(1) The crystals of the different members of an isomorphous series exhibit slight but real differences in their interfacial angles, the magnitude of the angle changing regularly with the alteration of the atomic weight of the interchangeable metals or negative elements of the same family group which give rise to the series, as one metal or acid-forming element is replaced by another. The amount of the difference increases as the symmetry of the system diminishes. Thus the maximum difference for the more symmetrical rhombic series of sulphates and selenates is 56′, which occurs in the case of one angle between potassium and cæsium selenates, and it is usually much less than this; in the case of the less symmetrical monoclinic series of double salts the maximum angular difference observed was 2° 21′, between potassium and cæsium magnesium sulphates. (2) The physical properties of the crystals, such as their optical and thermal constants, are also functions of the atomic weights of the elements of the same family group which by their interchange produce the series. (3) The dimensions of the elementary parallelepipedon of the space-lattice, or in other words, the separation of the molecular centres of gravity, the points or nodes of the space-lattice, along the three directions of the crystal axes, also vary with the atomic weight of the interchangeable elements. (4) Specific chemical replacements are accompanied by clearly defined changes in the crystal structure along equally specific directions. Thus, when the metal, say potassium, in an alkali sulphate or selenate is replaced by another of the same alkali-family group, rubidium or cæsium, there is a marked alteration in the crystal angles and in the dimensions of the space-lattice, corresponding to elongation of the vertical axis; and when the acid-forming element sulphur is replaced by selenium, its family analogue, a similar very definite change occurs, but the expansion in this case takes place in the horizontal plane of the crystals. Confirmatory results have also been obtained as regards the morphological constants, the investigations not extending to the optical or thermal properties, by Muthmann for the permanganates, and by Barker for the perchlorates, of the alkali metals. Hence, there can be no doubt whatever that, as regards the various series investigated, which are such as would be expected to afford the most definite results owing to the electro-positive nature of metals being at its maximum strength in the alkali group, the above rules are definite laws of nature.