CRYSTALLOGRAPHY 



601 





of no height, while the plane* oo P represent a 

 pyramid of infinite height. 



Drawing ami Mapping of Crystal*. Various 

 modes of representing crystals have been adopted. 

 Perspective drawings are made by projecting the 

 axes according to the rules of Projection (q.v. ), 

 then the various planes are indicated, and from 

 these their intersections are known, and these 

 intersections form the drawing of the crystal. 

 Fig. 7 represents one octant of the form 211 



Fig. 7. 

 Mode of drawing a crystal from projection of axes. 



drawn by this method. Some writers represent 

 crystal forms by orthographic projections that is, 

 represent them in plan and front elevation. Of 

 all methods, however, of representing crystals 

 from measurements made with the goniometer, 

 the most elegant and convenient is that of spher- 

 ical projections. Two kinds of spherical projec- 

 tion are in use viz. the gnomic and the stereo- 

 graphic. Imagine a glass sphere placed within a 

 crystal, as in tig. 8, and suppose the faces of the 

 crystal to move parallel 

 to their original posi- 

 tions until they touch the 

 sphere, and where the 

 faces touch let dots be 

 marked on the sphere. 

 Thus the face a will pro- 

 duce the dot a', the race 

 o the dot o', and so on. 

 When the sphere is thus 

 marked with dots corre- 

 sponding to the several 

 faces, the next thing is to 

 make a map of the dots 

 crystal, in their proper position, 

 moved If the map is to be made 

 on the gnomic projection, 

 the sphere is supposed 

 to be placed on the paper 



on which the map is to be made, and the eye 

 is then placed at the centre of the sphere. The 

 various dots when projected on to the paper as 

 seen by the eye placed at the centre of the sphere 

 produce the map. If the map is to be made on 

 the stereographic projection, suppose a piece of 

 glass to pass through the centre of the sphere as 

 in fig. 9, and let the eve be placed touching the 

 sphere at E, then the dots as they appear on the 

 glass to the eve "at E form the map. Such a map 

 of the crystal of fig. 8 is given in fig. 10. In the 

 Ktereographic projection all great circles on a 

 sphere are represented on the map by either straight 

 lines or arcs of circles, whereas in the gnomic pro- 

 jection they are represented by straight lines. The 

 map (fig. 10) shows not only the position of the 

 dots or polos, but also great circles passing through 



Fig. 8. 



Sphere within a 

 When planes are 



the sphere. These great circled correspond to the 

 planes of symmetry of the cube (tig. 2) and otln-r 

 forms of the cubic system. These stereographic 

 maps, as will be seen by reference to treatises on 



Fig. 9. 



The eye placed at E sees the dots on 

 lower part of sphere projected on 

 the plane abed. 



Fig. 10. 



Stereographic map of 

 the cryxtal of flg. 

 8 as obtained by 

 method in flg. 9 



the subject, convey a good deal of information 

 respecting the crystals they portray. 



Planes of crystals form a zone when the inter- 

 sections of the planes (i.e. the edges) are parallel 

 to each other. Thus, in fig. 6 the faces oP, AP, 

 P, and ooP form a zone. Now in Miller's notation 

 these forms have the indices 001, 112, 111, 

 110, and it will be noticed that all these symbols 

 have a common ratio thus, the first and 'second 

 index are equal to each other. It may be shown that 

 this is universally true ; hence, knowing the indices 

 of a plane, we can say whether it is on a particular 

 zone, or knowing that a plane lies in two zones, we 

 can determine its indices. Thus, the planes 1 2 3, 

 124, 125, &c., are all in one zone, as the 

 symbols have the common ratio 1 : 2, and the plane 

 345 cannot be on this zone, because its symbol 

 does not contain the ratio 1 : 2. 



Holohedrism and Hcmihedrism. Crystals which 

 have all faces present as required by the law of 

 symmetry are termed holohedral. Where, as is 

 often the case, onlj one-half of these faces are 

 present, the crystal is said to be hemihedral ; while 

 if only one-fourth of the full number of faces are 

 present, the crystal is said to be tetartohedral. 



Physical Crystallography. The physical pro- 

 perties of crystals have some interesting relations 

 to the symmetry and form of the crystal, and 

 these properties are included generally with crystal- 

 lography. Thug, if in the regular system a face 

 is striated or has any peculiarity, this striation or 

 peculiarity will be found on each face which is 

 present by the law of symmetry. Again, most 

 crystals cleave (i.e. break easily) in certain direc- 

 tions, and the cleavage planes* follow the law of 

 symmetry. Again, when examined by polarised 

 light, other properties of crystals in relation to 

 symmetry are brought out. Thus, crystals of the 

 regular system ( except in a few certain eases ) do 

 not doublv refract light, no matter in what direc- 

 tion the light is incident. With crystals of the 

 rhombohedral system and the pyramidal system 

 light is not doubly refracted when it falls parallel 

 to the vertical axis, but in other directions it is 

 doublv refracted ; while in the remaining systems 

 two directions can l>e found in which the crystals 

 of these systems do not doubly refract light, though 

 they do so in all other directions. Again, heat 

 is conducted differently in different systems of 

 crystals. Suppose crystals turned in a lathe into 

 spheres, and that the* centre is made suddenly hot, 

 then in the regular system the heat spreads equally, 

 and after a time the surface of the sphere is 

 uniformly raised in temperature ; with other sys- 

 tems the effect is different ; with the pyramidal 

 and rhombohedral systems a similar experiment 

 would result in the surface of the sphere being 

 heated uniformly over belts corresponding to an 

 equator and parallels of latitude, but the tempera- 



