whether a similar agreement occurs to that shown between the values in the first two columns in the preceding table for the magnesium and zinc salts.

It will be observed that the agreement is fairly close throughout. If, however, instead of the observed values of Rb2SO, and Cs2SO, corresponding to the values for Rb and Cs of 10.5 and 15:35 respectively, being used in the calculations, the usually accepted values for Kb and Cs, 12·1 and 19·1 are employed, the calculated values for the rubidium double salts will be 3-4 units higher than the observed values, and for the cæsium double salts 7-8 units higher, as in the cases of the magnesium and zinc salts.

It is, therefore, undoubtedly a fact that the same refraction equivalents which were observed in the case of the simple sulphates apply also to those salts when combined with the sulphates of magnesium, zinc, iron, nickel, cobalt, copper, manganese, and cadmium to form the double sulphates crystallising with 6 mols. of water.

It is interesting to note that the greater difference which is observed in molecular refraction between the cæsium and rubidium salts than between the potassium and rubidium salts, whether simple or double, is entirely in accordance with the relations of the difference between the atomic refractions of the alkali metals themselves. If the author's values, as derived from the sulphates and

double sulphates, are taken, the differences between the refraction equivalents of potassium and rubidium and cæsium and rubidium. respectively are 27 and 4.8. If Gladstone's values are taken, the differences are 4.3 and 70 respectively. In either case the ratio is of the same order as in the salts.

The optic arial angle phenomena of both simple and double sulphates were shown to be precisely in accordance with the requirements of the rule regarding the progressive change in the velocity ratios or the relationships of the axes of the optical ellipsoid. With regard to the double sulphates, in every group except that containing magnesium, where extraordinary relationships of those ratios are exhibited in the case of cæsium magnesium sulphate, the optic axial angle of any rubidium salt is intermediate between that of the potassium and that of the cæsium salt of the same group. In the case of the magnesium group the remarkable crossed axial plane dispersion of the optic axes of the cæsium salt, and the great sensitiveness of the optic axial angle to change of temperature, were shown to be the direct effect of the operation of the rule of convergence of the velocity ratios towards unity, which resulted in two of the axial values of the optical ellipsoid actually attaining unity, but at any one temperature only for a particular wave-length, hence the crossing of the optic axial plane and the simulation for that particular wave-length of uniaxial optical properties. In the simple sulphates the result of the operation of the same rule regarding the convergence of the maximum and minimum axes of the optical ellipsoid towards equality has been shown to lead to an even more extreme result, namely, that unity is almost attained at the ordinary temperature in the case of the rubidium salt, and actually so on slightly raising the temperature, causing the optic axial angle of that salt to be likewise extremely sensitive to change of wave-length and of temperature, and to exhibit the phenomenon of crossed axial plane dispersion at temperatures slightly elevated above the ordinary ; further, that in cæsium sulphate those axial values are again separated, but in the contrary direction, as would be expected after the meeting if the change were continuous; and hence this salt exhibits negative double refraction, and the plane of the optic axes is perpendicular to that in the potassium salt. The whole of these complicated and very beautiful, as well as unusual, phenomena are thus immediately explained on the assumption of progressive changes corresponding to the progressive change in the atomic weight of the alkali metal.

It has now been conclusively shown that the whole of the morphological and physical characters of the crystals of the rhombic normal sulphates of potassium, rubidium, and casium, and of any group of the

monoclinic double sulphates of the series R,M(SO4)2,6H2O, in which those simple salts of the three alkali metals are combined with the sulphate of either magnesium, zinc, iron, manganese, nickel, cobalt, copper, or cadmium, whilst conforming to the same symmetry and exhibiting the general similarities proper to isomorphous series, present well-defined differences which are functions of the atomic weight of the alkali metal which those salts contain, and usually functions which involve higher powers of the atomic weight than the first.

The completion of the work on the potassium, rubidium, and cæsium salts of sulphuric acid, therefore, establishes beyond doubt, as regards these three definitely related metals and this particular acid, that The characters of the crystals of isomorphous series of salts are functions of the atomic weight, that is to say of the energy of which atomic weight is the expression, of the interchangeable dominant elements belonging to the same family group of the periodic system which give rise to the series. There is strong presumptive evidence that this will eventually prove to be a general law of Nature. The investigation of the analogous selenates and double selenates which the author is now undertaking, will afford a substantial addition to the information already accumulated.

XXXVI.—The bearing of the Results of the Investigations of the Simple and Double Sulphates containing Potassium, Rubidium, and Casium on the Nature of the Structural Unit.

By ALFRED E. TUTTON, Assoc. R.C.S.

