Especial interest has recently been attracted on the part of chemists to the bearing of crystallography on their science by a remarkable theory which has been advanced by Pope and Barlow, connecting the internal structure of crystals with chemical valency, the power which the atom of a chemical element possesses of combining with the atoms of other elements, and which is generally expressed by the number of atoms of a monad element, such as hydrogen or chlorine, with which it is capable of combining chemically. Thus the electro-positive metal potassium is said to have monad valency because it is capable of combining with one atom of the electro-negative element chlorine to form the salt potassium chloride, KCl; calcium possesses dyad valency because it can unite with two atoms of chlorine to form calcium chloride, CaCl_{2}; aluminium is triadic as it can combine with three atoms of chlorine producing aluminium chloride, AlCl_{3}; carbon is a tetrad because it can take up four chlorine atoms, forming carbon tetrachloride, CCl_{4}, and phosphorus a pentad as it can fix five with production of phosphorus pentachloride, PCl_{5}; while sulphur is a hexad because it can take up as many as six atoms of chlorine, forming sulphur hexachloride, SCl_{6}. Occasion has already been taken in Chapter XI. to refer to the able work of Prof. Pope with regard to optically active carbon compounds, and in Chapter IX. the important contribution of Mr Barlow to the completion of the theory of the homogeneous partitioning of space has likewise been discussed. In collaboration these two investigators have now propounded a theory which connects the chemical and geometrical sides of crystallography in a somewhat startling manner, which has naturally aroused very considerable discussion, and which, whether right or wrong, cannot fail to have the best results in attracting investigators to the subject. Starting from the facts which have now been laid down in this book as having been firmly established by the most careful measurement and experimental investigation—notably the constancy of the interfacial angles of the crystals of the same substance, the fixed positions of the atoms or their spheres of influence in the molecule and in the crystal, and the arrangement of the molecules in space-lattices and the atoms in point-systems—Pope and Barlow assume that valency, the expression of the relative combining power of the chemical elements, is a question of the size of the sphere of influence of the atom of an element, and that the relative sizes of such spheres of influence determine the modes in which they can be packed, that is, the nature of the homogeneous crystal structure which they can build up. The theory consequently renders the chemical phenomenon of valency and the physical phenomenon of crystalline form mutually interdependent.