| s | M/s | Volume of Oxygen | |
| H2O | 1·0 | 18 | ?-22 |
| Li2O | 2·0 | 15 | -9 |
| Be2O2 | 3·06 | 16 | +2·6 |
| B2O3 | 1·8 | 39 | +10·0 |
| C2O4 | 1·6 | 55 | +10·6 |
| N2O5 | 1·64 | 66 | ?+4 |
| Na2O | 2·6 | 24 | -22 |
| Mg2O2 | 3·5 | 23 | -4·5 |
| Al2O3 | 4·0 | 26 | +1·3 |
| Si2O4 | 2·65 | 45 | +5·2 |
| P2O5 | 2·39 | 59 | +6·2 |
| S2O6 | 1·96 | 82 | +8·7 |
| Cl2O7 | ?1·92 | 95 | +6 |
| K2O | 2·7 | 35 | -36 |
| Ca2O2 | 3·25 | 34 | -8 |
| Sc2O3 | 3·86 | 35 | ?0 |
| Ti2O4 | 4·2 | 38 | +3 |
| V2O5 | 3·49 | 52 | +6·7 |
| Cr2O6 | 2·74 | 73 | +9·5 |
| Cu2O | 5·9 | 24 | +9·6 |
| Zn2O2 | 5·7 | 23 | +4·8 |
| Ga2O3 | ?5·1 | 36 | +4 |
| Ge2O4 | 4·7 | 44 | +4·5 |
| As2O5 | 4·1 | 56 | +6·0 |
| Sr2O2 | 4·7 | 44 | -13 |
| Y2O3 | 5·0 | 45 | ?-2 |
| Zr2O4 | 5·5 | 44 | 0 |
| Nb2O5 | 4·7 | 57 | +6 |
| MoO6 | 4·4 | 65 | +6·8 |
| Ag2O | 7·5 | 31 | +11 |
| Cd2O2 | 8·0 | 32 | +3 |
| In2O3 | 7·18 | 38 | +2·7 |
| Sn2O4 | 7·0 | 43 | +2·7 |
| Sb2O5 | 6·5 | 49 | +2·6 |
| TeO6 | 5·1 | 68 | +4·7 |
| Ba2O2 | 5·7 | 52 | -10 |
| La2O3 | 6·5 | 50 | +1 |
| Ce2O4 | 6·74 | 50 | +2 |
| Ta2O5 | 7·5 | 59 | +4·6 |
| W2O6 | 6·8 | 68 | +8·2 |
| Hg2O2 | 11·1 | 39 | +4·5 |
| Pb2O4 | 8·9 | 53 | +4·2 |
| Th2O4 | 9·86 | 54 | +2 |
As the volumes of the chlorides, organo-metallic and all other corresponding compounds, also vary in a like periodic succession with a change of elements, it is evidently possible to indicate the properties of substances yet uninvestigated by experimental means, and even those of yet undiscovered elements. It was possible by following this method to foretell, on the basis of the periodic law, many of the properties of scandium, gallium, and germanium, which were verified with great accuracy after these metals had been discovered.[23] The periodic law, therefore, has not only embraced the mutual relations of the elements and expressed their analogy, but has also to a certain extent subjected to law the doctrine of the types of the compounds formed by the elements: it has enabled us to see a regularity in the variation of all chemical and physical properties of elements and compounds, and has rendered it possible to foretell the properties of elements and compounds yet uninvestigated by experimental means; thus it has prepared the ground for the building up of atomic and molecular mechanics.[24]
Footnotes:
[1] For instance the analogy of the sulphates of K, Rb, and Cs (Chapter XIII., Note [1]).
[1 bis] The crystalline forms of aragonite, strontianite, and witherite belong to the rhombic system; the angle of the prism of CaCO3 is 116° 10′, of SrCO3 117° 19′, and of BaCO3 118° 30′. On the other hand the crystalline forms of calc spar, magnesite, and calamine, which resemble each other quite as closely, belong to the rhombohedral system, with the angle of the rhombohedra for CaCO3 105° 8′, MgCO3 107° 10′, and ZnCO3 107° 40′. From this comparison it is at once evident that zinc is more closely allied to magnesium than magnesium to calcium.
[2] Solutions furnish the commonest examples of indefinite chemical compounds. But the isomorphous mixtures which are so common among the crystalline compounds of silica forming the crust of the earth, as well as alloys, which are so important in the application of metals to the arts, are also instances of indefinite compounds. And if in Chapter [I.], and in many other portions of this work, it has been necessary to admit the presence of definite compounds (in a state of dissociation) in solutions, the same applies with even greater force to isomorphous mixtures and alloys. For this reason in many places in this work I refer to facts which compel us to recognise the existence of definite chemical compounds in all isomorphous mixtures and alloys. This view of mine (which dates from the sixties) upon isomorphous mixtures finds a particularly clear confirmation in B. Roozeboom's researches (1892) upon the solubility and crystallising capacity of mixtures of the chlorates of potassium and thallium, KClO3 and TlClO3. He showed that when a solution contains different amounts of these salts, it deposits crystals containing either an excess of the first salt, from 98 p.c. to 100 p.c., or an excess of the second salt, from 63·7 to 100 p.c.; that is, in the crystalline form, either the first salt saturates the second or the second the first, just as in the solution of ether in water (Chapter [I.]); moreover, the solubility of the mixtures containing 36·3 and 98 p.c. KClO3 is similar, just as the vapour tension of a saturated solution of water in ether is equal to that of a saturated solution of ether in water (Chapter I., Note [47]). But just as there are solutions miscible in all proportions, so also certain isomorphous bodies can be present in crystals in all possible proportions of their component parts. Van 't Hoff calls such systems ‘solid solutions.’ These views were subsequently elaborated by Nernst (1892), and Witt (1891) applied them in explaining the phenomena observed in the coloration of tissues.
