Sl^ Rev. W. Mitchell^ on Crystallography. [March 18, 



traces formed by an imaginary plane passing through the zones of the 

 sphere and its centre. It will now be seen that the cubical axes join 

 the opposite solid angles of the octahedron ; the rhombic axes, the 

 bisections of its opposite edges ; while the octahedral axes pass through 

 the intersections of the elastic cords, which join each solid angle of the 

 octahedron with the centres of the edges opposite to it. 



The points where the elastic cords meet, and the octahedral axes 

 pass through the faces of the octahedron are now fastened to cords. 

 1'hese cords are made to run round pulleys and are united together, so 

 that by pulling them simultaneously, the points uniting, every one of 

 the three elastic cords which are described on the the face of the 

 inscribed octahedron can be made to travel uniformly and symmetri- 

 cally along each of the octahedral axes from the face of the octahedron 

 to the solid angle of the circumscribing cube. Another series of cords 

 are united to each of the four elastic cords, which meet at the point 

 bisecting each of the edges of the inscribed octahedron. These, by a 

 similar contrivance, are made to draw these points along the rhombic 

 axes. The instrument is now completed. By simply pulling the 

 eight cords united together, which cause the elastic cords to ascend the 

 octahedral axes, the inscribed octahedron passes through every form of 

 the three faced octahedron till it reaches the limiting form of the rhom- 

 bic dodecahedron. Each three-faced octahedron being inscribed within 

 the cube, inscribed within the sphere. 



In a similar manner, by pulling the cords, running along the 

 rhombic axes in combination with those running along the octahedral 

 axes, all the other forms are shown as passing within their prescribed 

 limits. As soon as the cords are loosened, the elastic bands immediately 

 resume the form of the inscribed octahedron. In addition to these 

 forms, the instrument also can be made to demonstrate the passage of 

 all the hemihedral forms of the cubical system with inclined faces 

 within their limits. In this manner it was demonstrated that this 

 instrument can make visible to the eye all the changes and varieties of 

 an interesting series of forms and their mutual relations, which could 

 otherwise only be conceived by a considerable power of mathematical 

 abstraction. This armillary sphere, by some other small additions, can 

 be made use of for tracing out some of the most beautiful portions of 

 the zone-theory of the poles of crystals. 



[W. M.] 



