2. Semilunate facial ridge on the tripartite head-shield, no sutures, no eyes, but a hypostoma fused to the rostrum of the head and provided with maculæ. The adult animal with thorax and pygidium in the oldest Cambrium, the Olenellus zone. Genera: Olenellus, Holmia (with beginning suture), Mesonacis, Schmidtia. 3. The head quinquepartite with facial suture, short semilunate ridge in the adult, a long ridge in the young, no eyes. The genera occur in the Paradoxides-zones of the Cambrian formation. These genera are Paradoxides, Centropleura, Metadoxides, Hydrocephalus, which are direct descendants of the Olenellidæ. This line of evolution, in which the species never acquired eyes, was extinct in the sixth zone of the Swedish Cambrian, Centropleura Lovéni being the last. B. =The Sao line.= I call this so because we see in the development of Sao, as represented by BARRANDE, most of the different' phases in evolution, which the ridge bearing trilobites of this second group have experienced during the Cambrian times. I. The body consists only of the head, neither pygidium, nor thorax yet developed. 1. _Psilocephali_ (ψιλος, bald), primeval, precambrian, adult stage not found, supposed to be like the head shield of Agnostus glandiformis and A. biplicatus quite round and bare without any glabella nor sutures. The corresponding stage in development also wanted. 2. _Glabellate._ The entire animal only head with a mesial ridge, which at first is entire or unsegmented and later is metamorphosed into the segmented glabella. a. _unsegmented._, Precambrian, adult form unknown, supposed to be like the first larval stage of Liostracus according to the figure I of BRÖGGER and also as the head of Agnostus parvifrons LINNARSSON. Corresponding larval stages Liostracus (I). b. _segmented._ Probably precambrian, not represented as adult in the Cambrian strata. Supposed to be like the larval forms II and III of BRÖGGER'S Liostracus, consisting of the round or oval head shield and the segmented glabella. Also BARRANDE'S first stage of Sao (BARR., fig. 1 pl. 7). As a transition to the next phase forms may be imagined having head and the beginning pygidium, nearly as Agnostus atavus, minus the thorax. The corresponding larval stages are Liostracus (BRÖGGER'S figures IV, V, VI) and Sao (BARRANDE, pl. 7 fig. 2-4 a, b). Nearly so, though the pygidium is more developed, are the larva of Agn. bibullatus and Agn. nudus (BARR., pl. 49) both without thorax. II. These have the three chief parts of the body developed. 3. _The facial ridge._ Cambrian, adult with glabella and facial ridges, short or long, emanating from the top of the glabella, thorax and pygidium. Several American Conocoryphæ. Corresponding larval stage, Sao, stage 3, BARR. pl. 7 figs 4 d-9.