The chief arguments against its interpretation as a parietal eye seem to be that its structure is not absolute proof, being capable of other explanation; its position is variable, in front, between, or back of the eyes; it is exactly like other tubercles on the median line, especially the nuchal spine or tubercle, and the similar ones along the axial lobe of the thorax; and it is not present in the protaspis or very young trilobites. 1. The structure disclosed by Ruedemann's sections, a sort of sac-like cavity beneath a thinned test, can be explained as a gland, a ligamentary attachment, or a vestigial spine, as well as an eye. In a section of _Asaphus expansus_, which I made some years ago when trying to get some light on this problem, there is a similar cavity under the pustule, but a secondary layer of shell lay beneath it and apparently cut it off from the glabellar region, thus indicating that it had lost its function in the adult of this animal. Sections through the tubercles of the glabella of _Ceraurus_ show all of them hollow, with very thin upper covering or none at all, and their structure is not unlike that of the tubercle of _Cryptolithus_. In fact, sections can be seen in Doctor Walcott's slices which are practically identical with the one Ruedemann obtained from _Cryptolithus_. Since it is obvious that not all of the pustules of a _Ceraurus_ could have been eyes, the evidence from structure is rather against than for the interpretation of the median pustule as such an organ. 2. The position of the tubercle varies greatly in different genera. Where furthest forward (_Tretaspis_, _Goldius_), it is just back of the frontal lobe, while in some species of asaphids it is in the neck furrow. In species with compound eyes it is frequently between the eyes, but more often back of them. If its history be traced in a single family, it is generally found farthest forward in the more ancient species and moves backward in the more recent ones. The eyes do this same thing, but the median tubercle goes back further than the eyes. This can be seen, for example, in the American Asaphidæ, where the pustule is up between the eyes of _Hemigyraspis_ and _Symphysurus_ of the Beekmantown and back of the eyes of the _Isotelus_ of the Trenton. Turning now to the under side of the head, it appears that the tubercle bears a rather definite relation to the hypostoma. If the hypostoma is short, the tubercle is well forward. If long, it is far back on the head. It seems in many cases to be just back of the posterior tip of the hypostoma, or just behind the position of the mouth, while in others it is not as far back as the tip of the hypostoma.