The oxides Cu_{2}O, MgO, NiO, Fe_{3}O_{4}, CeO_{2}, crystallise in the regular system, although they are of very different atomic structure. Marignac demonstrated the perfect analogy of the forms of K_{2}ZrF_{6} and CaCO_{3}, and the former is even dimorphous, like the calcium carbonate. The same salt is isomorphous with R_{2}NbOF_{5} and R_{2}WO_{2}F_{4}, where R is an alkali metal. There is an equivalency between CaCO_{3} and K_{2}ZrF_{6}, because K_{2} is equivalent to Ca, C to Zr, and F_{6} to O_{3}, and with the isomorphism of the other two salts we find besides an equal contents of the alkali metal--an equal number of atoms on the one hand and an analogy to the properties of K_{2}ZrF_{6} on the other. The long-known isomorphism of the corresponding compounds of potassium and ammonium, KX and NH_{4}X, may be taken as the simplest example of the fact that an analogy of form shows itself with an analogy of chemical reaction even without an equality in atomic composition. Therefore the ultimate progress of the entire doctrine of the correlation of composition and crystalline forms will only be arrived at with the accumulation of a sufficient number of facts collected on a plan corresponding with the problems which here present themselves. The first steps have already been made. The researches of the Geneva _savant_, Marignac, on the crystalline form and composition of many of the double fluorides, and the work of Wyruboff on the ferricyanides and other compounds, are particularly important in this respect. It is already evident that, with a definite change of composition, certain angles remain constant, notwithstanding that others are subject to alteration. Such an instance of the relation of forms was observed by Laurent, and named by him _hemimorphism_ (an anomalous term) when the analogy is limited to certain angles, and _paramorphism_ when the forms in general approach each other, but belong to different systems. So, for example, the angle of the planes of a rhombohedron may be greater or less than 90°, and therefore such acute and obtuse rhombohedra may closely approximate to the cube. Hausmannite, Mn_{3}O_{4}, belongs to the tetragonal system, and the planes of its pyramid are inclined at an angle of about 118°, whilst magnetic iron ore, Fe_{3}O_{4}, which resembles hausmannite in many respects, appears in regular octahedra--that is, the pyramidal planes are inclined at an angle of 109° 28´. This is an example of paramorphism; the systems are different, the compositions are analogous, and there is a certain resemblance in form. Hemimorphism has been found in many instances of saline and other substitutions. Thus, Laurent demonstrated, and Hintze