THE VAEIATION OF ANGLES OBSERVED IN CRYSTALS. 
475 
wire oy, and the other two on the lines oa and o/3, which make an angle of 120° with 
oy in the field of view (fig. 12). This is a fact which is readily established by means 
of the micrometer eye-piece; the changes of the images, for example, during the 
growth of the crystal can be easily followed by the movable cross-wire when it has 
been adjusted so as to run along the line oa. This affords an even safer method of 
ascertaining the reading corresponding to the true octahedron face o ; for after it has 
been found that tlie images from the vicinal faces travel along the lines ao, jBo, and 
yo, making angles of 120° with each other, tlie reading for the true octahedron is 
known to be that corresponding to their intersection o. 
When examined in this way the two adjacent octahedron faces of potash-alum give 
readings which differ from each other by the true octahedron angle 70° 31|' within 
errors of observation; it has thus been possible to measure with accuracy the 
octahedron angle of potash-alum, although the faces of the octahedron are not 
themselves present. It is not necessary to multiply examples : other crystals led to 
the same result as that just described: namely, that the octahedron angle of potash- 
alum is not liable to any variation, but that the octahedron faces themselves are 
absent and their place is supplied by vicinal planes belonging to triakis-octahedra 
which are liable to continual variations. 
(G.) The Nature of the Vicinal Faces on Potash-alum and Ammonia-alum. 
In the course of the present research many attempts were made to discover some 
regularity in the angles or in the indices of the vicinal faces. That they possess 
rational indices is rendered possible by the established fact that they lie in certain 
well-defined zones, but the indices are in that case very complicated. A very well- 
defined set of faces, for examjile, on one crystal represented a triakis-octahedron 
inclined at 6' 7" to the octahedron; its symbol would, therefore, be {hhl), where 
A — 1-00378, or something approaching (251.251.250); but it is impossible to say 
whether these are the indices to be adopted, or some other numbers having nearly 
the same ratio. Clearly the indices cease to be of much use when they are such 
3 P 2 
