. 4)7. OF FORMS IN GENERAL. 39 



sphere ; and thus, it likewise acknowledges different degrees 

 of regularity. The degrees of regularity in Crystallography 

 are not the same with these. By the peculiar method of 

 treating its object, Crystallography is forced to ascribe the 

 same degree of regularity to forms, the angles of one of 

 which may lie in one, of another in two, of a third in three 

 different spheres, as to the hexahedron, to the monogram- 

 mic Tetragonal-dodecahedron (. 63.), and to the Tetracon- 

 ta-octahedron (. 77-) ; and it ascribes to others, as to the 

 Tetrahedron, a lesser degree of regularity, although its 

 angles altogether should be situated in the face of one and 

 the same sphere. 



. 47. DETERMINATION OF THE DEGREES OF 

 REGULARITY. 



The degrees of regularity of simple forms, are 

 determined according to the Kind and the Number 

 of their Axes. 



There are four degrees of regularity to be distinguished 

 in simple forms. 



Forms of the first degree of regularity contain four axes 

 of the first kind, three of the second, and six of the third ; 

 of the second degree of regularity, four of the first kind, some 

 of them at the same time three of the second, some three of 

 the third, some none besides those of the first ; of the third 

 degree of regularity, only one axis of either the first or the 

 second kind, and an undetermined number of axes of the 

 third kind ; of the fourth degree, three axes of the third 

 kind. 



Thus, first 436 



(430 



second 44 3 



(400 



third jj J undetermined, 

 fourth 003 



