128 



MINERALOGY 



measured directly, being the angle between the base and the 



orthopinacoid. 



Four angles are sufficient to determine the elements: ( 100 A 001), 



(101*100), (001 A Oil) and (110,100). 



Calculations. When p is not measured directly, generally 



(001 A 110) and (110 A 1 10) can 

 be obtained, Fig. 258. In the 

 right-angled spherical triangle, 

 right-angled at A, the two angles 

 8(001*110) and 0*1/2(110*110) 

 are known, the two sides c and 

 b can be calculated. C is the 

 angle of the right-angled triangle 

 of which a is one leg and b the 

 other, also p = 180 - b. 



Example. In orthoclase the 

 angle (001*110) = 67 47' and 

 the angle (110 A 110) = 61 13'; 

 as these are the angles between 

 the poles, in each case subtract- 

 ing from 180, B in the spherical 



triangle = 112 13' and C = 1/2 (118 47'). 



FIG. 258. 



COS b = 



cosB cos (112 13') 



sin C sin (59 24') 

 Log cos 112 13' = 9.577618 

 Log sin 56 24' = 9.934783 

 Log cos b = 9.642745 

 b = 116 3'. 

 P =180 - (116 3') = 63 57'. 



The axial ratio. In the spherical triangle ABC, with the side 

 b and the angle C known, being right angled at A, the side c is 

 calculated by Napier's rule. 



= sin_b = sin (116 3Q 



cot C cot (59 23' 30") ' 

 Log sin 116 3' = 9.953475 

 Log cot (59 23' 30") = 9.772312 

 Log tan c = 10.181 163 

 c = 5637'. 



