454 



MINERALOGY. 



Orjctogno- f. The magnitude; according to which crystals are 

 *! deeply acuminated, as in cubic crystals of fluor-spar, 



"""Y""" whose angles are acuminated with six planes ; slight- 

 ly acuminated, as in copper-pyrites or grey copper. 

 g. The termination, according as the accumination ends 

 in a point, which is the usual mode, or in a line or 

 edge, which is less frequent. 



In order to form a more distinct idea of truncation, 

 bevelment and acumination, let us take a cube, prism, 

 pyramid, or any other perfect fundamental figure re- 

 presented in wood, and cut off each of the edges or 

 angles at one stroke, so that in its stead a plane shall 

 appear ; this will be truncation. But if the terminal 

 planes, the edges, or the angles of any of these funda- 

 mental figures be cut off with two converging strokes, 

 the one from this side, the other from that, so that 

 two planes arise, which, terminating in a line, shall 

 present an edge ; this will be bevelling. And if the 

 terminal planes or the angles be cut off at several 

 strokes, all converging together, so that more than two 

 planes arise, commonly terminating in a point, we shall 

 obtain acumination. 



4. The Division of the Planes. 



The divi- Here the number of the planes of the fundamental 



sion of the figure is neither increased, nor is their figure changed, 



planes. as is the case with all the preceding alterations, but 



each plane is divided into a greater or lesser number of 



smaller planes that meet together under very obtuse 



angles. 



The number of compartments into which a plane is 

 divided, is two, three, four, and six. 



The dividing edges run either parallel to the diago- 

 nal, or from the centre of the plane of the fundamen- 

 tal figure towards the angles, or towards the middle of 

 the edges and the angles at the same time. Of the first 

 we have an example in the dodecahedral garnet ; and 

 of the second in grey copper-ore and diamond. 



5. Multiplied Alterations. 



Multiplied The various alterations of the fundamental figures 

 alterations, just enumerated, occur singly or several together in the 

 same fundamental figure. In the latter case, they are 

 placed either beside each other, when they are said to 

 be co-ordinate, or on one another, when they are said to 

 be superimposed. The alterations are considered to be 

 co-ordinate, when they occur in different places of the 

 same fundamental figure; of this we have an example 

 in fluor-spar, when the cube is bevelled on the edges, 

 and truncated on the angles. They are named super- 

 imposed, when they occur in the same part of the fun- 

 damental figure, and when the first alteration is modi- 

 fied by a second, as in a prism which is bevelled on the 

 terminal planes, and truncated on the bevelling edges. 

 Sometimes, as in topaz, three or more superimposed 

 alterations occur together in the same figure. Crystal- 

 lizations frequently occur which are so modified, that 

 they may be described in different ways, and referred 

 sometimes to one, sometimes to another fundamental 

 figure. This gives rise to two modes of description, 

 viz. the representative and the derivative. If a crystal 

 is described as it appears to the eye at first view, with- 

 out any reference to its relation to other crystallizations 

 of the game mineral, it is said to be described represen- 

 tatively. But if in the description we attend to its rela- 

 tions with the other crystals of the same mineral, and 

 also to its derivation from these, it is described deriva- 

 tively. Thus, in calcareous spar, we meet with forms, 



which, if described derivatively, would be considered Oryttogno- 

 as very low six-sided prisms, acuminated on both ex- 

 tremities with three planes, the planes set on the al- s ""V* 

 ternate lateral planes ; and the summits of the acumi- 

 nations so deeply truncated, that they touch the unal- 

 tered lateral planes in a line. But on a first view this 

 figure presents nothing prismatic ; and if ignorant of 

 its origin from the prism already mentioned, we would 

 rather consider it as a flat, double, three-sided pyramid, 

 in which the lateral planes of the one are set on the 

 lateral planes of the other, and the summits, and the 

 angles on the common basis deeply truncated. In the 

 same manner, many very broad prisms, as in rock- 

 crystal, at first sight appear like tables, but must be 

 considered as prisms, on account of their derivation 

 and other relations. 



The derivative mode is the most interesting and use- 

 ful, and is that which ought to be followed whenever 

 it is possible. 



In those cases, however, where the choice of the 

 fundamental figure is optional, and when it is not de- 

 termined by tracing it from other crystallizations, we 

 give the preference to that figure which enables us to 

 describe the crystal with the greatest facility and accu- 

 racy, and in the shortest manner. It is sometimes ad- 

 vantageous, and also facilitates our conception of the 

 crystal, when we unite together in our description 

 both the modes, using the derivative as the principal 

 one. Thus many varieties of the cube and the rhom- 

 boid are more clearly expressed, when we describe 

 them as double three-sided pyramids, in which the la- 

 teral planes of the one are set on the lateral edges of 

 the other. 



The different modes of describing crystals depend 

 on the transitions that so often occur between them, 

 by which one figure, owing to a succession of modifica- 

 tions, gradually passes into the other. Thus the cube, 

 by the truncation of its angles, passes into the perfect 

 octahedron. At first, the truncating planes on the 

 angles of the cube are small, but become gradually 

 larger and larger until they touch each other, when 

 the crystal exhibits a form intermediate between that 

 of the cube and the octohedron. If the truncating 

 planes still increase in size, they become larger than 

 those of the cube, and are now the principal planes of 

 the figure, while those of the cube are alterating planes, 

 and the whole represents an octahedron truncated on 

 the angles. If the original planes of the cube, which 

 now form truncating planes in the angles of the octa- 

 hedron, become smaller and smaller, and at length en- 

 tirely disappear, the perfect octahedron is produced. 



The modifications that give rise to these transitions 

 are the following. 



1. Alterations taking place in the proportional magnitude 



of the planes between themselves. 



Some planes increase in size, while others diminish, 

 and thus one figure is changed into another. When 

 the alternate lateral planes of the octahedron be- 

 come larger, while the others diminish, a tetrahe- 

 dron is formed, or the octohedron passes into the te- 

 trahedron. 



2. Alterations in the angles under which the planes meet. 

 Thus the common dodecahedron, by the increasing 

 obtuseness of its angles, at length passes into the 

 cube. 



3. The convexity of the faces of the crystals, which is 

 sometimes occasioned by the division of the planes. 



4. By the nener or alterating planes becoming gradually 



