ON THE PRIMITIVE FORMS OF CRYSTALS. 69 



placed * In the cube, each of the three axes is 

 perpendicular to three opposite pair of square sur- 

 faces by which the v solid is contained. In the 

 regular octohedron, each of them coincides with a 

 line joining the two opposite solid angles of the 

 figure ; and in the rhomboidal dodecahedron, each 

 of the three axes coincides with the lines which 

 join two of the opposite solid angles of the figure, 

 which are hounded by four acute angles of the rhom- 

 boidal planes. Hence the reason is obvious, why 

 the crystals belonging to the third class of primitive 

 forms have three axes, and consequently have nei- 

 ther double refraction nor polarisation. 



If we examine the results of the various combina- 

 tions of three equal axes in the whole series of rhom- 

 boids, from the most obtuse to the most acute, we 

 shall find them connected together by a very beauti- 

 ful law. 



In the first or most obtuse rhomboid with which 

 the series commences, the angle of the rhomboidal 

 planes is 120°, and the three axes perpendicular 

 to these planes, are parallel to each other, and 

 consequently form a resultant axis of the same 

 character, whose intensity is equal to thrice the 

 intensity of any of the separate axes. As their 

 angle increases, and the rhomboid becomes less 

 obtuse, the three axes become inclined to the 

 axis of the rhomboid, and compose a resultant axis 



* See pages 71, 72* 



