But other facts, which render the correlation of form and composition still more complex, have accumulated side by side with a mass of data which may be accounted for by admitting the conceptions of isomorphism and dimorphism. Foremost among the former stand the phenomena of _homeomorphism_--that is, a nearness of forms with a difference of composition--and then the cases of polymorphism and hemimorphism--that is, a nearness of the fundamental forms or only of certain angles for substances which are near or analogous in their composition. Instances of homeomorphism are very numerous. Many of these, however, may be reduced to a resemblance of atomic composition, although they do not correspond to an isomorphism of the component elements; for example, CdS (greenockite) and AgI, CaCO_{3} (aragonite) and KNO_{3}, CaCO_{3} (calc spar) and NaNO_{3}, BaSO_{4} (heavy spar), KMnO_{4} (potassium permanganate), and KClO_{4} (potassium perchlorate), Al_{2}O_{3} (corundum) and FeTiO_{3} (titanic iron ore), FeS_{2} (marcasite, rhombic system) and FeSAs (arsenical pyrites), NiS and NiAs, &c. But besides these instances there are homeomorphous substances with an absolute dissimilarity of composition. Many such instances were pointed out by Dana. Cinnabar, HgS, and susannite, PbSO_{4}3PbCO_{3} appear in very analogous crystalline forms; the acid potassium sulphate crystallises in the monoclinic system in crystals analogous to felspar, KAlSi_{3}O_{8}; glauberite, Na_{2}Ca(SO_{4})_{2}, augite, RSiO_{3} (R = Ca, Mg), sodium carbonate, Na_{2}CO_{3},10H_{2}O, Glauber's salt, Na_{2}SO_{4},10H_{2}O, and borax, Na_{2}BrO_{7},10H_{2}O, not only belong to the same system (monoclinic), but exhibit an analogy of combinations and a nearness of corresponding angles. These and many other similar cases might appear to be perfectly arbitrary (especially as a _nearness_ of angles and fundamental forms is a relative idea) were there not other cases where a resemblance of properties and a distinct relation in the variation of composition is connected with a resemblance of form. Thus, for example, alumina, Al_{2}O_{3}, and water, H_{2}O, are frequently found in many pyroxenes and amphiboles which only contain silica and magnesia (MgO, CaO, FeO, MnO). Scheerer and Hermann, and many others, endeavoured to explain such instances by _polymetric isomorphism_, stating that MgO may be replaced by 3H_{2}O (for example, olivine and serpentine), SiO_{2} by Al_{2}O_{3} (in the amphiboles, talcs), and so on. A certain number of the instances of this order are subject to doubt, because many of the natural minerals which served as the basis for the establishment of polymeric isomorphism in all probability no longer