The protractor of which an account is given in the following pages is intended to facilitate the construction of stereographic and gnomonie projections of the sphere, especially on the part of students of crystallography. The fundamental properties of these projections, on which its design depends, have long been known, and have been the basis in the past of methods somewhat similar to those about to be described. Any novelty there may be in the device is to be sought therefore in the convenient arrangement of its parts, and in the ease with which it may be constructed and used, rather than in the principles which it embodies. We will consider first the construction of the protractor, then its application in tile case of the stereographic and gnomonic projections, and in conclusion will deal with a few points of interest in the history of these projections.

Cornwall has long been famous for the occurrence of certain minerals, found in the neighbourhood of the great granitic intrusions, that are rare in, or absent from, the aureoles of metamorphism surrounding the granites of many other regions. It is now generally recognized that these minerals have been produced by the action of certain heated gases on the rocks they penetrate along cracks and fissures ; but the exact age of this type of alteration is not so well known. It is often held to be contemporaneous with the thermo-metamorphism produced by the granite, and rocks Containing these minerals are included in the description of the ‘contact rocks’ surrounding the granite.

In the year 1888 I gave before the Mineralogical Society an account of the forms and optical characters of some minute crystals of kaolinite from Anglesey. At that time I was unable to ascertain whether the mineral was optically positive or negative, and it was stated that the axial angle 2V would approximate to 90°. Subsequently, by the aid of oil-immersion lenses and condensers of high angular aperture (numerical aperture=1.25), it was found that the mineral is optically positive and that the acute bisectrix is normal to the clinopinacoid (the obtuse negative bisectrix emerging through the basal plane). The optic axial angle in air was determined with an eyepiece micrometer to be 2E = 121°, with a possible error of one or two degrees, due to the small size of the crystals and the consequent weak interference-figures.

The behaviour of a mass of molten but cooling igneous rock under moderate pressure may be compared to that of liquid cupelled silver, which at a certain temperature can no longer retain the oxygen, many times its volume, that it has occluded. Thus, during the submarine eruption off the island of Pantelleria in 1891, blocks of lava that swam for a while on the surface of the sea exploded with violence. Chilling by contact with sea-water had occasioned exactly what Lowthian Bell observed to happen on the sudden cooling of masses of slag by contact with water. There was a discharge within the set outer envelope, at something near a red heat, of previously dissolved water and gases, converting the floating ejectamenta into a species of bombs.

In a paper read before the Mineralogical Society on April 10, 1894, describing the details of the analysis of a meteoric stone which had been found at Makariwa in New Zealand, attention was called by the present author to the fact that the operation of extracting the nickel-iron by mercuric solution from the material separated from the powdered stone by the magnet was scarcely a terminable one; for even the twelfth extraction by means of a solution of mercuric ammonium chloride evidently contained an appreciable amount of colouring matter, while the colour of the extract indicated an increase in the proportion of the nickel. ‘It was clear that one or other constituent of the attracted material was being only slowly dissolved, and that it was practically useless to push the operation farther.

During recent years a considerable industry has grown up at Paris in the synthetical manufacture of corundum for jewellery purposes by means of the process devised by Professor A. Verneuil. In place of the fragments of natural ruby used in previous attempts, ammoniumalum is the material employed. After careful preparation to free it from potash and other impurities, it is ground to a powder and placed in a sieve at the top of the oxygen tube of an inverted blowpipe. The sieve is tapped by a hammer at regular intervals, and uniformity is in this simple way produced in the amount of powder that falls; the necessary adjustment is effected by varying the height through which the hammer falls. To minimize the cost of production, a few alterations have been made in the original apparatus.

The question of the system to which perovskite should be referred, and the explanation of the discrepancy between its form and optical-properties, have been the subject of much discussion among crystallograpbers ever since the discovery by Des Cloizeaux, in 1858, of the double refraction of crystals of calciam titanate from Zermatt, having the same composition as the crystals of cubic form from the Ural Mountains, to which the name perovskite had been given by G. Rose in 1889.

When mounted for measurement on the goniometer, the faces of the perovskite crystals described in the preceding paper yield, owing to the complex lamellated structure, a confused mass of images of the signal which cannot be analysed by the ordinary methods (such as using a lens in front of the eyepiece or shading portions of the face with a screen held in the hand), on account of the number and extremely small size of the reflecting surfaces. The apparatus described below was designed to give the means of identifying with certainty the image reflected from any given portion of such a face, and has been found to answer this purpose satisfactorily.