266 Notices of Memoirs — Professor H, A. Miers on Crystals. 



that only those cubic crystals which display birefringence exhibit 

 divergence from the theoretical angles, but Brauns showed that 

 in lead nitrate, ammonia-alum, and spinel, for both isotropic and 

 birefringent crystals alike, the octahedron angle may differ by as 

 much as 20' from that of the regular octahedron. 



The author has endeavoured to trace the changes of angle upon 

 one and the same crystal during its growth by measuring it at 

 intervals without moving it from the solution in which it is growing. 

 This is accomplished by means of a new telescope-goniometer in 

 which the crystal is observed through one side of a rectangular glass 

 trough, and the changes in the inclination of each face are followed 

 by watching the displacements of the image of a collimator slit 

 viewed by reflection in it. The crystal is held by a platinum clip 

 which it envelops as it grows. Small movements of the image are 

 followed by means of a special micrometer-eyepiece which accurately 

 measures the magnitude and direction of the displacement. 



Examined in this way an octahedron of alum (ammonium or 

 potassium) is found to yield, not one, but three images from each 

 face ; and closer inspection shows that the crystal is not really 

 an octahedron, but has the form of a very flat triakis-octahedron. 

 It often happens that of the three faces which nearly coincide, one is 

 large and the remaining two very small, so that of the three images 

 one is bright and the others are very faint and can only be discerned 

 with difficulty ; in such a case the crystal as measured in the ordinary 

 way would appear to be an octahedron whose angle differs from the 

 theoretical value by a few minutes. 



When a growing crystal of alum is watched for several hours or 

 days, it is found that the three images yielded by an apparent 

 octahedron face continually change their position ; one set fades 

 away and is replaced by another set which are generally more 

 widely separated than those which they succeed. The images move 

 in three directions inclined at 120° to each other, and indicate that 

 these faces always belong to a triakis-octahedron. The point in which 

 the lines of movement intersect within the field of view of the 

 telescope would, therefore, be the position of the image reflected 

 from the true octahedron face. Measured in this way the octahedron 

 angle of alum is found to be the theoretical angle 70° 31f . 



The images do not move continuously, but per saltum, indicating 

 that the reflecting planes are vicinal faces which probably possess 

 rational indices, and must therefore be inclined at certain definite 

 angles to the octahedron face ; but the indices are very high numbers. 



Observations upon sodium chlorate, zinc sulphate, magnesium 

 sulphate, and other substances show that other crystals exhibit the 

 same behaviour. The faces of a crystal are in general not faces with 

 simple indices, but vicinal planes slightly inclined to them, and they 

 change their inclinations during the growth of the crystal ; they also 

 change their inclinations when the crystal is immersed to a greater 

 or less depth in the solution. 



Every point within a crystal has at some time been a point on 

 the surface, and has been subject to the conditions of equilibrium 



