The gnomonic projection in which the faces of crystals are represented by the points where their normals through a fixed point–the centre of projection–meet a plane–the plane of projection–is already widely used by crystallographers. I propose in the following pages to show the advantages of the simultaneous use of two such planes of projection.

It is in most cases convenient for the two planes to be at right angles, and for the centre of projection to be at an equal (unit) distance from each. Circumstances, however, in some cases render it desirable to vary these conditions. When the planes are at right angles, one may conveniently be described as the horizontal plane, and the other as the vertical plane.

Before the value of hydrochloric acid forcblorine manufacture was recognized by soda-crystal makers, it was a common practice to get rid of the unpleasant fumes in the cheapest and most convenient way possible. At Messrs. Chance's works at Oldbury, near Birmingham, this was done by turning the gases from the salt-cake furnaces into a culvert which ran through some portion of the works. The better to condense the fumes, it seems probable that a brook, which runs near the works, was diverted into the culvert, thus forming a rough condenser. Some thirty years or so sgo, when alterations were being made at these works, a culvert of this description was unearthed and found to be lined with crystals of gypsum, which had formed on the brickwork. An old well, which was opened, was also studded with beautiful tufts of crystals. I am indebted to Mr. A. M. Chance for a handsome specimen with numerous attached crystals of gypsum, and also for some stereoscopic slides showing the well with the crystals in situ.

The determination of the amount and sign of the relative retardation of the wave-fronts of the two rays, into which a plane-polarized ray of light is resolved in passing through an anisotropic crystal, furnishes us with the readiest means of identifying transparent minerals occurring in thin sections or as minute fragments without definite crystalline form. In sections which are of practically the same thickness the individual crystals of each mineral show a certain range of colours resulting from the interference of the rays after resolution parallel to the principal plane of the analyser, and these colours are usually sufficient, with the help of other characters, for the identification of the mineral species.

To the north-west of Rathdrum, in the county of Wicklow, three important groups of lead mines were formerly worked, which are known respectively as the Glendasan or Luganure, Glendalough, and Glenmalure mines, after the mountain glens in which they are situated. The lodes traverse the granite in a north and south direction close to its junction with the mica-schist, and are somewhat remarkable for the variety of their mineral contents.

Mr. G. F. Herbert Smith has pointed out the advantages of the gnomonic projection for some special crystallographic problems. It seems to me that much of the labour in drawing the projections could be saved by a device similar to that employed by Fedorow, Wulff, Penfield, &c., in drawing stereographic projections.

Corresponding to the ‘stereographic net’ described by these authors (which is the stereographic projection of lines of latitude and longitude on a plane through a llne of longitude), we have the gnomonic net, which is the projection of the lines of latitude (l) and of longitude (m) on the tangent plane at the point whose latitude and longitude are zero. The lines m are parallel straight lines, the lines l are hyperbolae having double contact with each other at two fixed imaginary points.

The Silvermines mineral district is situated along the northern base of the Silvermine Mountains, five and a half miles south of the town of Nenagh in the county of Tipperary. The district is one which possesses somewhat remarkable features, of interest to both geologists and mineralogists. The mines extend over a narrow tract of country for a distance of about five miles along an extensive E. and W. line of fault, in which Silurian, Old Red Sandstone, and Carboniferous rocks are brought into juxtaposition. This line of fault has been traced for a distance of about thirty miles from Gallows Hill in co. Clare, on the west, to Toomavara in co. Tipperary, on the east. Along its course in at least two places mineralization has taken place, resulting in a somewhat complex series of contact-lodes and metasomatic deposits.

It will in the first place be assumed for the sake of simplicity that the crystal to be investigated is immersed in a liquid having a refractive index as nearly as possible equal to the intermediate refractive index (β), so that light travelling along the optic axis t is not appreciably refracted on entering or leaving the crystal.

The observation is made in parallel ight between crossed nicols, which are rotated together till a position of extinction is reached, when the directions of vibration of the nicols wilI be parallel to those in the crystal. If the latter be now rotated on an axis parallel to one of these directions, it will in general show light throughout the revolution, except in the original position and that opposite to it. Occasionally, however, it will remain dark throughout; in that case the axis of rotation is the bisectrix of an optic axial angle.

Amongst the specimens recently selected for the British Museum from the collection of South American minerals brought together by the late Theodor Hohmann, are two on which occurs a mineral in thin laminae resembling graphite. From the locality and associations, the mineral was at first presumed to be either franckeite or cylindrite, the two sulphantimonite-sulphostannates of lead from Bolivia, which were described in 1893 by Stelzner and Frenzel respectively. Qualitative analysis, however, soon showed that, although similar to them in physical characters, it differed chemically from both franckeite and cylindrite in containing no antimony, but only lead, tin, and sulphur.

Of the two specimens from the Hohmann collection, one was labelled ‘sulphoselenide of lead from Bolivia,’ and the other ‘selenide of lead from Atacama,’ so that unfortunately the precise locality of the mineral is at present unknown. In all probability both specimens came from the same district in Bolivla, since in appearance they are very similar.

Since the mineral gyrolite was described and analysed by Anderson from Storr in Skye in 1851, it has been recorded from a considerable number of other places in that island. The writer observed it at the mouth of the burn called Allt Mòr, between Loch Brittle and Loch Eynort, and has now to record it from Rudha nan Clach at the mouth of Loch Bracadale, which brings the number of localities at present known in Skye up to fourteen. In fact, the mineral may be said to occur all along the south-western shore, all along the eastern escarpment, and at the more isolated localities of Lyndale and Portree. Similarly, it occurs in the other trap islands—the Treshnish group, Mull, Muck, Eigg, Canna, and Sanday, upon the last of which it has been observed by the writer at Stac nan Faoilean.