[3] The cause of the difference which is observed in different compounds of the same type, with respect to their property of forming isomorphous mixtures, must not be looked for in the difference of their volumetric composition, as many investigators, including Kopp, affirm. The molecular volumes (found by dividing the molecular weight by the density) of those isomorphous substances which do give intermixtures are not nearer to each other than the volumes of those which do not give mixtures; for example, for magnesium carbonate the combining weight is 84, density 3·06, and volume therefore 27; for calcium carbonate in the form of calc spar the volume is 37, and in the form of aragonite 33; for strontium carbonate 41, for barium carbonate 46; that is, the volume of these closely allied isomorphous substances increases with the combining weight. The same is observed if we compare sodium chloride (molecular volume = 27) with potassium chloride (volume = 37), or sodium sulphate (volume = 55) with potassium sulphate (volume = 66), or sodium nitrate 39 with potassium nitrate 48, although the latter are less capable of giving isomorphous mixtures than the former. It is evident that the cause of isomorphism cannot be explained by an approximation in molecular volumes. It is more likely that, given a similarity in form and composition, the faculty to give isomorphous mixtures is connected with the laws and degree of solubility.
[4] A phenomenon of a similar kind is shown for magnesium sulphate in Note [27] of the last chapter. In the same example we see what a complication the phenomena of dimorphism may introduce when the forms of analogous compounds are compared.
[5] The property of solids of occurring in regular crystalline forms—the occurrence of many substances in the earth's crust in these forms—and those geometrical and simple laws which govern the formation of crystals long ago attracted the attention of the naturalist to crystals. The crystalline form is, without doubt, the expression of the relation in which the atoms occur in the molecules, and in which the molecules occur in the mass, of a substance. Crystallisation is determined by the distribution of the molecules along the direction of greatest cohesion, and therefore those forces must take part in the crystalline distribution of matter which act between the molecules; and, as they depend on the forces binding the atoms together in the molecules, a very close connection must exist between the atomic composition and the distribution of the atoms in the molecule on the one hand, and the crystalline form of a substance on the other hand; and hence an insight into the composition may be arrived at from the crystalline form. Such is the elementary and a priori idea which lies at the base of all researches into the connection between composition and crystalline form. Haüy in 1811 established the following fundamental law, which has been worked out by later investigators: That the fundamental crystalline form for a given chemical compound is constant (only the combinations vary), and that with a change of composition the crystalline form also changes, naturally with the exception of such limiting forms as the cube, regular octahedron, &c., which may belong to various substances of the regular system. The fundamental form is determined by the angles of certain fundamental geometric forms (prisms, pyramids, rhombohedra), or the ratio of the crystalline axes, and is connected with the optical and many other properties of crystals. Since the establishment of this law the description of definite compounds in a solid state is accompanied by a description (measurement) of its crystals, which forms an invariable, definite, and measurable character. The most important epochs in the further history of this question were made by the following discoveries:—Klaproth, Vauquelin, and others showed that aragonite has the same composition as calc spar, whilst the former belongs to the rhombic and the latter to the hexagonal system. Haüy at first considered that the composition, and after that the arrangement, of the atoms in the molecules was different. This is dimorphism (see Chapter [XIV.], Note [46]). Beudant, Frankenheim, Laurent, and others found that the forms of the two nitres, KNO3 and NaNO3, exactly correspond with the forms of aragonite and calc spar; that they are able, moreover, to pass from one form into another; and that the difference of the forms is accompanied by a small alteration of the angles, for the angle of the prisms of potassium nitrate and aragonite is 119°, and of sodium nitrate and calc spar, 120°; and therefore dimorphism, or the crystallisation of one substance in different forms, does not necessarily imply a great difference in the distribution of the molecules, although some difference clearly exists. The researches of Mitscherlich (1822) on the dimorphism of sulphur confirmed this conclusion, although it cannot yet be affirmed that in dimorphism the arrangement of the atoms remains unaltered, and that only the molecules are distributed differently. Leblanc, Berthier, Wollaston, and others already knew that many substances of different composition appear in the same forms, and crystallise together in one crystal. Gay-Lussac (1816) showed that crystals of potash alum continue to grow in a solution of ammonia alum. Beudant (1817) explained this phenomenon as the assimilation of a foreign substance by a substance having a great force of crystallisation, which he illustrated by many natural and artificial examples. But Mitscherlich, and afterwards Berzelius and Henry Rose and others, showed that such an assimilation only exists with a similarity or approximate similarity of the forms of the individual substances and with a certain degree of chemical analogy. Thus was established the idea of isomorphism as an analogy of forms by reason of a resemblance of atomic composition, and by it was explained the variability of the composition of a number of minerals as isomorphous mixtures. Thus all the garnets are expressed by the general formula: (RO)3M2O3(SiO2)3, where R = Ca, Mg, Fe, Mn, and M = Fe, Al, and where we may have either R and M separately, or their equivalent compounds, or their mixtures in all possible proportions.