An extensive literature has grown around the subject of calcium sulphate, embracing work prompted not only by the technical importance of plaster of Paris but also by the peculiar inter-relations between the several forms of calcium sulphate. The dihydrated salt (gypsum, selenite) and the orthorhombic anhydrous salt (anhydrite) have long been known as common minerals and their chemical and crystallographic characters are well established. About the hemihydrate (plaster of Paris) and the active, hard-setting anhydrous modification (soluble anhydrite), which do not occur in nature, there is less certainty. Agreement has so far not been reached upon these substances as crystal species, nor yet upon the nature of the changes by which they pass one into another and into the stabler modifications. Conflicting statements are, moreover, to be found in the literature as to whether there are polymorphs of each of the above-named substances, and if so, how many. The Hemihydrate Crystal Since the substances was first isolated in the form of prismatic crystals, not exhaustively examined, various authors have prepared and described crystalline hemihydrate. This latter may be obtained either by protracted contact of the solid dihydrate with hot acid or saline solutions, or by crystallization, at temperatures well above the ordinary, out of solutions or calcium sulphate in moderately concentrated hydrochloric or nitric acid. The crystal has variously been assigned to all the known systems except the cubic and the tetragonal; but there is unanimity to the effect that it is of acicular habit and consists of six-sided prisms. The crystals observed appear for the most part to have been of microscopic size. Recently, however, Onorato and Gallitelli have dealt with crystals large enough for goniometric and X-ray investigations, and to the latter, especially, we owe a thorough study of the crystal and its structure. Both authors consider the crystal to be monoclinic, the former finding a = 12·07 A, c = 6·40, β = 92°, z = 6; the latter a = 11·94, b = 6·83, c = 12·70, β = 89° 24´, z = 12. Now for the monoclinic system the number of molecules Z per unit cell is normally 2, 4, or 8, and such Z numbers as 6 and 12 could only be accounted for by somewhat improbable hypotheses. A re-examination of the crystal has therefore seemed desirable.