present impossible) to explain a natural monophyletic system of this large legion. The greatest difficulty is presented by the fact that the three structural elements mentioned above, viz., the sagittal ring, the basal tripod, and the latticed cephalis, are not constantly united, but each alone may also constitute the skeleton by itself. In this respect the following seven cases are possible, and are actually realised.

A. The skeleton is composed of the sagittal ring only and of its spiny appendages, without basal tripod and without latticed cephalis. This is the case in the majority of Stephoidea (Stephanida, Semantida, Coronida, and Tympanida).

B. The skeleton is composed of a basal tripod only (Plagiacantha), or of a tripod in the centre of which arises a vertical apical horn (Plagoniscus), and often of an irregular framework, arising from the rods of the tripod; but there is neither a trace of a sagittal ring nor a complete latticed cephalis. This is the case in the remarkable suborder Plectoidea (Plagonida and Plectanida).

C. The skeleton is composed of a latticed cephalis only, a simple ovate or subspherical fenestrated shell, which encloses the monopylean central capsule; there is no trace of a sagittal ring nor of a basal tripod. This is the case in the remarkable family of Cyrtocalpida (Archicorida and Archicapsida), in numerous Botryodea and in other Cyrtellaria.

D. The skeleton is composed of a sagittal ring and a basal tripod, without latticed cephalis. This is the case in a few, but very important forms of Stephoidea: Cortina, Stephanium, Cortiniscus, Stephaniscus, Podocoronis, and some allied genera.

E. The skeleton is composed of a sagittal ring and a latticed cephalis, but without basal tripod. This is the case in numerous Cyrtellaria, in the Circospyrida (or Zygospyrida apoda: Dictyospyris, Circospyris) and some other Spyroidea; and in a large number of Botryodea and Cyrtoidea eradiata (a part of the Sethocyrtida, Theocyrtida, Lithocampida, and others).

F. The shell is composed of a basal tripod and a latticed cephalis, but without any trace of the sagittal ring. This is the case in numerous Cyrtoidea triradiata and multiradiata, and perhaps in the majority of the following families—Tripocalpida, Tripocyrtida, Podocyrtida, and Podocampida.

G. The shell is composed of all three above-mentioned elements, of a sagittal ring, a basal tripod, and a latticed cephalis. This is the case in the great majority of Spyroidea (with a few exceptions only), and perhaps also in the majority of Cyrtoidea.

The survey of these seven groups, A to G, each of which is represented by numerous living forms, shows clearly how difficult and complicated the morphology and phylogeny of the numerous Nassellaria must be. For all possible combinations of the three original structural elements are realised abundantly, and in such complicated relations, and so intermingled in the different orders and families, that it seems nearly hopeless to answer the question of their true origin. The identity in the structure of the central capsule, however, in all these Monopylea, makes it probable that they have all arisen originally from the skeletonless Nassellida (Cystidium, Nassella), either in a monophyletic or in a polyphyletic way. In this respect the following phylogenetical hypotheses are possible.

1. Monophyletic hypothesis, deriving all Nassellaria from a simple sagittal ring (Archicircus, Lithocircus, &c., Pl. 81). The groups A, D, E, and G may be derived easily from such a ring, but the groups B, C, and F only by means of the hypothesis that the original ring may be completely reduced and finally lost. This hypothesis was stated by me in the years 1877 to 1879, when I had got the first general survey of the astonishing number of new Nassellaria in the Challenger collection, and as I had found the sagittal ring in the majority of them. This, my former hypothesis, is mentioned by Richard Hertwig (1879, loc. cit., pp. 68, 126). It was afterwards supported with particular energy by O. Bütschli (1882, Zeitschr. für wiss. Zool., Bd. XXXVI.).

2. Monophyletic hypothesis, deriving all Nassellaria from a basal tripod (Triplagia, Plagoniscus, &c., Pl. 91). The groups B, D, F, and G, all triradiate, may be derived easily from such a tripod; but the groups A, C, and E only by means of the hypothesis that the original tripod may be completely reduced and finally lost. This hypothesis was employed in 1881 in my Prodromus, since I had convinced myself that the "triradial structure" is prevalent in the great majority of Nassellaria, and is perhaps more important than the sagittal ring.

3. Monophyletic hypothesis, deriving all Nassellaria from a latticed cephalis, a simple ovate or subspherical fenestrated shell without ring and tripod (Cyrtocalpis, Archicapsa, &c.). The groups C, E, F, and G may be derived easily from such a cephalis, but the groups A, B, and D only by means of the hypothesis that the sagittal ring as well as the basal tripod may remain as the last remnants of a reduced cephalis. This hypothesis was given in 1862 in my Monograph, where I constructed the first pedigree of Radiolaria (p. 234). I there derived all the Cyrtida from the Sphæroidea (Cyrtidosphæra), supposing that Cyrtocalpis and some other Monocyrtida may form a direct phylogenetical passage from the Sphæroidea to the Cyrtoidea.

4. Polyphyletic hypothesis, deriving the different groups of Nassellaria from different skeletonless Nassellida, by development of simple siliceous skeletons in different ways. Among the numerous polyphyletic hypotheses which are possible, one of the simplest would be the supposition that three different fundamental forms of skeleton may have arisen independently one from another: (1) a simple sagittal ring as original form of the Stephoidea and Spyroidea (A); (2) a simple basal tripod as original form of the Plectoidea (B); (3) a simple latticed cephalis as original form of the Botryodea and Cyrtoidea (C). This triphyletic hypothesis is supported by R. Hertwig (1879, loc. cit., p. 136); he assumes that the original skeletonless Nassellida (Cystidium) have produced three different branches, his "Acanthodesmida" (= Stephoidea and Spyroidea) with a primary ring, his "Plagiacanthida" (= Plectoidea) with a primary tripod, and his Cyrtida (= Botryodea and Cyrtoidea) with a primary cephalis. This hypothesis seems rather probable on the first view; but it meets with the greatest difficulties in view of the fact that these three original elements of the skeleton are more or less evidently combined in the great majority of Nassellaria. The greatest difficulty arises from the fact that often among very similar and closely allied forms the first exhibits all three elements (A, B, C) combined, whilst the second has a combination of A and B, the third of B and C, the fourth of A and C; and