654 REPORT — 1894. 



3. On a New Method of Measuring Crystals, and its Ajjplication to the 

 Measurement of the Octahedron Angle of Potash Alum and Amvionia 

 Alum. By H. A. Miers, 3f.A., F.G.S. 



The two fundamental laws of crystallography — namely, (1) the constancy of the 

 angle in crystals of the same substance, and (2) the law of simple rational indices — • 

 seem to be violated by those crystals which are liable to irregular variations in 

 their angles, or those which have the simple faces replaced by complicated ' vicinal ' 

 planes. 



Both these anomalies are exhibited by potash and ammonia alum. Brilliant 

 and apparently perfect octahedra of these salts show large variations in the octa- 

 hedron angle ; other crystals show low vicinal planes in place of the octahedron 

 faces. 



If it be trne, as is supposed, that the octahedron angle varies in different 

 crystals, it would be interesting to ascertain whether progressive variations can be 

 traced during the growth of a single crystal, and whether some or all of the octa- 

 hedron faces change their direction in space it the crystal be held fixed during 

 growth. 



In order to solve this problem a new goniometer has been constructed, in which 

 the crystal is fixed at the lower end of a vertical axis, so that it can be immersed 

 in a liquid during measurement. 



This device is in reality an inversion of the ordinary goniometer with horizontal 

 disc; the liquid is contained in a rectangular glass trough with parallel-plate sides; 

 one side is placed rigidly perpendicular to the fixed collimator, and the other is 

 perpendicular to the telescope, which is set at 90° to the collimator. The trough is 

 supported on a table which can be raised and lowered, so that the crystal can be 

 placed at any required depth in the liquid. If the liquid used be its own concen- 

 trated solution the crystal can be measured during growth, and the changes of 

 angle, if any, can be observed at diflerent stages. 



In order that it may be held rigidly, the cry.stal is mounted, when small, in a 

 platinum clip, which it envelops as it grows larger. 



The results derived from the measurement of a large number of alum crystals 

 are as follow : — • 



(1) The faces of the regular octahedron are never developed upon alum growing 

 from aqueous solution. 



(2) The reflecting planes (which are often verj' 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 unequal in size. 



(4) The triakis octahedron which replaces one octahedron face may be diflerent 

 from that which replaces another octahedron face upon the same crj'stal. 



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

 inclinations; the triakis octahedron becomes in general more acute, z'.c, deviates 

 further from the octahedron which it replaces, as the crystal grows. 



(6) This change takes place not continuously, but jjer 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 develop d : since these succeed one another ^)er saltum they doubtless 

 obey the law of riUional indices, though not that o( simple rational indices. 



From the mutual inrlinatioLS of these vicin-al faces it is possible to calculate 

 with absolute accuiacy the angle of the faces to which they symmetrically approxi- 

 mate. This angle is found to be that of the regular octahedron, 70° 31 1'. The 



