47G 
PROFESSOR HENRY A. MIERS: AN ENQUIRY INTO 
high numbers, and tlie position of tlie faces can be equally u-ell and conveniently 
represented by their angles. 
In a paper on the vicinal faces of celestite (‘Zeits. f. Kryst.,’ XL, 1886, p. 220), 
Hintze suggested that their relations are better expressed by the angles that they 
make with each other than by the indices to which they can be referred ; and, in fact, 
that they do not necessarily possess rational indices. 
Whether this he so or not, it will be safer for the present purpose to define the 
vicinal faces of the growing alum crystal by their actual angles than by their possdfie 
indices. One reason why I am led to believe that they are really referable to rational, 
although not to simple, indices is the following During the growth of the crystal, 
one set of vicinal faces is being continually replaced by another along certain zones ; 
each image of the collimator signal fades away like a dissolving view and another 
makes its appearance ; but the change is not gradual, neither are the surfaces cum ed ; 
one plane reflecting-surface is replaced by another plane; and although the images 
may for a time he multiple and confused, sharply defined images emerge successively 
by the substitution of one image for another saltum. 
This extremely important fact is illustrated by some of the 
examples quoted above, and instances might be multiplied 
to any extent. 
It is sufficient here to record the well-defined faces which 
have been observed during the experiments upon potash- 
alum and ammonia-alum. 
If a, (B, y (fig. 12) he the three images obtained from 
three facets belonging to the same form, then if o be the 
position of the image which would be yielded by the ideal 
octahedron face, the readings actually made in the course of the observations 
are;— 
(1) That for which y coincides with the vertical cross-wire; 
(2) That for which a and /3 simultaneously coincide with the vertical cross-wire. 
The difTerence between these readings is nearly the angle between y and the face 
which would truncate the edge ; if this face be called /r, the angle between 
y and o, i.e., the inclination of the vicinal form to the true octaliedron, is given by 
tan oy ~ 2 tan o/x. 
For very small angles oy may be taken as f y/x. The best readings obtained on a 
large number of crystals were the following . 
