The researches upon which this memoir is based were prosecuted more than four years since, and the illustrations which accompany it were mostly executed at nearly as distant a date— before I was aware that this interesting and obscure subject had ever been investigated by competent observers. And though it appears that some of my own observations (independent as they were) have been anticipated, there is so much of this ground of inquiry untrodden, and the accounts published of the structures in question are so very imperfect and often incorrect, that I have been induced to put together in this paper the results of my own more extended investigations. The literature of this subject is confined to very narrow limits; for though comparative anatomists, from the time of Aristotle, have not failed to describe the curious apparatus of teeth and jaws in the Echinus, I am not aware that any observer had investigated the structure and growth of the teeth themselves, or published any account of their intrinsic anatomy, before the Essay on the genus Echinus was written by Valentin as one portion of a general monograph on the Echinodermata published by Agassiz, and which appeared in 1841.