THE ultimate structure of organised solid matter, to which we assign the term crystalline, is undoubtedly one of homogeneity, and to the variations in the type of homogeneity are due the variations in crystalline form which such solid matter presents. The truth of this important statement can no longer be seriously disputed, in view of the comparatively complete state to which our knowledge regarding the possible homogeneous partitioning of space has now been brought by the labours of Barlow, following upon those of Sohncke, Schönflies, and Federow, and the fact that the possible types of homogeneous structures correspond precisely with the observed varieties of crystalline symmetry. In its most recent form, as stated to the Mineralogical Society on November 19, 1895, Barlow's definition of a homogeneous structure is substantially as follows. A homogeneous structure is one to every point in which there correspond other precisely similar points which are uniformly distributed in space, and round every point in such a system the arrangement of the remainder

is the same as round every other; the whole rigid structure may consist of an arrangement of material of any nature, the only conditions being that it shall be constant in form and uniformly repeated throughout its whole extent. Barlow especially insisted in his latest communication referred to that, if the structure is divided into space units, it is not necessary that such space units which compose the homogeneous structure should individually have the symmetry of the homogeneous structure itself; it is only necessary that any point taken upon, within, or about it should be represented by precisely similar corresponding points upon every other unit of material which makes up the homogeneous structure.

The question next arises: What is this unit of material or space unit? Is it the chemical molecule of the substance which by its uniform repetition builds up the crystal of the particular chemical compound, and some point upon, within, or about which may be considered as a Sohnckian point as now defined by Barlow, or is it a unit of greater complexity than the chemical molecule? The evidence at the present time available regarding the nature of the crystal element will first be briefly reviewed, and afterwards reinforced by the teaching of the investigation of the simple sulphates of potassium, rubidium, and cæsium, and of the double sulphates of the series R,M(SO4)2,6H2O, in which R is represented by the same three metals of the alkalies.

The main evidence, which is usually regarded as favouring the assumption that the molecular condition of a substance in the solid state is more complex than in the liquid and gaseous states, is that afforded by polymorphism. It is assumed that the fact that many substances are capable of existing in different types of homogeneous structures, differing greatly in symmetry, is due to the different nature of the units of which these structures are composed, that is, to different states of polymerisation of the chemical molecule. The thermal changes which invariably accompany the conversion of any one such form into any other favours this view, inasmuch as it closely resembles the display of thermal activity which accompanies purely chemical changes. Moreover, whenever rise of temperature occurs on the conversion of one modification into another, the relative density is found to increase, as, for instance, when the best known monoclinic form of sulphur changes into the more stable and denser rhombic form. One of the most striking and instructive cases is that of ammonium nitrate described by Lehmann. This salt melts at about 168°, and when the liquid is allowed to cool crystals belonging to the cubic system, and therefore isotropic, commence to separate; when the temperature has fallen to 1272, doubly refracting rhombohedral crystals form, and at 87° rhombic crystals develop,

and are deposited in regular order about the rhombohedra. Hence it would appear that these different forms of ammonium nitrate are due to a difference in the state of aggregation, probably a difference in the molecular complexity of the crystal element. In all probability the liquid consists of chemical molecules corresponding to the simple empirical formula, the first solid form may also consist of molecules of like simplicity whose freedom of rolling motion is now arrested, or it may consist of double molecules, and each further form may be due to the addition of a further simple chemical molecule to the structural unit. Anyhow, each successive crystalline form produced during the cooling of the liquid is denser than the previous one. In the case of sulphur, it is the form of least symmetry, the monoclinic, which is first produced on cooling of the liquefied substance, the higher rhombic being the denser and more stable form into which the monoclinic crystals become eventually transformed with loss of heat. So that it is not the general rule that the higher type of symmetry is first assumed on cooling from a state of liquefaction, and consequently the degree of symmetry of a homogeneous crystal structure does not depend entirely on the simplicity of structure of the crystal element if the above explanation is correct.

In explanation of these facts concerning polymorphism or physical isomerism, two alternative assumptions are open to us. The first is that each different form corresponds to a crystal element containing a specific number of chemical molecules, or, possibly, if two or more of the forms belong to the same system of symmetry, as is frequently the case, to a different arrangement of the chemical molecules within the crystal element. The second is that the same simple molecular state exists throughout, the crystal element consisting of the chemical molecule, and that the different types of homogeneous structures owe their origin to contiguous molecules being separated at different distances, with all the attendant consequences as regards the forces, attributable either to the various atoms composing the molecule or to the molecule as a whole, which determine the nature of the symmetry of the homogeneous structure. It is quite conceivable that a rigid structure should be produced at a temperature but slightly below the melting point, and stable for this temperature, which would prove unstable and tend to collapse at a lower temperature, naturally with evolution of heat. The first assumption, however, appears to be supported by the preponderating weight of evidence, and is quite in accordance with the facts concerning numerous well investigated cases of-so-called-physical isomerism among the carbon compounds. An admirable résumé of the large amount of data now available is given by Arzruni in his Physikalische Chemie der Krystalle.