In the plurality of species there are two tiny patches or maculæ, sometimes elevated above the surrounding surface like tubercles and so they have also been called by some authors. But I have preferred to use the name »macula» for them, as the plurality does not form tubercles. They are generally entirely smooth and glossy and situated next to the anterior groove, either above it or in it, at a regular distance from each other and the lateral margins. They may form a sunk spot or, as commonly, an ovoid or elliptic area surrounded by a linear elevated border. Thus amongst the Asaphidæ. In others, again, (Bronteus, Illænus etc.) they form a moderately elevated tubercle. The direction in which they are oriented in relation to the longitudinal axis of the hypostoma is quite as variable. It is to the closer consideration of the nature of these macula that this memoir will be chiefly devoted. They have been delineated several times, but very seldom has any accurate attention been paid to them by previous authors. It is highly doubtful if BARRANDE ever alluded to them, when he in his »Système Silurien de Bohéme» vol. I, p. 156, in describing the hypostoma, says: »Cette plaque bombée porte souvent des saillies et des empreintes creuses, dans le voisinage de la bouche. Leurs formes varient suivant les espèces mais en conservant toujours les caractères génériques. Nous les considérons comme les points d'attaches des muscles et des màchoires.» In the numerous specific descriptions in his grand work there is never any mention made of the macula and in contemplating the figures and reading the explanations of these, we shall find that he meant something more comprehensive with his statement, to wit, the entire groove where these tubercular macula are situated. In NOVÁK'S third paper, p. 4, we see the figures of two Phillipsiæ with tubercles on the hypostoma and he says only that in the anterior groove there are two such symmetrically placed ... glandular intumescences.[1] [Footnote 1: »In der Mittelfurche sitzen 2 kleine symmetrisch gelegene, nicht immer dentliche drüsenartige An schwellungen.»] BRÖGGER again in his paper on the »Ausbildung des Hypostoms» devotes a page (p. 19) to explain the nature of these maculæ and regards them as the exterior marks of two muscular impressions or points of attachment on the inside for muscles which have attached the hypostoma to the walls of the glabella or the head. The real nature of these so variable tubercular maculæ is, however, a quite different one, as we hope to be able to demonstrate in describing all their varying shapes in several genera.