present their original composition, but one which has been altered under the influence of solutions which have come into contact with them; they therefore belong to the class of _pseudomorphs_, or false crystals. There is, however, no doubt of the existence of a whole series of natural and artificial homeomorphs, which differ from each other by atomic amounts of water, silica, and some other component parts. Thus, Thomsen (1874) showed a very striking instance. The metallic chlorides, RCl_{2}, often crystallise with water, and they do not then contain less than one molecule of water per atom of chlorine. The most familiar representative of the order RCl_{2},2H_{2}O is BaCl_{2},2H_{2}O, which crystallises in the rhombic system. Barium bromide, BaBr_{2},2H_{2}O, and copper chloride, CuCl_{2},2H_{2}O, have nearly the same forms: potassium iodate, KIO_{4}; potassium chlorate, KClO_{4}; potassium permanganate, KMnO_{4}; barium sulphate, BaSO_{4}; calcium sulphate, CaSO_{4}; sodium sulphate, Na_{2}SO_{4}; barium formate, BaC_{2}H_{2}O_{4}, and others have almost the same crystalline form (of the rhombic system). Parallel with this series is that of the metallic chlorides containing RCl_{2},4H_{2}O, of the sulphates of the composition RSO_{4},2H_{2}O, and the formates RC_{2}H_{2}O_{4},2H_{2}O. These compounds belong to the monoclinic system, have a close resemblance of form, and differ from the first series by containing two more molecules of water. The addition of two more molecules of water in all the above series also gives forms of the monoclinic system closely resembling each other; for example, NiCl_{2},6H_{2}O and MnSO_{4},4H_{2}O. Hence we see that not only is RCl_{2},2H_{2}O analogous in form to RSO_{4} and RC_{2}H_{2}O_{4}, but that their compounds with 2H_{2}O and with 4H_{2}O also exhibit closely analogous forms. From these examples it is evident that the conditions which determine a given form may be repeated not only in the presence of an isomorphous exchange--that is, with an equal number of atoms in the molecule--but also in the presence of an unequal number when there are peculiar and as yet ungeneralised relations in composition. Thus ZnO and Al_{2}O_{3} exhibit a close analogy of form. Both oxides belong to the rhombohedral system, and the angle between the pyramid and the terminal plane of the first is 118° 7´, and of the second 118° 49´. Alumina, Al_{2}O_{3}, is also analogous in form to SiO_{2}, and we shall see that these analogies of form are conjoined with a certain analogy in properties. It is not surprising, therefore, that in the complex molecule of a siliceous compound it is sometimes possible to replace SiO_{2} by means of Al_{2}O_{3}, as Scheerer admits.