The Crystallography of Anatase Crystals. 
301 
These results again represent averages of several readings obtained on 
four different individual crystals. The greatest divergence from the 
average (120° 33') obtained in any one reading was +7'. 
From this angular result and the axial ratio we derive for this 
Second-Order Pyramid the symbol (101). 
Forms other than (111) and (101). 
The minuteness of the remaining faces mentioned above necessitates 
one's being satisfied with measurements of angles taken with the telescope 
focused on the crystal face to observe the flash of the reflection from the 
faces, too minute to give efficient Schrauf signals. Consequently for each 
face the mid-position between angle readings taken (1) just when the flash 
begins to be observed, and (2) just when it is about to disappear, must be 
taken as indicative of the position of the face-normal. The accuracy of 
these angles is therefore of a lower order than in the previous cases, but 
several measurements were taken and the error of each of these averages 
is probably well within the limits of + 1°. 
The position angles of the forms obtained in this way, together with 
the two forms already described, were observed in terms of Goldschmidt's 
angle co-ordinates," </>, p, and for purposes of comparison and identifica- 
tion of these forms Goldschmidt's standard values of 0, p, in each case 
together with the corresponding Miller Symbols and Dana face letters, are 
given in parallel column. 
Face 
Letter. 
Miller 
Symbol. 
Goldschmidt's 
Standard Values. 
Values obtained on 
Johannesburg Crystals. 
Differences 
from 
Standard. 
P- 
p 
<P 
p 
V 
Ill 
45° 
68° 18' 
45° 
68° 18' 
e 
101 
0° 
60° 38' 
0° 
60 17'° 
0° 21' 
c 
001 
0° 0' 
0 0'° 
l.l.U 
45° 
10° 10' 
45° 
9 50'° 
0° 20' 
V 
117 
45° 
19° 44' 
45° 
19 40'° 
0° 4' 
I 
331 
45° 
82° 26' 
45° 
82 47'° 
0° 21' 
X 
5.5.11 
45° 
48° 48' 
45° 
49 8'° 
0° 20' 
? 
021 
0° 
74° 17' 
0° 
74 2'° 
0° 15' 
The form q was observed on only one of the crystals examined, while 
the other forms were observed on all four crystals. 
* Goldschmidt, " Kristallographische Winkeltabellen," pp. 3, 39. Berlin, 1897. 
