This interesting and beautiful investigation of Miers thus gave us an inkling of the truth, that small angular differences do exist between the members of isomorphous compounds. It paved the way for, and indeed partly suggested, the author’s systematic investigation of the sulphates, selenates, and double salts of the alkali series of metals, a brief account of the main results of which will be given in Chapter X. CHAPTER IX THE CRYSTAL SPACE-LATTICE AND ITS MOLECULAR UNIT CELL. THE 230 POINT-SYSTEMS OF HOMOGENEOUS CRYSTAL STRUCTURE. The interval between the morphotropic work described in the last chapter and the present time has been remarkable for the completion of the geometrical and mathematical investigation, and the successful identification, of all the possible types of homogeneous structures possessing the essential attributes of crystals. It has now been definitely established that there are 230 such types of homogeneous structures possible, and the whole of them conform to the conditions of symmetry of one or other of the thirty-two classes of crystals. This fact is now thoroughly agreed upon by all the authorities who have made the subject their special study, and may truly be considered as fundamental. There has long been a consensus of opinion that the crystal edifice is built up of structural units which can be likened to the bricks or stone blocks of the builder, but which in the case of the crystal are so small as to be invisible even under the highest power of the microscope. The conceptions of their nature, however, have been almost as numerous as the investigators themselves, everyone who has thought over the subject forming his own particular ideas concerning them. We have had the “Molécules intégrantes” of Haüy, the “Polyhédres” of Bravais, the “Fundamentalbereich” of Schönflies, the “Parallelohedra” of von Fedorow, and the fourteen-walled cell, the “Tetrakaidecahedron” of Lord Kelvin, and again the “Polyhedra” of Pope and Barlow. Ideas have thus been extremely fertile, and indeed almost every variety of speculation has been indulged in as to the shape and nature of the unit of the structure which can exhibit such remarkable evidences of organisation and such extraordinary optical and other physical properties as those of a crystal.