360 THE PRINCIPLES OF SCIENCE. 



length : (i) they may be all equal, or (2) two equal and 

 one unequal, or (3) all unequal. They may also be varied 

 in four ways as regards direction : (i) they may be all at 

 right angles to each other ; (2) two axes may be at right 

 angles and the third perpendicular to one of them and 

 oWique to the other ; (3) two axes may be at right angles to 

 each other and the third oblique to both ; (4) the three 

 axes may be all oblique to each other. Now if all the 

 variations as regards length were combined with those 

 regarding direction, it would seem to be possible to have 

 twelve classes of crystals in all, the enumeration being- 

 then logically and geometrically complete. But as a 

 matter of empirical observation, many of "these classes are 

 not found to occur, oblique axes being seldom or never 

 equal. There remain in all seven distinct classes of 

 crystals, but even of these one class is not positively 

 known to be represented in nature. 



The first class of crystals is defined by possessing three 

 equal rectangular axes, and equal elasticity in all direc- 

 tions. The primary or most simple form of the crystals 

 is the cube , but by the modification or removal of the 

 corners of the cube by planes variously inclined to the 

 axes, we have the regular octohedron, the dodecahedron, 

 or various combinations of these forms. Now it is a law 

 of this class of crystals that as each axis is exactly like 

 each of the other two, every modification of any corner of 

 a crystal must be repeated symmetrically with regard to 

 the other axes ; thus the forms produced are symmetri- 

 cal or regular, and the class is called the Regular System 

 of Crystals. It includes a great variety of substances, 

 some of them being elements, such as carbon in the form 

 of diamond, others more or less complex compounds, such 

 as rock-salt, potassium iodide and bromide, the several 

 kinds of alum, fluor-spar, iron bisulphide, garnet, spinelle, 

 &c. No correlation then is apparent between the form of 



