THE VARIATION OF ANGLES OBSERVED IN CRYSTALS. 
487 
10.30 P.M. ; t = IG'5° 
m 
M 
J 103° 3', 
1102° 50', 
f 12° 32V, 
\ liras', 
I 17', 
f 283° 8', 
[282° 55', 
M' 192° 17'. 
ni 
Tlie value generally given for the prism angle of magnesium sulphate is 00° 35'. 
The above observations indicate vicinal planes belonging to prisms whose angle would 
differ from this by more than 20'. 
I have given these two examples from the orthorhombic system in order to point 
out liow the mean of a number of measurements may with crystals of comparatively 
low symmetry give a result very far from the truth. In alum, although the true 
octahedron angle might never he observed, the mean of a sufficiently large number of 
measurements would probably give the exact octahedron angle, for the three vicinal 
planes which replace the octahedron face are, hy the symmetry oj the crystal, inclined 
to it in three different directions, so that some of the measured angles are too large 
and some too small. But in the case of a rhombic prism, each face would, in 
accordance with the symmetry of the crystal, he replaced by only one vicinal plane, 
and the prism angle, as measured, would Ije consistently either too large or too small, 
'j’he true j)osition of the prism face could not he ascertained, as that of the octahedron 
face was in alum, by the convergence upon it of three zones of vicinal faces, and by 
the limit to which they tend. 
To determine with absolute accuracy the true angles of such crystals it would be 
necessary to study tlie variations of their vicinal faces in the manner described above 
—hut hy means of a two-circle or three-circle goniometer. 
A number of observations were also made upon crystals of sodium arsenate as an 
Example of a substance belonging to the monoclinic system : l3ut since they do not 
affect the general results they are not described in the present paper. 
(8.) The Efeegt on Alum of Diluting the Solution. 
During the experiments descriljed in this paper there were naturally many 
occasions on which the crystal was not growing in a saturated or supersaturated 
solution, hut was being cori'oded by a more dilute medium, and in such cases it was 
sometimes possible to obtain quite good reflections from the prerosion faces ; several 
experiments were also made in which the solution was purposely diluted or warmed 
in order to observe the etched faces. 
