The genus Acidaspis has been a peculiarly unfortunate one in Britain. Several of the specific names which are in common use are manuscript terms, or but little better; and the species to which they are applied have never been described. It is impossible, therefore, without access to standard collections, to determine to what forms the names refer. Even the species which have been described have in many cases been imperfectly figured, and the result is endless confusion. The common English trilobite, A. coronata , has received abroad no less than three names, all of them different from ours; while in England, on the other hand, the foreign name A. crenata is often applied to a species which is quite distinct from the original A. crenata , and which in fact has never yet been found out of Britain. The disorder is worst among the Silurian forms, although these are much the most perfect. The Ordovician species are usually fragmentary, but the fragments have been fully described. It is the object of the present paper to attempt to reduce the specific terminology to some sort of order, and to rescue the common manuscript names from the obscurity in which such terms tend to become involved after a lapse of time. Only the Silurian forms are here described; the Ordovician species have been left in the hope that better material may be forthcoming in the future. Even the name of the genus itself is matter of controversy. Murchison employed the term Acidaspis in 1839