It will thus be apparent that the essence of their conception is that the chemical molecule may be considered as made up of a number of spheres corresponding to, and representing, the spheres of influence of the atoms composing it, and that the volume of each sphere is roughly proportional to the valency of the atom which it represents. They then assume that the sum of the valencies of the atoms present in the molecule may be substituted for the molecular volume, and the quantity thus arrived at is termed by them the “valency volume.” By using the valency volume instead of the molecular volume in the author’s formulæ for calculating the molecular distance ratios, which have been shown in Chapter X. to afford the relative dimensions of the unit cell of the space-lattice, and the distances of separation of the centres of gravity of the molecules from each other along the directions of the crystal axes, Pope and Barlow arrive at new ratios, which they term equivalence parameters. By the use of these latter they have attempted to account for the crystalline structure of a number of substances—chiefly organic compounds, in the investigation of which Prof. Pope has proved so adept—which are connected morphotropically in the manner described in Chapter VIII., and of others which are still less intimately connected. Unfortunately, the equivalence parameters do not make clear the relationships in an isomorphous series, as do the molecular distance ratios; for they are, from their very nature and mode of derivation, almost identical for all the members of an isomorphous series, the valencies of the interchangeable elements being the same. The molecular distance ratios have also the great advantage of being derived from the three measurements which have now been brought to the highest pitch of experimental accuracy, namely, atomic weight determinations, density determinations by the Retgers immersion method, and goniometrical and physical measurements (optical and thermal) with instruments now available of the utmost refinement. Structural constants thus derived are obviously of especial value. It would thus appear that the theory requires modification so as to take account of the experimentally proved regular increase in volume and in the directional dimensions of the structural unit cell of the crystal space-lattice, when one element of the same family group and of the same valency is interchanged for another. Indeed, as the theory stands at present it entirely ignores and fails to offer any explanation of the highly important physical property of density, specific gravity. That this physical constant, and the equally important constant molecular volume, derived by dividing the molecular weight by the density, possess a real and significant meaning in isomorphous series, formed by the interchange of elements of the same family group, has been clearly proved in Chapter X. This fact is,