ON THE PRIMITIVE FORMS OF CRYSTALS. 67 



3. Four axes, perpendicular to the four faces of 



the pyramids ; or into 



4. Four axes, parallel to the four faces of the pyra- 



mids, and perpendicular to the sides 

 of the square base ; or into 



5. Four axes, parallel to these common sections. 

 These four axes will be of the same name with 



the single axis, when their inclination to the result- 

 ant axis is less than 54° 44/ 8"; and of an opposite 

 name when the inclination is greater. 



The very same results are true of the Acute 

 Rhomboid with a square base, mutatis mutandis. 



The obtuse and acute octohedron may also have 

 three axes coinciding with the three rectangular axes 

 of the solid, and having their intensities propor- 

 tional to their lengths, as will afterwards be ex- 

 plained. 



In these cases, all the lines supposed to possess 

 the dignity of an axis, have a symmetrical position 

 in the solid ; and it must be allowed to be a singular 

 fact, that, without a single exception, all the primi- 

 tive forms which compose the first class, cannot pos- 

 sibly have more than one axis, whether we consider 

 this axis as an independent line, or as the resultant 

 of various other lines, occupying a symmetrical po- 

 sition around it. 



If we now extend the same reasonings to the Se- 

 cond Class of Forms, it will be found that if 

 we give the hypothetical axes a symmetrical position 

 in the solid, and consider their intensities as re- 



x I 



