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, CaCO3 (aragonite) and KNO3, CaCO3 (calc spar) and NaNO3, BaSO4 (heavy spar), KMnO4 (potassium permanganate), and KClO4 (potassium perchlorate), Al2O3 (corundum) and FeTiO3 (titanic iron ore), FeS2 (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, PbSO43PbCO3 appear in very analogous crystalline forms; the acid potassium sulphate crystallises in the monoclinic system in crystals analogous to felspar, KAlSi3O8; glauberite, Na2Ca(SO4)2, augite, RSiO3 (R = Ca, Mg), sodium carbonate, Na2CO3,10H2O, Glauber's salt, Na2SO4,10H2O, and borax, Na2BrO7,10H2O, 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, Al2O3, and water, H2O, 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 3H2O (for example, olivine and serpentine), SiO2 by Al2O3 (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 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, RCl2, 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 RCl2,2H2O is BaCl2,2H2O, which crystallises in the rhombic system. Barium bromide, BaBr2,2H2O, and copper chloride, CuCl2,2H2O, have nearly the same forms: potassium iodate, KIO4; potassium chlorate, KClO4; potassium permanganate, KMnO4; barium sulphate, BaSO4; calcium sulphate, CaSO4; sodium sulphate, Na2SO4; barium formate, BaC2H2O4, and others have almost the same crystalline form (of the rhombic system). Parallel with this series is that of the metallic chlorides containing RCl2,4H2O, of the sulphates of the composition RSO4,2H2O, and the formates RC2H2O4,2H2O. 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, NiCl2,6H2O and MnSO4,4H2O. Hence we see that not only is RCl2,2H2O analogous in form to RSO4 and RC2H2O4, but that their compounds with 2H2O and with 4H2O 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 Al2O3 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, Al2O3, is also analogous in form to SiO2, 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 SiO2 by means of Al2O3, as Scheerer admits. The oxides Cu2O, MgO, NiO, Fe3O4, CeO2, crystallise in the regular system, although they are of very different atomic structure. Marignac demonstrated the perfect analogy of the forms of K2ZrF6 and CaCO3, and the former is even dimorphous, like the calcium carbonate. The same salt is isomorphous with R2NbOF5 and R2WO2F4, where R is an alkali metal. There is an equivalency between CaCO3 and K2ZrF6, because K2 is equivalent to Ca, C to Zr, and F6 to O3, 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 K2ZrF6 on the other. The long-known isomorphism of the corresponding compounds of potassium and ammonium, KX and NH4X, 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, Mn3O4, belongs to the tetragonal system, and the planes of its pyramid are inclined at an angle of about 118°, whilst magnetic iron ore, Fe3O4, 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 confirmed (1873), that naphthalene derivatives of analogous composition are hemimorphous. Nicklès (1849) showed that in ethylene sulphate the angle of the prism is 125° 26′, and in the nitrate of the same radicle 126° 95′. The angle of the prism of methylamine oxalate is 131° 20′, and of fluoride, which is very different in composition from the former, the angle is 132°. Groth (1870) endeavoured to indicate in general what kinds of change of form proceed with the substitution of hydrogen by various other elements and groups, and he observed a regularity which he termed morphotropy. The following examples show that morphotropy recalls the hemimorphism of Laurent. Benzene, C6H6, rhombic system, ratio of the axes 0·891 : 1 : 0·799. Phenol, C6H5(OH), and resorcinol, C6H4(OH)2, also rhombic system, but the ratio of one axis is changed—thus, in resorcinol, 0·910 : 1 : 0·540; that is, a portion of the crystalline structure in one direction is the same, but in the other direction it is changed, whilst in the rhombic system dinitrophenol, C6H3(NO2)2(OH) = O·833 : 1 : 0·753; trinitrophenol (picric acid), C6H2(NO)3(OH) = 0·937 : 1 : 0·974; and the potassium salt = 0·942 : 1 : 1·354. Here the ratio of the first axis is preserved—that is, certain angles remain constant, and the chemical proximity of the composition of these bodies is undoubted. Laurent compares hemimorphism with architectural style. Thus, Gothic cathedrals differ in many respects, but there is an analogy expressed both in the sum total of their common relations and in certain details—for example, in the windows. It is evident that we may expect many fruitful results for molecular mechanics (which forms a problem common to many provinces of natural science) from the further elaboration of the data concerning those variations which take place in crystalline form when the composition of a substance is subjected to a known change, and therefore I consider it useful to point out to the student of science seeking for matter for independent scientific research this vast field for work which is presented by the correlation of form and composition. The geometrical regularity and varied beauty of crystalline forms offer no small attraction to research of this kind.
