DOUBLE REFRACTION IN ISOMORPHOUS SUBSTANCES. 269 



with the inferior and superior base. The other crystals were 

 very thick ; and all the inferior and superior lateral edges pre- 

 sented the same facettes, accompanied by others, forming with 

 the same bases angles of 130° 15' and 105° 50'. 



These different systems of facettes tend to the formation either 

 of rhombohedrons or of birhombohedric isoscelohedrons, the 

 principal axes of which bear the same proportions to each other 

 as the numbers 2, 1, ^, |. 



It is impossible to measure directly the indices of refraction 

 of these three salts ; but the circular rings may be easily ob- 

 served through the natural bases. The optical axis of the hy- 

 posulphate of lime is that of maximum elasticity, as is the optical 

 axis of the hyposulphate of strontia. The optical axis of the 

 hyposulphite of lead is that of minimum elasticity. 



Crystals with Two Optical Axes. 



Right prismatic system with a rhombic base. 



Sulphates of magnesia and zinc. 

 Chromate of magnesia. 



BOR03 + 7H^O. 



All these salts crystallize in right rhombic prisms of about 

 90° 38' with one of the faces of truncation at the acute edge of 

 89° 22', parallel to an easy cleavage. They bear on their sum- 

 mits only the faces of an octahedron with a rhombic base 

 127° 22' and 126° 48', resting upon the horizontal edges of the 

 prism, rarely truncating faces of the obtuse edges of this octa- 

 hedron, which form with each other an angle of about 120°. 



The plane of the optical axes is parallel to the rhombic base ; 

 the bisecting line is parallel to the major diagonal of this base. 

 When, therefore, the faces of the prisms 120° and 60°, which 

 truncate the obtuse edge of the octahedron, are placed vertically, 

 by which means the plane of easy cleavage becomes parallel to 

 the new base, the plane of the optical axes will be parallel to 

 the major diagonal of this new rhombic base and to the height 

 of the prism, the bisecting line parallel to this height. 



I have measured the apparent angle of the optical axes as seen 

 across the parallel faces of easy cleavage, and the indices neces- 

 sary for deducing the true interior angle. 



