688 -THE PRINCIPLES OF SCIENCE. [CHAP. 



Nearly the same statement may be made concerning the 

 third or hexagonal or rhombohedral system of crystals, in 

 which there are three axes lying in one plane and meeting 

 at angles of 60, while the fourth axis is perpendicular to 

 the other three. The hexagonal prism and rhombohedron 

 are the commonest forms assumed by crystals of this system, 

 and in ice, quartz, and calc-spar, we have abundance of 

 beautiful specimens of the various shapes produced by the 

 modification of the primitive form. Calc-spar alone is said 

 to crystallise in at least 700 varieties of form. Now of all 

 the crystals belonging both to this and the dimetric class, 

 we know that a ray of light passing in the direction of the 

 principal axis will be refracted singly as in a crystal of 

 the regular system ; but in every other direction the light 

 will suffer double refraction being separated into two rays, 

 one of which obeys the ordinary law of refraction, but the 

 other a much more complicated law. The other physical 

 properties vary in an analogous manner. Thus calc-spar 

 expands by heat in the direction of the principal axis, but 

 contracts a little in directions perpendicular to it. So 

 closely are the physical properties correlated that Mits- 

 cherlich, having observed the law of expansion in calc- 

 spar, was enabled to predict that the double refracting 

 power of the substance would be decreased by a rise of 

 temperature, as was proved by experiment to be the 

 case. 



In the fourth system, called the trimetric, rhombic, or 

 right prismatic system, there are three axes, at right angles, 

 but all unequal in length. It may be asserted in general 

 terms that the mechanical properties vary in such crystals 

 in every direction, and heat spreads so that the isothermal 

 surface is an ellipsoid with three unequal axes. 



In the remaining three classes, called the monoclinic, 

 diclinic, and triclinic, the axes are more or less oblique, 

 and at the same time unequal. The complication of 

 phenomena is therefore greatly increased, and it need only 

 be stated that there are always two directions in which a 

 ray is singly refracted, but that in all other directions 

 double refraction takes place. The conduction of heat is 

 unequal in all directions, the isothermal surface being an 

 ellipsoid of three unequal axes. The relations of such 

 crystals to other phenomena are often very complicated, 



