From the foregoing brief description it appears that the pygidium of the protaspis varies in different groups from as little as 15 per cent of the total length in the Mesonacidæ to as much as 50 per cent in the Agnostidæ; that the axial lobe varies from as little as 14 per cent of the total width in one _Ptychoparia_ to as much as 50 per cent in _Phalacroma nudum_; that the glabella reaches the anterior margin in the Olenidæ, Solenopleuridæ, and _Phalacroma bibullatum_, while there is a brim in front of it in the Olenellidæ, Paradoxidæ, and three of the species of the Agnostidæ. The decision as to which of these conditions are primitive may be settled quite satisfactorily by study of the ontogeny of the various species. ORIGIN OF THE PYGIDIUM. Taking first the pygidium, it has already been pointed out that in each case the pygidium of the adult is proportionally considerably smaller than the pygidium of the protaspis. The stages in the growth of the pygidium are better known in Sao hirsuta than in any other trilobite, and a review of Barrande's description will be advantageous. Barrande recognized twenty stages in the development of this species, but there was evidently a still simpler protaspis in his hands than the smallest he figured, for he says, after describing the specimen in the first stage: "We possess one specimen on which the head extends from one border to the other of the disk, but as this individual is unique we have not thought it sufficient to establish a separate stage." This specimen is important as indicating a stage in which there was not even a suggestion of division between cephalon and pygidium. In the first stage described by Barrande, the form is circular, the length is about 0.66 mm., and the glabella is narrow with parallel sides and no indications of lateral furrows. The neck segment is indicated by a slight prominence on the axial lobe, and back of it a constriction divides the axial lobe of the pygidium into two nodes, but does not cross the pleural lobes. The position of the nuchal segment permits a measurement of the part which is to form the pygidium, and shows that that shield made up 30 per cent of the entire length. In the second stage, when the test is 0.75 mm. long, the cephalon and pygidium become distinctly separated, and the latter shield shows three annulations on the axial and two pairs of ribs on the pleural lobes. It now occupies 33-1/3 per cent of the total length. In the third stage, when the total length is about 1 mm., the pygidium has continued to grow. It now shows five annulations on the axial lobe, and is 46 per cent of the total length. In the fourth stage, two segments of the axial lobe have been set free from the front of the pygidium. The length is now 1.5 mm. and the pygidium makes up 32 per cent of the whole. From this time the pygidium continues to decrease in size in proportion to the total length, as shown in the following table.