صور الصفحة
PDF
النشر الإلكتروني

sections are highly instructive, and shew the extraordinary rate at which alluvial matter will sometimes accumulate. I wished also to have noticed the formation of recent sand-stone on the north coast; which appears to have been well known to some of those who collected for Dr. 'Woodward, as I find several characteristic specimens of it in the old cabinets of our Museum. But this communication has already extended to so great a length, that I shall not trespass any further on the attention of the Society.

XXII. On Double Crystals of Fluor Spar.

By W. WHEWELL, M. A. F. R. S.

FELLOW OF TRINITY COLLEGE,

AND OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY.

[Read Nov. 26, 1821.]

EVERY one who has noticed the specimens of Fluor Spar, of which a great number have lately been brought to Cambridge, and generally designated by the name of Aldstone Moor Fluor, although they are, I believe, found in a district more extensive than that designation would imply, must have observed the peculiarity of their crystallization. The crystals of this substance, are, in their most common form, cubes: but, in the specimens now referred to, these figures are almost universally aggregated in pairs with a certain uniformity of appearance. The cubes seem to intersect and enter each other obliquely; as the proportions of the parts, and number of the angles developed are different, the appearances undergo variations; so that we see sometimes a large cube, with only one corner of a smaller one appearing above its surface; and at other times, two crystals, nearly equal, seem to penetrate and pierce through each other in a very curious manner, which is best understood by specimens. The effort towards this kind of aggregation, at the time of the

[blocks in formation]

formation of these crystals, appears to have been exerted almost universally, and in some places it is rare to find a single crystal which has escaped its influence. And so far as the eye can judge, the angles made by the planes and lines of these crystals, are the same in all cases, however different the general form and proportions.

The number and uniformity of these appearances induced me to examine the mode in which the crystalline particles are arranged to produce them, and the result at which I have arrived, though perhaps not very difficult to obtain, may be worth notice, as marked with the simplicity and beauty which nature every where exhibits in the laws which regulate her crystalline productions. To explain my view of the subject, let Fig. 1, represent a double crystal or macle, as it is sometimes called, in the form of most usual occurrence, and which may be considered as the representative of all others. ABCD is the face of a cube, and through this protrudes EFGH the corner of another. It will be observed that so far as the eye can estimate, the pyramid EFGH is similarly situate as to angular position with respect to AB and AC: EGH is an isosceles triangle, and EG, EH make equal angles with AB, AC respectively, so that GH makes angles of 45° with DB, DC. Also the dihedral angles which the planes EFG, EFH make with ABCD, will be equal, and, as has already been observed, these are apparently equal in all our specimens of this substance.

To learn the constitution of these crystals we must examine their planes of cleavage. It is well known that in a cube of fluor we may with ease split off each of the eight corners of the cube, so as to cut off from each a regular pyramid, and this division may be carried on so as to produce either a regular tetrahedron or a octahedron. Now it will be found in all cases that one of these planes of cleavage is common to the two associated cubes.

This plane may be distinguished from the others in this manner; it will cut off that corner (A) of the more complete cube (ABCD), towards which is pointed the vertex (E) of the isosceles triangle (EHG), on which the pyramid (EFGH) stands. It will be found that plates parallel to this plane may be split off through both cubes, and generally without any interruption to mark the transition from one to the other. All the other planes. of cleavage which pass through the first cube, it will be found do not belong to the other, and vice versa. If to this observation we add what has already been mentioned, that EF makes equal angles with AB and AC, which is also confirmed by the other fissures of the two crystals, we shall be able to explain their relation.

Let the plane of cleavage LMN, Fig. 2, pass through the point E, making AL= AM = AN, and LMN an equilateral triangle. Conceive the cube, of which F is the visible corner, to be produced within the other, so that O may be the corner which is cut off by the common plane LMN, and therefore OE, OP, OQ equal and EPQ an equilateral triangle. And EO will cut LM at right angles; hence EP and EQ make angles of 60° with LM, and therefore if we suppose E to bisect LM, P and Q will bisect LN and MN. Now the triangles LMN, QPE may be considered as corresponding faces of the tetrahedrons to which the two cubes may respectively be reduced. And the sides of EQP make angles of 60° respectively with those of LMN. Hence it appears that the relative position of the two tetrahedrons is such, that if we conceive a face of one of them to revolve in its own plane through an angle of 60°, it will come into a position parallel to the other.

It is found that if after splitting the crystals by the plane which cuts off A, we split off the corner F and the one diametrically opposite to D, the new planes of fissure will cut the former plane in parallel lines.

manner.

This will, perhaps, become more intelligible in the following A line A a, joining two opposite corners of the cube, will manifestly be perpendicular to the surface LMN or EPQ. Hence the diagonal of the cube 0, &c. is parallel to A a; and this cube 0, &c. may be conceived to have removed into its present position by revolving round this diagonal through an angle of 60°, from a position parallel to the first cube.

[ocr errors]

Here, as in all other parts of crystallography, it is the angles only which planes and lines make with each other, and not their magnitudes or places, which we must consider. The point E may be situate any where in the plane ABCD, as at A; and the points G and H may be in DB and DC. Also whatever has been said of the angle F of the parasite cube, if I may be allowed to call it so, is true of any other angle, which might appear on the other surfaces of the principal cube. We may then suppose the two cubes equal, their diagonals coinciding, all their angles developed, and we shall have them in such a situation as is represented in Fig. 3. The two cubes may be supposed at first to have exactly coincided, and then one of them having revolved through one-sixth of a whole revolution, would come into its present position, in which the position of its faces and edges, with respect to those of the other cube, are exactly what are found to exist in what I have called the parasite cubes, with respect to the principal ones, in fluor spar.

From this mode of conceiving the constitution of these crystals, we can easily calculate the angles of the different planes, &c., and compare them with those obtained by measurement. It is to be observed, however, that this comparison is not so much to be trusted as the results obtained by cleavage, because the surfaces, when of any extent, are not accurately plane, as may be seen by inspection, and also, because the form in most cases, is not, strictly speaking, a cube simply; but each face of the cube is replaced by a very

« السابقةمتابعة »