of the Trimetric System. 49 



If, therefore, we compare the regular octahedron with the 

 rectangular octahedron that would result from the united domes 

 21 and 21 in the species of section I., we find them nearly iden- 

 tical. We observe, further, the important fact, that the axes of 

 the regular octahedron correspond to diagonals betvieen the apices of 

 the basal angles of the rectangular octahedron. But these axes in 

 the latter solid cross at oblique angles equal to the angle of the 

 rhombic prism I, instead of right angles; and they correspond 

 to lines between the centres of opposite lateral faces of the 

 rhombic prism, I, and not to those between the centres of its 

 opposite lateral edges. In other words, these lines are not the 

 crystallographic axes of the Trimetric system, but what the au- 

 thor has called the crystalhgenic axes. This is one reason allud- 

 ed to on a preceding page for believing that the crystallogenic 

 axes are not necessarily the same lines with the crystallographic. 

 The latter are lines assumed for the convenience of calculation. 



If instead of the domes li in section I., the species had af- 

 forded \i as common and dominant forms, and these were taken 

 as the unit domes, then the unit octahedron, in place of the domes, 

 would have the pyramidal angles near 109°, approaching those 

 of the regular octahedron. Could we therefore assume this as 

 the fundamental octahedron for the species, the derivation of the 

 octahedron from the regular octahedron would be a change in 

 the lengths only of the axes, and not in their angles of intersec- 

 tion. But this assumption would do violence to the facts. Still 

 in Antimony Glance, we have an example probably of this 

 form and mode of derivation; the dominant form is an octahe- 

 dron, with the pyramidal angles 109° 16' and 108° 10', and ba- 

 sal 110° 58'. Bournonite and Poly erase may be other exam- 

 ples of a similar nature, though diverging more in their angles. 



Although the two sections are strongly marked in the above 

 table, still the species of one may be regarded as homceomor- 

 phous with those of the other. Thus Chrysolite of Group II., 

 and Chondrodite of Group I., have been recognised by Scacchi 

 as homceomorphous. So also Andalusite and Topaz are essen- 



