Page:The American Cyclopædia (1879) Volume V.djvu/543

 CRYSTALLOGRAPHY 539 FIG. 25. three other forms (eight-sided pyramids) whose axes are severally 3a : 3 : 1 (33, fig. 25) ; 4a : 4 : 1 (44, ib.) ; 5a : 5 : 1 (55 ib.) ; or writing out the value of a, they are 1-9221 : 8 : 1 ; 2*5628 : 4 : 1 ; 3-2035 : 5 : 1. Through these numerical ratios the planes or fig- ures of crystals are con- veniently lettered, as in this example of zircon, i being used in place of the sign for infinity. The same numerical ax- ial ratios run through all crystalline forms, and by means of them the values of the angles are calculated. These facts show that the modifications which co- hesive attraction (or, what is the same, crystallogenic attraction) undergoes in order to produce the various derivative forms of any substance take place according to a law of simple ratios. VIII. The physical characters of crystals have a direct relation to the forms and axes. Cleav- age, hardness, color, elasticity, expansibility, and conduction of heat differ in the direction of different axial lines, and are alike in the direction of like axes. The difference of color between light transmitted along the vertical and lateral axes of a prism is often very marked, and the name dichroism (Gr. dig, twice, and xp^ a -> color), or the more general term pleochroism, is applied to the property. The hardness often differs sensibly on the terminal and lateral planes of a prism, and also, though less sensibly, in other different directions. IX. The angles of the crystals of a species, though essentially constant, are sub- ject to small variations. The unequal expan- sion of inequiaxial crystals along different axial directions, alluded to under the last head, oc- casions a change of angle with a change of temperature ; other small variations arise from impurities, or isomorphous substitutions, or ir- regularities of crystallization. There are also many instances of curved crystallizations which are exceptions to the general rule. A familiar example of curving forms is af- forded by ice or frost as it covers windows and pavements. Diamonds have usually convex instead of plane faces. Ehombohedrons of dolomite and spathic iron often have a curv- ing twist ; half the faces are concave and those opposite con- vex. Other imperfec- tions arise from an oscillating tendency to the formation of two planes, ending in making a stri- ated curving surface. Thus nine-sided prisms of FIG. 26. tourmaline are reduced to three-sided prisms with the faces convex. X. While simple crystals are the normal result in crystallization, twins or compound crystals are sometimes formed. The six-rayed stars of snow (fig. 26) and the arrow-head forms of gypsum are examples of compound crystals. In the stars of snow there are three crystals crossing at middle ; in the arrow-shaped crystal of gypsum two crystals are united so as to form a regular twin. Many of these twin crystals may be imitated by cut- ting a model of the form in two, through the middle, and then inverting one part and uni- ting again the cut surfaces. Fig. 27 represents FIG. 27. FIG. 23. an octahedron placed on one of its faces with a plane intersecting at middle, and fig. 28 is the same form with the upper half revolved 60. To explain its formation, it is necessary to suppose that the nucleal or first particle of the crystal was a double molecule made up of two molecules, in which one was thus inverted or revolved on the other. Another example is shown in fig. 30. Fig. 29 is a common form of tin ore ; the four-sided prism has a pyramid at each end. It is represented as intersected by a diagonal plane. Fig. 30 is the same form after one half is revolved 90, and this also is very common in tin ore. Such twins, as well . 29. FIG. 30. as other facts ? prove that molecules have a top and bottom, or, in more correct language, po- larity, one end being positive and the other negative, this being the only kind of distinc- tion of top and bottom which we can sup- pose. Axial lines or directions of attraction are in fact necessarily polar, if it be true, as is supposed, that molecular force of whatever kind is polar. In the case of the compound crystal of snow, the nucleal particle must have consisted of three or six molecules com- bined. Those prismatic substances are com- pounded in this way which have the angles of the prism near 60 and 120, and for the reason that 3 times 120 or 6 times 60 equal 360, or the complete circle. In a case where this an- gle is nearly one fifth of 360 (as in marcasite),