the planes composing the pyramid of fig. 11. It will hereafter be shewn in describing the apparently dodecahedral macle, fig. 188. that it results from a section of the prism, both in the direction described by L'hermina, and in the opposite direction. Let these sections be described by the dotted lines, b g d h and f g c h, fig. 11.
Now, it may be noticed that by a practicable cleavage each way through the centre of a crystal similar to fig. 11. but parallel with the planes of the prism, it is divisible into four parts, similar in form to the fracture described by fig. 9. On one of these portions similar to that figure let the sections given on fig. 11. be represented by the lines b g d h and c g d h, fig, 12. and it will be seen that a b c d on that figure will represent a fracture similar to fig. 4. If this be pursued still further it may be observed by representing the lines of section b g d b fig. 12. on fig. 13. that by the parallel section b c g, a tetrahedron a b c g is obtainable.
The fragments represented by fig. 8. were obtained by a cleavage of others represented by fig. 4. in the direction of its diagonal c i f. If therefore a section of fig. 9. be made in the direction of that diagonal, one portion of that figure so divided, will agree in form with fig. 14. which figure exactly corresponds with one fourth part of a crystal represented by fig. 15. by a section along the edges both of the prism and the pyramids, the planes PP and b resembling each other. The planes PP and b' fig, 15. also correspond with those of PP 6, fig. 16. which planes are usually supposed to arise from a decrement on the edges of a crystal similar to fig. 27. Pl. 16.
I presume it has been satisfactorily demonstrated, that by the fractures represented by rigs. 4, 5, 6, 7, 8, and 9, Pl. 15. a mechanical division of the oxyd of tin is unquestionably obtainable, parallel with the planes of the prism, as well as, by figs. 5, 7, and 8,