September, 1918] 



The Ottawa Naturalist 



51 



It will be noted that the Miller- Bravais symbols 

 used in this table are not the same as those given 

 in the Winkeltabellen for the corresponding angles. 

 This IS due to the difference of orientation, Gold- 

 schmidt using for the tourmaline an orientation G.. 

 in which the crystal has been turned 30 around 

 the vertical axis, from Dana's orientation Gj. 



If ghkl and g'h'k T are the Miller-Bravais symbols 

 of a certain face, respectively in the orientations G, 

 and G^, those symbols are related by the following 

 equations: 



g = h'-k' 



h = k'-g' 



k = g'-h' 



Example: g'h'k'l'^ 1 120 

 g=l+2=3 



h = 2 1=3 

 k=I 1=0 

 1 = 



ghkl = 3300 =1100 

 The calculated angles of Goldschmidt are based 

 on Miller's ratio c = 0.4477. The tourmaline from 

 Baffin Land has a slightly different parameter. We 

 may calculate this from the measurements made on 

 the terminal faces, which gave very good or good 

 reflections, by applying the formula: 



The results are indicated in the following table: 



In order to calculate the average value of c, we 

 omit the exceptional value found from the measure- 

 ments made on face 27 and take the average of the 

 first six values of c. This leads us to: 

 c = 0.45216 : 



Such a high value of c indicates that the tourma- 

 line from Baffin Land probably contains ferric oxide 

 Fe.O,, a fact that is emphasized by the dark green 

 color. Tourmalines containing alkalis, magnesia 

 or ferrous iron show a vertical parameter smaller 

 than 0.45 and their color is lighter. A chemical 



analysis could not be performed on account of the 

 small dimensions of the crystal. 



The correspondence between the measured angles 

 and the calculated angles of Goldschmidl is as a 

 whole satisfactory ; nevertheless some k and u faces 

 gave poor reflections due to natural corrosion figures. 

 In such cases the difference between measured and 

 calculated angles become abnormal. 



I am greatly indebted to Professor T. L. Walker 

 and Professor A. L. Parsons for valuable sugges- 

 tions and assistance in many ways. 



