237 



CRYSTALLOGRAPHY. 



CRYSTALLOGRAPHY. 



238 



Fig. 1. 



Fig. 3. 



cube, and those which would res'ilt from the truncation of its edges 

 would correspond in position with those which would result from the 

 truncation of the edges of 'the cube. The cube might therefore be 

 regarded as the secondary form of the octahedron, arising from the 

 truncation of its six solid angles. Relations of the -same nature subsist 

 among the original and derived figures belonging to each kind of the 

 primary forms except the rhomboid. The reason for preferring the 

 one or the other of these as the primary will be considered when we 

 treat of the relations of the different forms of crystals. 



We have, for reasons which we shall then state, assumed the fol- 

 lowing figures as the primary or fundamental forms of all known 

 crystals. 



The Cube, /jr. 1. 



The Square Prism, in which, supposing the base of this prism to be 

 of the same dimensions as a side of a given cube, and this and the 

 cube to be both standing on a table, the upright edges would be longer 

 or shorter than those of the cube. 



A Right Rhombic Prism, flg. 4. 



An Oblique Rhombic Prism, fig. 5. 



A Double-Oblique Prism, fig. 6. 



A Rhomboid or Rhombohedron, fly. 7. 



Fig. 4. 



Fig. 5. 



Fig. c. 



Fig. 7. 



The Cube being bounded by six equal square planes, the minerals 

 which assume this form are not distinguishable by the figure of their 

 crystals ; but minerals which occur under the other forms may gene- 

 rally be distinguished as follows : 



Those which can be referred to square prisms, by the different 

 proportions which, in each particular case, the lateral edges bear to 

 the terminal edges ; and those which belong to the other prisms and 

 to the rhomboid, by the angles at which their planes intersect each 

 other. The ratios of the edges of square prisms may be determined 

 by known algebraical formulae from the angular measurement of some 

 of the secondary forms, and the angles at which the planes of the 

 other forms meet, may, in many cases, be ascertained by measurement 

 with an instrument called a Goniometer, but in others they must 

 be deduced mathematically from some of their respective secondary 

 forms. 



These six primary forms stand in certain relations to each other, 

 which it may not be useless to point out. If the lateral edges of the 

 cube be supposed to be longer or shorter than, the terminal edges, a 

 square prism, as we have already seen, would be produced ; if two 

 opposite lateral edges of a square prism could be pressed towards each 

 other, the parallelism being kept, a right rhombic prism wotdd be 



formed ; if this prism could be pressed in the direction of either of 

 the diagonals of its terminal plane, so as to make the figure overhang 

 the base in that direction, an oblique-rhombic prism would be repre- 

 sented ; and if again pressed in the direction of the other diagonal, so 

 that it would overhang the base in both directions, a doubly-oblique 

 prism would be formed. If we suppose a cube to be made to stand 

 on one of its solid angles by placing the fingers on an opposite one, 

 and if, while held in tlu's position, the two solid angles could be 

 pressed nearer together or drawn further apart, the altered cube 

 would become a rhomboid. 



2. Secondary Forms. 



These might be produced, and are most conveniently described, by 

 supposed truncations of the solid angles or edges of any of the pre- 

 ceding forms ; but as in nature the most minute crystals appear in the 

 shape of secondary forms, it is to be inferred that these modifications 

 of the primary are occasioned by some natural influence operating 

 upon the first germ of the crystal, and continuing during the period of 

 its increase in size. 



Secondary Crystals are sometimes altered from the primary only 

 by single sets of planes replacing some of the solid angles or edges ; in 

 other cases both the solid angles and edges are replaced by planes in 

 the same secondary crystal ; and in others, several different sets of 

 planes appear replacing the solid angles and edges of the same crystals, 

 and producing very numerous and complicated secondary forms. 

 Thus it occurs that the solid angles of the cube are sometimes replaced 

 by three and sometimes by six symmetrical planes, of which several 

 sets may occur on the same crystal, and perhaps with other planes 

 replacing the edges. Similar changes of figure may also occur on 

 each of the other kinds of the primary forms, thus producing the 

 different systems of crystallisation before referred to. 



The number of known secondary forms belonging to each system is 

 already very great ; in one mineral, carbonate of lime, they amount to 

 many hundreds ; but thousands and tens of thousands more might 

 occur under the operation of only a few of the laws of which we shall 

 afterwards treat. 



Among the secondary forms of crystals there are some which differ 

 in their characters from those already described. Let us suppose two 

 diagonal lines to be drawn through opposite angles, and crossing each 

 other on the faces of the cube. It may be observed, by referring to 

 fig. 2, that the solid angles at the extremities of all these diagonals are 

 truncated to produce the octahedron ; but it sometimes happens that 

 the solid angles at the extremities of only one of those diagonals on 

 one plane, and a transverse diagonal on a parallel plane are truncated, 

 producing a four instead of an eight-sided secondary figure ; these are 

 termed hemi forms, from their presenting only half the number of 

 planes which might be expected from the symmetry of the primary 

 crystal. These defective figures, as they may be termed, from their 

 wanting the number of faces which might be expected on the crystal, 

 are frequently troublesome to the mineralogist, and occasionally 

 mislead him; but there is another, of a much more capricious 

 deviation from the regularity of the simple forms, which is still more 

 troublesome than the preceding ; these are what have been termed 

 Hemitrope and Twin Crystals. In twin crystals the two individuals 

 are united in such a manner that if one of them be made to describe 

 a half-revolution round an axis perpendicular to a plane, which is 

 either a face of one of the crystals or which might be one in virtue of 

 the laws of crystallography, it comes into the position of the other. 



Twin Crystals are produced by the union of two or more crystals 

 according to some regular plan, so that if any number of twin crystals 

 of the same kind of mineral should be found, they would be fashioned 

 in the same manner. Hence these apparently capricious composite 

 figures are subject to definite laws, and are not the results of merely 

 accidental aggregation. There are also two other classes of irregular 

 forms of crystals, one of which, termed by Haiiy ' Epigene," occurs 

 where a crystallised mineral has undergone a chemical change without 

 disintegration or suffering any change of figure ; the form in the 

 altered state of the mineral not being proper to the new substance, 

 but remaining that of the original body. 



The other class, termed Pseudomorphous, appears as if they had 

 been produced in moulds resulting from the destruction of crystals of 

 other substances which had been inclosed or imbedded in them, and 

 which moulds being filled with some new kind of mineral, the new 

 and intrusive matter assumes the form of the originally inclosed body, 

 and one altogether foreign to its proper shape. 



3. The secondary forms of crystals are not derived from the primary 

 by accidental and indefinite truncations of the solid angles and edges, 

 but according to known and definite laws, so that all the possible 

 alterations of figure which any given primary form can undergo, 

 might be determined a priori, if the extreme limits of the relative 

 proportions of the edges considered to be cut off in producing new 

 planes were known. Within well ascertained limits however many 

 thousand of possible secondary forms, belonging to each kind of 

 primary, might be determined with absolute precision. 



The laws according to which any secondary planes are produced 



are termed the laws of those planes. To illustrate the nature of 



these laws, let fig. 8 represent a square prism, whose edges ab c are 



each divided into any equal number of parts, which parts are corise- 



| quently proportional to the respective edges. Now a new plane. 