[6] The still more complex combinations—which are so clearly expressed in the crystallo-hydrates, double salts, and similar compounds—although they may be regarded as independent, are, however, most easily understood with our present knowledge as aggregations of whole molecules to which there are no corresponding double compounds, containing one atom of an element R and many atoms of other elements RXn. The above types embrace all cases of direct combinations of atoms, and the formula MgSO4,7H2O cannot, without violating known facts, be directly deduced from the types MgXn or SXn, whilst the formula MgSO4 corresponds both with the type of the magnesium compounds MgX2 and with the type of the sulphur compounds SO2X2, or in general SX6, where X2 is replaced by (OH)2, with the substitution in this case of H2 by the atom Mg, which always replaces H2. However, it must be remarked that the sodium crystallo-hydrates often contain 10H2O, the magnesium crystallo-hydrates 6 and 7H2O, and that the type PtM2X6 is proper to the double salts of platinum, &c. With the further development of our knowledge concerning crystallo-hydrates, double salts, alloys, solutions, &c., in the chemical sense of feeble compounds (that is, such as are easily destroyed by feeble chemical influences) it will probably be possible to arrive at a perfect generalisation for them. For a long time these subjects were only studied by the way or by chance; our knowledge of them is accidental and destitute of system, and therefore it is impossible to expect as yet any generalisation as to their nature. The days of Gerhardt are not long past when only three types were recognised: RX, RX2, and RX3; the type RX4 was afterwards added (by Cooper, Kekulé, Butleroff, and others), mainly for the purpose of generalising the data respecting the carbon compounds. And indeed many are still satisfied with these types, and derive the higher types from them; for instance, RX5 from RX3—as, for example, POCl3 from PCl3, considering the oxygen to be bound both to the chlorine (as in HClO) and to the phosphorus. But the time has now arrived when it is clearly seen that the forms RX, RX2, RX3, and RX4 do not exhaust the whole variety of phenomena. The revolution became evident when Würtz showed that PCl5 is not a compound of PCl3 + Cl2 (although it may decompose into them), but a whole molecule capable of passing into vapour, PCl5 like PF5 and SiF4. The time for the recognition of types even higher than RX8 is in my opinion in the future; that it will come, we can already see in the fact that oxalic acid, C2H2O4, gives a crystallo-hydrate with 2H2O; but it may be referred to the type CH4, or rather to the type of ethane, C2H6, in which all the atoms of hydrogen are replaced by hydroxyl, C2H2O42H2O = C2(OH)6 (see Chapter XXII., Note [35]).
[7] The hydrogen compounds, R2H, in equivalency correspond with the type of the suboxides, R4O. Palladium, sodium, and potassium give such hydrogen compounds, and it is worthy of remark that according to the periodic system these elements stand near to each other, and that in those groups where the hydrogen compounds R2H appear, the quaternary oxides R4O are also present.
Not wishing to complicate the explanation, I here only touch on the general features of the relation between the hydrates and oxides and of the oxides among themselves. Thus, for instance, the conception of the ortho-acids and of the normal acids will be considered in speaking of phosphoric and phosphorous acids.
As in the further explanation of the periodic law only those oxides which give salts will be considered, I think it will not be superfluous to mention here the following facts relative to the peroxides. Of the peroxides corresponding with hydrogen peroxide, the following are at present known: H2O2, Na2O2, S2O7 (as HSO4?), K2O4, K2O2, CaO2, TiO3, Cr2O7, CuO2(?), ZnO2, Rb2O2, SrO2, Ag2O2, CdO2, CsO2, Cs2O2, BaO2, Mo2O7, SnO3, W2O7, UO4. It is probable that the number of peroxides will increase with further investigation. A periodicity is seen in those now known, for the elements (excepting Li) of the first group, which give R2O, form peroxides, and then the elements of the sixth group seem also to be particularly inclined to form peroxides, R2O7; but at present it is too early, in my opinion, to enter upon a generalisation of this subject, not only because it is a new and but little studied matter (not investigated for all the elements), but also, and more especially, because in many instances only the hydrates are known—for instance, Mo2H2O8—and they perhaps are only compounds of peroxide of hydrogen—for example, Mo2H2O8 = 2MoO3 + H2O2—since Prof. Schöne has shown that H2O2 and BaO2 possess the property of combining together and with other oxides. Nevertheless, I have, in the general table expressing the periodic properties of the elements, endeavoured to sum up the data respecting all the known peroxide compounds whose characteristic property is seen in their capability to form peroxide of hydrogen under many circumstances.
