Kingdom.]

Class 1.—MINING AND MINERAL PRODUCTS.South Side—Areas S. 1 to S. 27.

121

Every crystal may be referred to one or other of threeclasses or systems.

These three classes are dependent on the relative direc-tion of three lines not all in the same plane, indicative ofthe direction from a common centre of origin of thenatural forces by which the crystal has been formed;such three lines are termed the gubernatorial axes.

The three classes are as follows:—

Class 1. Rectangular . All the axes at right angles toeach other.

Class II. Oblique rectangular. One axis oblique tothe other two, which are rectangular.

Class III. Oblique. All three axes making equaloblique angles with each other.

All the axes are of equal length, and in the second andthird class the prevailing angle of obliquity is nearly(if not invariably) 101° 49' 9’4", and its supplement78° 10' 50*6".

It is a very simple but important law, easily demon-strated, and greatly facilitating crystallographic investi-gations, that any plane of any crystal whatever mustbelong to one or other of the three following forms,which may be designated and defined as follows:—

Trisecant. Cutting all three gubernatorial axes.

Duosecant. Cutting only two axes, and thereforeparallel to the third.

Ultimate. Cutting only one, and therefore parallel tothe other two.

A set of fundamental forms, similarly constituted,belongs to each of the three classes.

This circumstance, viz., the existence of such a set offorms, characterizes a class or system.

Each fundamental form is produced by six similarand equal four-sided pyramids, one being placed at eachend of every gubernatorial axis, so that the diameters ofthe base of the pyramid coincide with or bisect the othertwo gubernatorial axes.

When the diameters of the base of the pyramid coin-cide with or are parallel to the gubernatorial axes, theform produced is trisecant. When, on the contrary, thediameters of the base of the pyramid bisect or are parallelto the line of bisection of the gubernatorial axes, theform produced is duosecant.

The series of fundamental forms is produced by asuccessive diminution in the height of the pyramid,according to a regular law. The diameter of the base ofthe pyramid in the trisecant series, and the sides of thebase in the duosecant series, being a multiple of itsheight by some integer. Wien the diameter of the basebecomes infinitely extended, or the height of thepyramid becomes 0, we arrive at the ultimate form,which is a cube in the rectangular class, a right rhombicprism in the oblique rectangular class, and a rhombohe-dron in the oblique class.

The most frequent, if not the only series, is that inwhich the ratio of height in the pyramid to the diametersor sides of its base is as 1 to some power of 2, thoseactually observed being 2 1 , 2 2 , 2 ;i , 2 4 , and 2 s . In thisseries we may pass from the trisecant to the duosecant,and from the duosecant to the trisecant forms, by a con-tinual replacement of edges by planes. Thus commencingwith the octohedron, and replacing its edges by planes,we pass to the dodecahedron, or first duosecant form.Thence to the trapezohedron, or second trisecant form.Thence to the pyramidal hexahedron, or second duosecantform. Thence to a flatter trapezohedron, and so on, tillwe arrive at the ultimate form, or cube, when, byreplacement of its edges, we may return to the dodeca-hedron, or first duosecant form.

A new set of forms is produced by rotating, inverting,or altering the position of the pyramids 45°, so as tomake trisecant pyramids duosecant, and duosecant pyra-mids trisecant; and next, by combination of two equaland similar fundamental forms, a set of forms having aneight-sided pyramid is produced at each end of the guber-natorial axes: thus, two octohedrons joined together pro-duce the triakis octohedron ; two trapezohedrons joinedtogether produce the hexakisoctohedron, and so on.

It appears as if these forms, like macled crystals, arise

from a simultaneous development of two crystals inopposite directions, and then what would be re-enteringangles are filled up, so that only the edges of the twocrystals remain. Thus each eight-sided pyramid consistsof planes joining the four lateral edges of one pyramidwith those of the four lateral edges of another equal andsimilar pyramid. Lastly, from the forms thus describedan infinite variety of others are obtained, first by theunequal development of particular planes, and next bycomposition of two or more forms.

In natural crystals, it is frequently observed thatcertain planes are extended more than others ; indeed,it will be found that unequal development is the rule,and perfect forms are the exception. In the case of thediamond, which very commonly crystallizes in the regu-lar octohedral form, the octohedron is constantly un-equally developed, giving rise to the various forms ex-hibited in the drawing.

When unequal development does not occasion the lossof any plane, the form is termed simply imperfect; butwhen, as in the passage of the octohedron into the tetra-hedron, or into the rhombohedron, certain planes areobliterated, the form is termed defective.

The law of unequal development shows that whateverforms can be produced thereby from the series of formsalready described, they may possibly have existence with-out any dimorphism in the substance examined. Pro-ceeding on this basis, the exhibitor has discovered thatall the unequal-axed crystals are merely unequal develop-ments which have concealed the true character of thecrystals, but which have been abundantly and conclusivelyexplained by the small remnants of planes to which littleattention has been heretofore directed, but which becomeof great significancy in relation to the law in question.

9 Mitchell, Rev. Walter, St. Bartholomew'sHospital —Designer and Inventor.

Series of models in paper, representing all the primaryand secondary forms of crystals, and the most importantcombinations of these forms.

10 Dyer, William, Little Hampton, near Arundel —Proprietor and Inventor.

Sussex coast agates, found on the sea-beach; manycontaining specimens of petrified sponges, sea anemones(Choanites Konigii), and other zoophytes. Specimensfashioned and polished for ornaments.

[The agates on the Sussex coast are, to a great extent,if not entirely, chalk flints in a peculiar state; and theyfrequently exhibit very beautiful indications of organicstructure. The definition of agate generally in mineralogyhas reference to an apparently banded structure, or con-centric arrangement of silicious matter, often showingdifferent tints of colour. When of considerable size, thecentral part is generally clear. The essential materialis, in all cases, silica, and the colour is, no doubt, dueto metallic oxides, chiefly of iron and manganese.—D. T. A.]

11 Slater & Wright, Whitby — Manufacturers.

Specimens of rough jet, and articles manufactured fromjet for ornamental purposes.

[Jet is a variety of coal occurring abundantly in certainlocalities, but not associated with true coal. At Whitbyit is found in the lias beds of that district, and has longbeen known and worked. It is also common in France (Languedoc), the Alps, Spain (the Asturias ), andGallicia,and in the United States at Massachusetts . Very largequantities are used for ornamental purposes, and forrosaries, crosses, &c., in Roman Catholic countries. Thetrue jet is much lighter and pleasanter to wear than thenumerous imitations that abound everywhere, D. T. A.]