ON THE PRIMITIVE FORMS OF CRYSTALS. 65 



Bi-pyramidal dodecahedron, all enjoy the same 

 property of being the only lines which can be placed 

 symmetrically in these different solids, and which 

 can be regarded as the axes of polarisation *. 



In all these forms, however, the axis of the crys- 

 tal may be the resultant of several axes which pos- 

 sess the conditions required by the general principle. 



In the Obtuse Rhomboid, for example, the sin- 

 gle axis may be resolved into 



1. Three axes in the direction of lines joining the 

 six acute solid angles of the rhomb, 

 which have their inclinations and their 

 directions symmetrically related to the 

 short diagonal, or into 



SL Three axes, perpendicular to any of the 

 three planes which contain the obtuse 

 angle ; or into 



3. Three axes, parallel to the common sections 



of these three planes ; or into 



4. Three axes, perpendicular to these common 



sections, and bisecting the angles form- 

 ed by the planes ; or into 



5. Three axes, parallel to these common sec- 



tions ; or into 



6. All these axes, taken together, or any number 



of them taken symmetrically. 

 These axes will be of the same character as the 

 single axis, if their inclination to the axis of the 



* There is an exception to the generality of this remark, 

 which will be presently explained. 



VOL. III. E 



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