Hallite occurs in large rough six-sided prisms, with easy micaceous cleavage. There are two varieties, differing markedly in colour-green and yellow; and I am indebted to Mr. Hall for the following facts in regard to the locality and associations of this species. Mr. Hall writes::- "The mineral is found at East Nottingham, in the serpentine formation of south-eastern Pennsylvania, three miles south of Oxford, in Chester County; and I know of no other locality. I think the green and yellow. varieties are very closely related, and may possibly pass from one into the other; but I have no positive proof that they do. The crystals are found in nests or pockets; and the two colours are not found in the same nests. The green crystals are imbedded in a steatite earth or base of the same colour as the crystals, and the yellow in a yellow earth; and sometimes nests containing the opposite varieties are only a few feet apart in seams of the serpentine rock."

As the following analyses show, the two varieties have essentially the same composition; and the only difference that could be detected was in the degree of oxidation of the iron. The yellow crystals appeared to be more weathered than the green; and on the last the green colour frequently fades out towards the centre of crystals, thus giving indications of a metamorphosis by which one variety may pass into the other.

Under the microscope these scales of the mineral show a remarkable appearance. Between the greenish or nearly colourless plates are seen elongated scales of a yellow mineral resembling closely in colour thin scales of Jefferisite. They are more or less spear-shaped in form, although usually very narrow, and lie accurately in parallel lines, which cross at angles of 60° and 120°, like the magnetic oxide of iron in the Muscovite from Pennsbury, Pa., or the microscopic crystals in the Biotite of South Burgess of Canada; and the phenomenon of asterism, seen so beautiful with the plates of the last, can also be seen with thin laminæ of Hallite. It was impossible to free the mineral from this admixture; but specimens were selected for analysis as free from it as possible. It was also impossible to determine its exact nature. The scales had not a definite form; but there was a tendency to a rhombic shape, which is well described by the term "spear-shaped ;" and though the material is so widely distributed through the crystal, the total mass must be very small.

This mineral is not so hygroscopic as Jefferisite, and no difficulty was found in drying the material for analysis. When ignited, it exfoliates like other species of vermiculite, but not nearly to so great an extent as Jefferisite. After ignition it is decomposed by hydrochloric acid. The specific gravity of the green variety, mean of four determinations, 2.398; that of the

yellow variety, mean of two determinations, 2-402. Before the blowpipe, fuses with difficulty to a brown enamel. The following analyses were made by Mr. C. E. Munroe, assistant in the laboratory of Harvard College :

It will be seen from the above analyses that, although the atomic ratio between all the basic radicals and the silicon is the same as in Culsageeite, Jefferisite, and Biotite, the ratio between the protoxide and sesquioxide radicals is very different. In this respect the mineral resembles the phlogopite micas, in which also the protoxide radicals preponderate; and the symbol given above for Hallite, less the water, is identical with that given by Professor Dana as the more probable formula of the phlogopites.

The opacity produced by the interspersed material made it difficult to determine the optical characters of the mineral, as the rings produced with polarized light could only be seen with very thin plates, and the cross was therefore ill defined; so that, although in some cases there appeared to be a separation of the hyperbolas, the plates could not be distinguished from uniaxial. On one specimen the hexagonal form was very perfect, and the crystal presented the planes of a rhombohedron having an angle *Trace of manganese.

over the basal edge of about 122°, resembling the crystals of Biotite from Greenwood Furnace. Mr. Hall informs me that these more perfect crystals have only been found in one pocket of the serpentine.

VI

The distinction, however, between the phlogopites and the Biotites is not fundamental, either chemically or physically. Chemically, both species are orthosilicates; that is, the atomic ratio between the silicon and the sum of the basic radicals is 1:1. The species differ in composition only in the relative proportion of the sesquioxide and protoxide radicals. In the phlogopite the ratio of R to R is probably normally 2:1; but of the published analyses the value varies between that ratio and the ratio 3:2. In the Biotites the same ratio is probably normally 1:1; but here, again, the different analyses which have been made give values varying between 5: 3 and 1: 2. In like manner the optical distinction between the phlogopites and Biotites, of which so much has been made, is equally indefinite. Between a socalled phlogopite like that from Jefferson County, N. Y., with an angle of about 15°, and the apparently uniaxial plates of Biotite from Vesuvius, there is every possible gradation-sometimes, as I have shown, on one and the same mica plate; and I have endeavoured in this paper to explain the cause of this variation. With the Vesuvian Biotites themselves (if the specimens in the mineralogical cabinet of Harvard College are fair representatives of the mineral from that locality) it is only occasionally that we find a perfectly uniaxial plate. More commonly there are distinct evidences of twinning; and on the borders of the hexagonal plate may be discovered a biaxial structure, of which the optical plane is parallel to different edges of the hexagon on different parts of the plate.

