112 MINERALOGY 



Example. Sodium periodate, NaIO 4 , 3 H 2 O, crystallizes in trig- 

 onal hemi pyramids. Fig. 215 is a combination of two plus upper 

 hemipyramids of the second order and one of the first order with 

 the lower base. 



Crystalline Characters 



Like the tetragonal system, the hexagonal system has but one 



4 & 



variable crystalline character, the axial ratio, -.-This is calcu- 

 lated in a similar way, by means of the angle between the basal 

 pinacoid and the pyramid face of the first or second order. 



I. When the pyramid of the second order is used, 



/ 



- = tan (oooi) A (ii22). 

 a 



Example. In the mineral beryl, the angle between the normal 

 to the base and that of the unit pyramid of the second order is 26 



31', - = 0.4988+ , and as a = 1, c = 0.4988 + , which is the unit 

 a 



of measurement on the c axis. 



II. When the pyramid of the first order is used, 



- = tan (0001)*(1011) X 1/2V3. 

 a 



Figure 216, CO = c and 

 OA = a = i. 



tan CDO = ^ ; 



CO = tan CDO X DO. 



In the triangle aDO, right- 

 angled at D, and DOa = 30, 

 Fi<T2i6. DO = 1/2 V3, then c= tan CDO 



X 1/2 V3, but the angle CDO 



is equal to the angle between the poles of the base and the unit 

 pyramid of the first order, (0001J011). 



In the mineral beryl the angle OOOlJOll is 29 56', 



c = tan 29 56' X 1/2V3. 

 Log tan 29 56^= 9.760272 + 10 

 Log l/2y3"= 1.937530 

 Log c + 10 = 9.697802 

 c= .4988 + 



