Notices of 3femoirs — S. A. Miers — On Measuring Crystals. 519 



(2) The reflecting planes (which are often very perfect) are those 

 of a very flat triangular pyramid (triakis octahedron), which overlies 

 each octahedron face. 



(3) The three faces of this triangular pyramid may be very un- 

 equal in size. 



(4) The triakis octahedron which replaces one octahedron face 

 may be different from that which replaces another octahedron face 

 upon the same crystal. 



(5) During the growth of the crystal the reflecting planes change 

 their mutual inclinations ; the triakis octahedron becomes in general 

 more acute, i.e. deviates further from the octahedron which it re- 

 places as the crystal grows. 



(6) This change takes place not continuously, but per saltum, each 

 reflecting plane becoming replaced by another which is inclined at a 

 small angle (generally about three minutes) to it. 



(7) During growth the faces are always those of triakis octahedra; 

 if, owing to rise of temperature, re-solution begins to take place, 

 faces of icositetrahedra are developed. 



Conclusions : — The above observations prove that the growth of an 

 alum crystal expresses an ever-changing condition of equilibrium 

 between the crystal and the mother liquor. It does not take place 

 by the deposition of parallel-plane layers ; new faces are constantly 

 developed : since these succeed one another per saltum they doubtless 

 obey the law of rational indices, though not that of simple rational 

 indices. 



From the mutual inclinations of these vicinal faces it is possible 

 to calculate with absolute accuracy the angle of the faces to which 

 they sj^mmetrically approximate. This angle is found to be that of 

 the regular octahedron, 70° yif . The octahedron angle of alum is 

 not, therefore, as appeared from the observations of Pfaff and Brauns, 

 subject to any variation. 



The angle at which a given vicinal plane is inclined to the 

 octahedron is independent of the area of the plane, and of the 

 temperature of the solution, and of the barometric pressure : it 

 appears to be conditioned by the concentration of the solution at the 

 surface of the plane. 



In confirmation of this view it is found that the upper and lower 

 portions of an octahedron face which stands vertical are often re- 

 placed by two different triangular pyramids ; also that the three 

 faces of one such pyramid are, at a given moment, not necessarily 

 equally inclined to the octahedron face which it replaces. 



When, as is often the case, one of the three vicinal planes is large, 

 and the other two are too small to give a visible reflection, the face 

 appears to be a single reflecting plane. It is this which has been 

 mistaken for the octahedron face in previous observations. 



Similar phenomena of growth are exhibited by crystals of other 

 substances belonging to different systems. The conditions of equi- 

 librium between the crystal and the solution are such that vicinal 

 planes appear in place of simple forms; these vary with the 

 concentration of the solution, and give rise to variations in the 



