Ergo, they can not be nerves in either case, and that they have anything to do with the eyes is highly improbable. The eye was merely superimposed upon these structures. The relation of the genal cæca to the ocelli on the cheeks is best shown in the Trinucleidæ. In all species of _Tretaspis_ simple eyes are present, and in most of them there are very narrow eye-lines. The latter are occasionally continued beyond the ocular tubercle back to the genal angle. A similar course is seen in _Harpes_. If the simple eye is the homologue of the compound eye, and the eye-line here the homologue of the eye-line in _Ptychoparia_, why does it continue beyond the eye? In any case, it can not be interpreted as a nerve. _Cryptolithus tessellatus_, when the cephalon is 0.45 mm. to 0.65 mm. long, shows short eye-lines and a small simple eye on each cheek. In some half-grown specimens, traces of the ocelli can be seen, but the eye-lines are absent. In the adult, both the eye-lines and the ocelli are entirely wanting. Reed states that "nervures" are also absent, and so they are from most specimens, but well preserved casts of the interior from the Upper Trenton opposite Cincinnati show them, and one cheek is here figured (fig. 25). As apparent from the figure, the main trunk is very short and gives rise to two principal branches, the first of which in its turn sends off lines from the anterior side. It was a specimen showing these lines which Ruedemann (1916, p. 147) figured as showing facial sutures. The interest lies in the fact that while the ocelli and eye-lines were lost in development, the genal cæca are present in the adult, showing that they are different structures. [Illustration: Fig. 25.--_Cryptolithus tessellatus_ Green. Side view of the cheek of a specimen from the top of the Trenton opposite Cincinnati, Ohio, to show the branching genal cæca. These are the "facial sutures" of Ruedemann.] _Harpides_ is another genus in which genal cæca are strikingly shown, and in this case they completely cover the huge cheeks, radiating from two main trunks to the front and sides. I have seen no good specimens, but it would appear from Angelin's figure (1854, pl. 41, fig. 7) that the rather large, simple eyes are not situated exactly on the vascular trunks. In the _Harpides_ from Bohemia, the main trunks extend out with many branches beyond the simple eyes. It should be stated that the courses of the genal cæca are not correctly figured by Barrande (Supplement, 1872, pl. 1, fig. 11), as shown by casts of the original specimen in the Museum of Comparative Zoology. From Barrande's figure, one would suppose that the eye-lines and their continuation beyond the "ocelli" were superimposed upon the genal cæca without having any definite connection with them, but as a matter of fact the radial markings really diverge from the main trunks as in _Elyx_ and similar forms. _Summary._