[8] The periodic law and the periodic system of the elements appeared in the same form as here given in the first edition of this work, begun in 1868 and finished in 1871. In laying out the accumulated information respecting the elements, I had occasion to reflect on their mutual relations. At the beginning of 1869 I distributed among many chemists a pamphlet entitled ‘An Attempted System of the Elements, based on their Atomic Weights and Chemical Analogies,’ and at the March meeting of the Russian Chemical Society, 1869, I communicated a paper ‘On the Correlation of the Properties and Atomic Weights of the Elements.’ The substance of this paper is embraced in the following conclusions: (1) The elements, if arranged according to their atomic weights, exhibit an evident periodicity of properties. (2) Elements which are similar as regards their chemical properties have atomic weights which are either of nearly the same value (platinum, iridium, osmium) or which increase regularly (e.g. potassium, rubidium, cæsium). (3) The arrangement of the elements or of groups of elements in the order of their atomic weights corresponds with their so-called valencies. (4) The elements, which are the most widely distributed in nature, have small atomic weights, and all the elements of small atomic weight are characterised by sharply defined properties. They are therefore typical elements. (5) The magnitude of the atomic weight determines the character of an element. (6) The discovery of many yet unknown elements may be expected. For instance, elements analogous to aluminium and silicon, whose atomic weights would be between 65 and 75. (7) The atomic weight of an element may sometimes be corrected by aid of a knowledge of those of the adjacent elements. Thus the combining weight of tellurium must lie between 123 and 126, and cannot be 128. (8) Certain characteristic properties of the elements can be foretold from their atomic weights.
The entire periodic law is included in these lines. In the series of subsequent papers (1870–72, for example, in the Transactions of the Russian Chemical Society, of the Moscow Meeting of Naturalists, of the St. Petersburg Academy, and Liebig's Annalen) on the same subject we only find applications of the same principles, which were afterwards confirmed by the labours of Roscoe, Carnelley, Thorpe, and others in England; of Rammelsberg (cerium and uranium), L. Meyer (the specific volumes of the elements), Zimmermann (uranium), and more especially of C. Winkler (who discovered germanium, and showed its identity with ekasilicon), and others in Germany; of Lecoq de Boisbaudran in France (the discoverer of gallium = ekaaluminium); of Clève (the atomic weights of the cerium metals), Nilson (discoverer of scandium = ekaboron), and Nilson and Pettersson (determination of the vapour density of beryllium chloride) in Sweden; and of Brauner (who investigated cerium, and determined the combining weight of tellurium = 125) in Austria, and Piccini in Italy.
I consider it necessary to state that, in arranging the periodic system of the elements, I made use of the previous researches of Dumas, Gladstone, Pettenkofer, Kremers, and Lenssen on the atomic weights of related elements, but I was not acquainted with the works preceding mine of De Chancourtois (vis tellurique, or the spiral of the elements according to their properties and equivalents) in France, and of J. Newlands (Law of Octaves—for instance, H, F, Cl, Co, Br, Pd, I, Pt form the first octave, and O, S, Fe, Se, Rh, Te, Au, Th the last) in England, although certain germs of the periodic law are to be seen in these works. With regard to the work of Prof. Lothar Meyer respecting the periodic law (Notes [12] and [13]), it is evident, judging from the method of investigation, and from his statement (Liebig's Annalen, Supt. Band 7, 1870, 354), at the very commencement of which he cites my paper of 1869 above mentioned, that he accepted the periodic law in the form which I proposed.
In concluding this historical statement I consider it well to observe that no law of nature, however general, has been established all at once; its recognition is always preceded by many hints; the establishment of a law, however, does not take place when its significance is recognised, but only when it has been confirmed by experiment, which the man of science must consider as the only proof of the correctness of his conjectures and opinions. I therefore, for my part, look upon Roscoe, De Boisbaudran, Nilson, Winkler, Brauner, Carnelley, Thorpe, and others who verified the adaptability of the periodic law to chemical facts, as the true founders of the periodic law, the further development of which still awaits fresh workers.
[9] This resembles the fact, well known to those having an acquaintance with organic chemistry, that in a series of homologues (Chapter [VIII.]) the first members, in which there is the least carbon, although showing the general properties of the homologous series, still present certain distinct peculiarities.