( 382 ) 



great the extinction is with regard to the trace of a cleavage plane. 

 For this, if the angle of extinction with regard to the acute bisectrix 

 he known, is oidy necessary Ihe value of the apjuxrent angle between 

 the trace mentioned and the same bisectrix. One value need only 

 be subtracted from the other. 



If ZZ' be the axis of a zone, in which ZQZ^ represents an arbi- 

 trary plane, N the corresponding pole, and l)c the plane determined 

 again by a and OQz^x; if UWU' be an arbitrary cleavage plane, 

 determined by io and W() = y, then VO is the line of intersection 

 of both planes, \ Q=^ /^ QNV =^ 0, the apparent angle between 

 the acute bisectrix [(J) and VO. 



Now VQ = — — VZ, and in A VUZ is 

 2 



So 



cot VZ = tg 6 



sin («J — «) 



If we apply this formida to the cleavage planes h^ (J 00) and^(/^ (010) 

 of olivine, then with 



h' (100) ... to ::=: , ,y = 



./^(OlO) .... to=='^,// = 



and (1 1 ) passes into : 



t(j & z:^ sin X t(j a 

 tg 6" -=■ — sin X cot a 



in wiiich S' and 6" are successive!}' the apparent angles between 

 the traces of y' (010) and h' (100) on the plane (.Y). 



Now if we (hiidv both ,/• and a to vary between and — , we 



find Ihe followinjj: values for ^' and 6*": 