The mineral sartorite (of Dana) or scleroclase (of v. Waltershausen) appears to have been found much more frequently in latter years in the well-known dolomite at the Lengenbach, in the Binnenthal, Switzerland, than was formerly the case, and it may now be considered to be one of the commonest of the group of sulpharsenites of lead which have made this locality famous. Large, detached, longitudinally striated, prismatic crystals, mostly devoid of terminal faces, have been especially frequent, the majority of which are doubtless sartorites.

In connexion with the systematic examination of the minerals of Ceylon, which is being conducted in the Scientific and Technical Department of the Imperial Institute, the authors have recently examined a large quantity of coarse gem-gravel refuse obtained from the Balangeda and Rakwana districts of Ceylon.

The material varies somewhat in character, but zircon generally pre-dominates, while tourmaline, corundum, and pleonaste are fairly abundant. Among other minerals present in noticeable quantities are geikielite, picroilmenite, ordinary ilmenite, rutile, and fergusonite, all of which are generally in the form of rounded or sub-angular pebbles.

In November, 1836, Captain (afterwards Sir) James Edward Alexander was at Henkrees (29° S., 18° E.) on the southern side of the Orange River, South-West Africa, and sought for information as to what he might expect to find during his intended journey across Great Namaqualand. He says :—

‘A respectable old Bastaard lived at Henkrees, Balli by name; he was the owner of a thousand head of cattle, of many horses and sheep. … He also told me of great quantities of copper far up the Great Fish River, and of hills from which malleable iron could be cut out.

The instrument described in this paper is identical in principle with the small refractometer designed by the author more than three years ago, but differs from it in several details which are of considerable practical importance. As in the earlier form, a compensative lens is introduced of such curvature and focal length that the focal surface of the optical combination is a plane within the range for which the instrument is required, and consequently the critical edges are sharply defined in monochromatic light for all positions. It will be more convenient, before entering into the description, to take the features which have been changed.

The references to the occurrence of the titanium dioxide minerals as rock constituents have been so recently summarized in the ‘Mineralogical Magazine, that it is unnecessary to repeat them, except to refer again to Mr. J. J. H. Teall's record of anatase in the Cleveland ironstone.

Wishing to procure some of these crystals, a pound of ore from the Main Seam at Upleatham mines was treated by the usual processes of solution, washing by decantation, and separation by heavy solution. The residue obtained was equal to 0.16 per cent. of the material taken, and consisted mainly of anatase, mostly in sharply developed pyramidal crystals, with some pyrites in nodular concretions, possibly in replacement of some of the oolitic grains, together with other minerals of derived origin, among which futile and tourmaline were the most prominent.

Professor Becke's paper on skiodroms marks an important advance in our knowledge of the shadows, or isogyres, which are seen when sections of crystals are examined in convergent polarized light. The isogyres can also be advantageously studied in mineral grains, where the irregular shape disturbs the distribution of the interference colours, but has much less effect on the shadows due to the coincidence of directions of vibration in the crystal with those of one of the nicols.

§ 1. It is proposed in this paper to describe some simple graphical constructions of theoretical or practical interest. They may be easily performed with ruler and compasses, though the stereographic and gnomonic nets will often save labour. To economize space the proofs of the constructions are left to the reader.

§ 2. First take the case of the gnomonie projection. Given the projections A, B, C, Q (fig. 1) of the poles of the faces (100), (010), (001) (111); find the projection of the pole of any other face (hkl).

Previous work on the regular growth of crystals of salts on those of Minerals belonging to the same isostructural series led the author to the discovery that parallel deposition is conditioned by closeness, not of angle nor of axial ratios, but of molecular volume. Now although the substances previously examined resemble each other crystallographically, yet they exhibit such great differences in chemical properties, that reasonable doubt might be entertained whether conclusions drawn from them can be directly applied to isomorphous substances ; and it therefore became advisable to extend the observations to a group of the latter.

The mineral dundasite was first described by W. F. Petterd in 1893, a ‘Catalogue of Minerals known to occur in Tasmania’. It was found in small, silky, milk-white, spherical aggregates incrusting a ‘ferro-manganese gossan’ at the Adelaide Proprietary mine, Dundas. In this catalogue, and in a subsequent one dated 1896, it was stated, as the result of qualitative tests, to be a hydrated carbono-phosphate of lead and aluminium ; but a quantitative analysis (see below under II), made later by S. Pascoe, showed that the mineral is a hydrated carbonate of lead and aluminium, and that the traces of phosphoric acid were due to a thin coating of pyromorphite. In this analysis the water and carbonic acid were determined together, by loss on ignition, and consequently hitherto no chemical formula has been attributed to the mineral.

A small specimen (weighing 20 grams), with a label carrying the inscription ‘Meteoric Iron from the banks of the Great Fish River, South Africa,’ was included in a mineral collection presented to the British Museum in 1878 by Mr. Benjamin Bright, of Bristol; the collection had been begun by Mr. Richard Bright (1754-1840), and increased by his son, Mr. Benjamin Heywood Bright (1787-1843), father of the donor. No lists or letters were handed over with the collection, and the history of the specimen and its label, prior to 1878, was thus unknown : as no additions to the collection seem to have been made by Mr. Benjamin Bright himself, the Great Fish River specimen had probably been acquired not later than 1848, the year in which his father had died.

If a straight line making an angle with a zone-axis of a crystal be rotated about the zone-axis while the crystal remain fixed, the physical characters of that line will pass through a cycle of changes. If these changes repeat themselves n times during the course of a complete revolution, the zone-axis is said to have an nth-turn or n-fold cyclic symmetry. If the line be at any time normal to a crystal-face it will be normal to a face with the same physical characters n times during such a revolution.