It must, however, be remembered that as, by the process of twinning we have described, the structure of the magnesian micas approaches that of uniaxial crystals, rhombohedral and other planes characteristic of the hexagonal system begin to appear on the crystal. This is illustrated not only by the crystals of Biotite from Vesuvius and from Greenwood Furnace, N. Y., but also by the more perfect crystals of Hallite from Chester County, Pa. In other words, the process of twinning we have illustrated in this paper produces hexagonal crystals in external form as well as in optical characters; and the question naturally arises, May not the hexagonal crystals of other minerals be formed in a similar way? that is, may they not be developed from twinned molecules, which, though in their aggregate producing an hexagonal structure, singly would develop into biaxial crystals? Bearing on this point we have discovered some very remarkable evidence.

We have in our possession a plate of Elba tourmaline cut perpendicular to the axis, in which the polarizing microscope shows on different zones a separation of the hyperbolas, which amounts in some positions to 8 degrees; and in moving the plate across the field the optical divergence varies precisely as on plates of phlogopite and vermiculite. There is certainly no external evidence of lamination on tourmaline crystals; for the mineral is remarkably compact, and the crystals have not even a basal cleavage: but it will be remembered how readily some of the varieties pass by alteration into micas of the magnesian type; and this change to a foliated structure, in which the lamination is parallel to the base of the original hexagonal crystal, may be facilitated by a grouping of the molecules of the tourmaline in the manner represented by fig. 12.

We have also a plate of amethystine quartz, in which a beam of parallel polarized rays of light exhibits a twinning almost as symmetrical as that shown in fig. 10, the three zones being most beautifully mapped out by the alternating bands of right- and left-handed quartz, which are such a familiar phenomenon of these crystals. But, besides this, in each of these zones, near the border of the plate, can be distinguished a biaxial structure with an optical divergence of several degrees; and on one other plate of amethyst we have had an opportunity of examining, we have also seen under the polarizing microscope the biaxial curves at one or more points.

These facts most distinctly suggest the theory that the optical phenomena of quartz are produced by a molecular structure similar to that by which we have obtained identical phenomena in our artificial plates of mica, and that the two orders of crystals are aggregates of compound molecules, whose parts are twinned together in the one case in right-handed, and in the other in left-handed spirals, and, lastly, that the simple molecule, if developed normally, would produce a biaxial structure*. This theory is most markedly in harmony with the chemical relations of silica. The compound SiO2 is the only one of the tetrad

* Since the above was in type we have received the Amer. Journ. Sci. (IV.) February 1874, containing a description of the rhombic silica which Professor Maskelyne, of the British Museum, has discovered in the meteorite of Breitenbach. This new species of silica, which Professor Maskelyne calls Asmanite, has the form of a right rhombic prism, with an angle of 120° 20', and the crystals are optically biaxial; but while the specific gravity of quartz is 2-6, that of Asmanite is said to be 2.245. It is perhaps to be expected that such a molecular macling as we have described would determine an increase of density, since thereby three molecules coalesce to form one; or it is possible that the remarks made infrà in regard to calcite apply also to quartz; but still the marked difference remains to be explained.

oxides which crystallizes in the hexagonal system; and ever since, by the study of the organic compounds of silicon, the quadrivalent character of the element has been made evident, this fact has been a striking anomaly in our chemical classification. Assume, however, that the molecule SiO2 would develop normally into a rhombic structure, and that the hexagonal form of quartz is solely a result of molecular twinning, and the anomaly disappears. The molecule SiO2 may be approximately of the same form as the molecule TiO2 in Brookite; but having the exact dimensions and polar conditions which favour the mode of molecular twinning, described above and represented by fig. 12, it may always develop into hexagonal shapes.

Are, then, all hexagonal forms thus closely related to the rhombic systems of crystals? And do all molecules of the dimensions and polar conditions illustrated by the figures of this article (that is, those which correspond to the rhomb of 60° and 120°) usually develop into hexagonal forms? May not the whole difference between an hexagonal and a rhombic form arise from a slight difference of dimensions, which determines a molecular macling in the one case, and a normal development of the single molecules in the other? These questions point out most interesting lines of investigation, and will recall to the mineralogist a number of facts bearing upon the subject. Allow me to refer to two of the most striking and most obvious.

On the crystals of chrysoberyl the rhombic angle is 119° 46′; and every mineralogist is familiar with the hexagonal macling, similar to fig. 7, which is so very characteristic of this species*. Corundum differs chemically from chrysoberyl in that a portion of the alumina in the former is replaced by glucina in the latter. Corundum has a perfect hexagonal form; and, fundamentally, may not the only crystallographic difference be that, in consequence of the replacement, a rhomb of 120° changes to a rhomb of 119° 46'? Now we have a plate of macled chrysoberyl, showing the normal wide divergence of the optical axes at certain points on its borders, and a nearly uniaxial structure at the centre, where there is an obvious interpenetration between the individuals of the macle, and where the superposition of the several laminæ is most beautifully shown by a polarized beam of parallel rays. We have also a section of a corundum crystal, presenting phenomena similar to those seen with the plate of tourmaline, described above. Further, we have observed like phenomena on a section of phenacite; and although the last mineral contains silica, yet if the molecules of SiO2 are crystallographically equivalent to those of Al2O3, it may be that the molecular structure * See also Dana's 'System of Mineralogy,' fifth edition, figs. 154, 155,

p. 156.