plane. The three simplest genera of the Pylonida—Monozonium, Dizonium, Trizonium—represent these three different stages, with one, two, or three girdles. These three genera constitute the first subfamily, Haplozonaria (with one single system of girdles); all three girdles lie in the surface of a simple lentelliptical cortical shell.

From this first subfamily the other two subfamilies of Pylonida must be derived, by repetition of the same characteristic process of growth. In the Diplozonaria a second system of girdles has been developed, constituting a second (outer) cortical shell of lentelliptical form, concentric with the first. Also in this second system the transverse girdle is first developed, secondly the lateral girdle, thirdly the sagittal girdle. The three genera Amphipyle, Tetrapyle (with Octopyle), and Pylonium represent these three different stages of growth.

Commonly the growth of the Pylonida stops with the completion of the second system but sometimes the same process is once repeated and a third system of girdles is formed, constituting a third lentelliptical shell; in this case also the succession of the three latticed girdles is the same; firstly the (third) transverse girdle is formed, secondly the (third) lateral girdle, and thirdly the (third) sagittal girdle. Each of these three girdles of the third system encloses concentrically the corresponding girdles of the second and first system. The three corresponding genera of this third subfamily (Triplozonaria) are Amphipylonium, Tetrapylonium, and Pylozonium. But in general this highest number of girdles (nine) is very seldom reached; commonly the growth of the Pylonida stops with five girdles (Tetrapyle and Octopyle). More than nine girdles I have never observed, though there remains the possibility of the apposition of a fourth system owing to the peculiar imperfect character of the growth itself.

The central or primordial chamber of the shell, with which in all Pylonida the shell-building commences, is a quite simple, very small fenestrated shell. Commonly one sees on the surface only five to ten small pores (three to four on the diameter). Its form seems to be sometimes spherical, sometimes elongated, ellipsoidal or probably lentelliptical. It may be originally a small Cenolarcus. This simple central chamber, the true "medullary shell" of the small Haplozonaria, is quite different from the medullary shell of the larger Diplozonaria, and particularly of the well-known Tetrapyle. The former observers, J. Müller as well as R. Hertwig, have described in these forms also the medullary shell as a simple spherical or oblong body. But a careful comparison of many hundred specimens of them and of their dimensions, has convinced me that this was an error, and that the small spherical or elliptical medullary shell of Tetrapyle and the other Diplozonaria possesses already the same complex structure, composed of a system of three girdles, as Trizonium and Larnacilla. Whilst in the Haplozonaria probably the simple central chamber only represents the medullary shell (enclosed in the central capsule), and the first system of girdles (complete in Trizonium) the external cortical shell, with the progressive growth this latter becomes enclosed in the central capsule and so constitutes the "trizonal medullary shell" of the Diplozonaria and Triplozonaria.

A very difficult matter is the mode of connection between the cortical and medullary shell. In most of the Pylonida it seems that the first or transverse girdle (in each system) is produced by the formation of two lateral wings or chambers (one on each side of the medullary shell), so that each wing (or half girdle) represents a short and wide, nearly cylindrical tube, the axis of which (with free openings on both poles) is parallel to the principal axis of the medullary shell. In this case (probably the ordinary one) both principal faces of the medullary shell itself (dorsal and ventral face) constitute the middle part of the first girdle whilst its lateral parts are formed by the wings (comparable to the lateral chambers of Amphitholus).

In the second case (probably a much rarer one) there is a free ring-shaped space between the medullary shell and the first (transverse) girdle, and both are connected by a small number of very short and small radial beams (R. Hertwig, loc. cit., p. 52, line 19 to 21 from above). This mode of connection would be the same as is common between the concentric shells of the Sphæroidea and Prunoidea. The distinction between these two different modes of connection is often very difficult.