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83 



Example. - Tin- ;ixi:il ratio of zircon is calculated directly from 

 the pyramid of the second order (101), Fig. 147; the angle cao is 

 found l>v mra.-uivmcnt to be 

 18' I", in the triangle coa 

 right -anglc-d at o. Tan cao = 



CO 



, but oc = c and oa = a; tan 

 a 



cao = - = .6404. In the tetrag- 

 a 



onal system the lateral axis a 

 -umed as the unit of meas- 

 urement, therefore c = . 

 is the axial ratio of zircon. 



When the pyramid of the first order is the fundamental form 

 in which the angle is measured (111), Fig. 148 at a', at right 



oc 



FIG. 147. Zircon, (101). 



angles to aai ; tan ca'o = 



oa 



oc = oa' (tan ca'o), also oa' = 

 a' ai = aai = \ V2. /.c=jV2 

 (tan ca'o). 



In rutile ca'o is 42 10'. 

 Log tan 42 10' = 9.959616 +10 

 Log ^V2 = 1.849485 

 Log c = 9.809101 -10 

 c = .644 + , the axial 

 ratio of rutile. 



When the axial ratio is 

 known, it is an easy problem to calculate the value of the variables 

 m and n in any set of parameters ; thus in rutile there is a pyra- 

 mid of the second order in which the angle corresponding to cao, 



Fig. 147, is 78 15' ; tan 78 15' = - = - = 4.8 or nearly 5 ; its pa- 



a i 



rameters- would be (a : oo a : 5 c), and indices (501). 



FIG. 148. Cassiterite, (111). 



