1. A great number of species, belonging to more than thirty genera, possess a distinct tubercle on the glabella. This tubercle occurs alone in many genera, otherwise smooth, as in the Asaphidæ, and is hence of functional importance. 2. In certain cases, as in _Cryptolithus tessellatus_, distinct lenticular bodies [not lenses] were recognized; in others, as in _Asaphus expansus_, only a thinner, probably transparent test. Many other species show a distinct pit in interior casts of the tubercle, indicating a lens-like thickening of the top of the tubercle. The median eye therefore probably possessed all the different stages of development seen in other crustaceans. 3. As in the parietal eyes of the crustaceans and the eurypterids, the tubercles are most prominent and distinct in the earlier growth-stages, notably so in _Isotelus gigas_. 4. The tubercle is especially well developed in the so-called blind forms where the lateral eyes are abortive, as in _Cryptolithus_ (_Trinucleus_), _Dionide_, _Ampyx_. 5. The tubercles always appear on the apex on the highest part of the glabella, where their visual function would be most useful. 6. The tubercle is generally situated between the lateral eyes, like the parietal eye in crustaceans and eurypterids, on account of its close connection with the brain. 7. Frequently it forms the posterior termination of a short crest, also as in certain eurypterids (_Stylonurus_), indicating the direction of the nerve. 8. The median eye is borne on a tubercle or mound in the Ordovician and Silurian trilobites, while the tubercle is rarely noticed in the Devonian and in few Cambrian forms. In the Devonian forms, similarly as in many crustaceans and in later growth-stages of some asaphids, the strong development of the lateral eyes may have led to a loss of the parietal eyes. In the Cambrian genera evidence is present to suggest that the parietal eyes consisted only of transparent spots or lens-like thickenings of the exoskeleton, hardly noticeable from the outside. 9. It is _a priori_ to be inferred that the trilobites should, as primitive crustaceans, have possessed median or parietal eyes. As a student, I accepted Professor Beecher's dictum that this tubercle represented a median _ocellus_, but more recently a number of things have led me to the view that it is the point of attachment of the ligament by which the heart is supported.