THE VARIATION OF ANGLES OBSERVED IN CRYSTALS. 
519 
The crystal was re-immersed at 7.45 P.M., and allowed to rotate during tlie whole 
night. 
Next morning at 9.30 a.m., t = 11°, it was measured again and gave upon another 
octahedron face 
a : C,, = 0° 371', 
these readings being again very good. 
The same crystal was re-immersed at 3.30 p.m., t = 17°, and the trough was set 
rotating. 
At 9.0 P.M., t = 10|-°, it gave 
a : C,, = 0° 391', 
the readings being very good. 
The corresponding readings for the other vicinal forms were :—• 
On A 
) 5 
? ? 
B 
D 
Before rotation. 
0° 32' 
0° 311' 
0° 3-3' 
After rotation. 
0° 331' 
0° 31' 
0° 29' 
As a result of these experiments it may be asserted that, in alum at any rate, the 
vicinal faces are neither produced nor appreciably affected by the concentration 
streams in the solution. 
The vicinal faces may, however, vary with the average concentration of the 
solution in their neighbourhood, or—what may amount to the same thing—with 
their rate of growth. In fact, it is difficult to think of any other nearly constant, 
but slightly variable, condition to which they may reasonably be attributed. In any 
case, the fact to which I wish to draw attention is that the faces which actually occur 
upon a crystal are not those with simple indices and great reticular density, but 
those with complex indices and low reticular density. 
The faces of alum whose angles were measured by Brauns, and whose rate of 
growth was measured by Weyberg, were, therefore, not octahedron faces at all, hut 
vicinal faces, and in the arguments relating to them we are not at lilrerty to assume 
that they are faces of high reticular density. 
Whatever structures may be necessary to account for otlier features of crystals, 
there is little doubt that we are justified in regarding their faces as the planes of a 
space-lattice. Now there is one remarkable property of the space-lattice which bears 
closely upon the present problem. In general, two planes of tlie lattice which are 
nearly coincident in direction are by no means alike in other respects. In the cubic 
lattice, for example, the cube face is the most dense, and the faces which approximate 
most closely to it in density are not the planes which most nearly coincide with it 
