( 369 ) 



Olivine and Talc. 



If () be tlie iiilerseclioii of (lie acute bisectrix with the globe of 

 projection (> = i, -1 'M\i\ H the |)r()jectioiis of the optic axes, /^^> the 

 axis of a zone, from which Z(ll> i-epresents an arbitJ'ary pUine with 

 its pole N, then, according' to Fkksnki,, the extinction on the plane 

 Z(2l), with respect to tlie zone-axis, is re[)resente(l by the curve Zc, 

 wheji the phme cN (li\i(l(>s the angle BNA into two equal parts. 

 Suppose we call -^ OQ, the inclination of the plane {jS!) with regard 

 to the acute bisectrix, r, and the angle of extinction with respect 

 to the zone-axis, ^^ Zc = ij, then, according to Michel Levy ^) the 

 value of // can be calculated from the equation : 



cot 2y = cot (aZ -f- bZ). 







Fig. 1. 



aZ—^ — / ANd, 

 2 ^ 



Now in the right-angled i\ANa' 



tq Ad 

 tijANd -^ 



cot II 



sin Nd cos [x -\~ v) 

 so that : 



t</ aZ = rot ANd ■=. tg (i cos {.v -}- y). 

 In the same way we tind : 



1) Les Miiiéraux des Roches, p. 9. 



25* 



