462 
PROFESSOR HENRY A. MIERS : AN ENQUIRY INTO 
It must be ol)served that two interpretations are possible :— 
(1) That the faces really have simple Indices, but are liable to irregular 
variations; 
(2) That they have not really simple indices, but are vicinal faces. 
Thus an octahedron whose angle is found to be. not 70° 31^ 44'', but 69 41', would 
on the first interpretation be an octahedron of which one or more faces are distorted 
from their true position by some unexplained cause ; on the second interpretation 
they would not be faces of the octahedron at all, but a vicinal form having the indices 
(65.65.64), of which each face is inclined at 25 minutes to the octahedron face with 
which it nearly coincides. 
In the simple case here contemplated it ought to be quite easy to distinguish 
between the two Interpretations, for the form (65.65.64) consists of, not 8, but 24 
laces, and eacli face of the apparent octahedron should yield, when measured on the 
o’oniometer, not one image of the collimator slit, but three images, due to three facets, 
each deviating by 25 minutes from the true octahedron face. 
Very careful observations upon the angles of cubic crystals have been made by 
several investigators. Pfaff pulihshed m 1878" an investigation on the variations 
of crystal angles, in which he found that angles wliich were known from the 
symmetry of the system might differ by 30 minutes from the theoretical value, or 
inio-ht auree with it to within 1 minute. He came to the conclusion that the 
variations of angle are related to the existence of optical anomalies, and that in the 
cubic system those ciystals which are birefiingent exhibit these variations, wliereas 
those which are isotropic do not. A natural deduction would be that the observed 
variations are the result of strain. 
Some years later this problem was proposed for a prize essay by the Philosopliical 
Faculty of the University of Marburg, and the inquiry was limited to crystals 
belonging to the cubic system; candidates were directed to measure isotropic and 
liirefringent crystals of the same substance with the view of ascertaining whether any 
such relationship exists. 
The prize essay, by 11. Brauns, was published in 1887.t He carefully measured 
octahedra of lead nitrate, of spinel, and of ammonia-alumina-alum, choosing both 
isotropic and birefiingent crystals, and came to the conclusion that there is no 
difference between the angles of i.sotropic and birefiingent cubic crystals. Of 120 
measured angles (on 15 crystals) 86 gave a deviation of 5 minutes or less, and 63 a 
deviation of more than 10 minutes. The largest deviation from the theoretical value 
was 19'20"; the largest deviation for the angle as measured between laces which 
gave very perfect images was 13' 20", in the case of a crystal of lead nitrate. 
Brauns further made an interesting suggestion regarding the cause of these 
* ‘ Sitzungsber. d. Fhysik. Med. Soc. zu Erlangen,’ Heft 10, p. 59. 
t ‘ Neues Jahrbuch,’ 1887, (1), p. 138. 
