Found often on the coast of North America, cast up by the waves, the animals sometimes still living. Forms masses of various sizes and figures, generally more or less rounded or lobed, and composed of a great number of concentric layers. The number of these strata seems to be regulated in some degree, by the quantity of surface they have to cover. Thus if the nucleus happens to be a small shell, such as the _Naticæ_, _Nassæ_, &c. of our coast, or even the oyster, (_O. virginica_,) clam, (_V. mercenaria_,) &c. the strata are often very numerous; but on the thoracic plate of _Limulus polyphemus_, having a considerable space over which to extend themselves, the strata are but few, not more than 2 or 3. I have seen the thoracic plate of this animal so entirely covered by the _Alveolite_, as to have the eyes and stemmata concealed so as to be perfectly blind. When composed of a single layer only, it much resembles a _Flustra_, or a _Cellapore_ of which the convex surfaces have been removed by attrition. The animal I have not yet examined. The alveoles or cells of a layer, are arranged in lines of different degrees of curvature, obscurely radiating from different centres; these lines are placed side by side, the alveoles alternating with each other throughout the layer in a quincunx manner; the thickness of the paries is somewhat equal to one half of the conjugate diameter of the alveole, the length of which, or thickness of the layer, is scarcely more considerable; but these proportions vary. The species to which it seems allied, are _madreporacea_ and _incrustans_. The former is fossil, and differs in being subramose; the latter forms but a single expansion. _Genus Favosites, Lam._ Coral lapideous, simple, of a variable form, composed of parallel prismatic and fasciculated tubes; tubes contiguous, pentagonal, or hexagonal, more or less angular, rarely articulated. _Species._ _F. striata_, more or less turbinate; _paries of the alveoles_ longitudinally striated within, and fenestrate with minute osculi; _alveoles_ with very numerous septæ. (_Cabinet Acad. Nat. Sciences; and Peale's Museum--common._) Found fossil in various parts of the United States, at the falls of the Ohio; Genessee, New-York; Pittsburg and Wilksbarre, Pennsylvania; Missouri, &c. &c. but not yet in the alluvial deposit of New-Jersey. The tubes are generally, partially, or entirely filled with silicious matter, sometimes so completely so, as to resemble in miniature, basaltic columns; when the alveoles are free on the surface, these fossils are known by the name of _petrified wasp-nests_, from the resemblance they bear to the nests of those insects. The silex is usually only infiltrated into the cavities, leaving the substance of the coral in its original calcareous state, but the specimens which are found amongst the rolled pebbles of the Delaware River, near Philadelphia, are completely silicified.