and in some instances I obtained perfect co-incidences by the reflecting goniometer between the faces P and a fig. 9. and those of P and a, fig. 11. having eight fractures of the figs. 4. and 9. which permit the use of that goniometer.
On three fragments similar to fig. 9. I have attempted a mechanical division in the direction of the small planes a f c fig. 10. and have succeeded in obtaining one or the other on each, so as to warrant the conclusion of the practicability of the whole. It will be noticed that if a division were still pursued in the direction of the planes a f e, the consequence would be that the planes on the summit of fig. 10 would become in form similar to those of P P fig. 11.
The cleavages obtained by the planes a f c demonstrate the possibility of a mechanical division parallel with each terminal face of a crystal similar to fig. 11. The probability of this in two out of the four directions may be argued from what is known respecting the formation of the macles of this substance.
It was long since determined by L'hermina that the common macle represented by fig. 186. Pl. 24. as will hereafter be further noticed, is the result of a section of a common prismatic crystal, fig. 27. Pl. 16. in a direction parallel with one or the other of the edges of its pyramid. The planes forming the pyramid of fig. 11. Pl. 15. are usually considered to be the effect of a decrement on those edges, but the reverse is the fact; for, by figs. 18, 19, 20, 21, 25, 26, 27, it will be seen that the pyramid of fig. 27. is the result of a modification of the primitive crystal described by the planes 2,2 on fig. 22; and it will be equally obvious that if the section determined by L'hermina be parallel with one or other of the edges of the pyramids of fig. 27. it must also be parallel with one or the other of the planes of the primitive octahedron, consequently with one or the other of