( i2^ ) 



Fig. 1. 



included by the traces of the phiiies V^ and I^^ with the tictive 

 trace S: T {= OG) in the slide, will be given by : 



cos Otg \\ — sm ö cos (q — n^) 



cot /t, ::= 



vot h 



sin {q — fij) 



cos Ö tij r J — sin <1 cos {q 



!*,) 



!^,) 



(1) 



(2) 



8171 {q 



whilst the optic extinction t/ := / EOG, with regard to (he Irace 

 S : T, can be found from the relation: 



1 — shf V COS' Q — (1 — sin'^ V sin^ q) sin' G 



cot 2y = 



{'■'>) 



sin 2^ sin o sin'^ V 



in wiiicli V represents half the axis-angle (= \ --- AB). 



In the slide one can oidy measure the angle ti between (he (races 

 of the planes V^ and V.^, and likewise (he extinc(iou-angle ,:? wi(h 

 regard to one of these traces e.g. of 1^,. If one introduces for 

 A, and // the values h., :=: h^ -\- a, j/ z= h^ -\- 1^, then in the erpiations 

 (1), (2) (3) besides q and o only A, appeai-s as unknown, which can 

 be eliminated. Trying to solve the two equalions by algebi-aic-gonio- 

 metric methods in order to lind 'j and <>, one however meels widi 

 unsurmountable diflicuhies, so (hat one has to recur to a gra|)hical 

 method. 



The latter may be demonstrated by a concrete case. 



In tig. 2 (he partial projecdon of an oligoclase-crystal of B.\mi,k 

 is represented. A and fJ are the loci of the o[)tic axes, a and c tiiose 

 of the obtuse resp. acute bisectrix ( P'"--=4(^°35'1Ö"). 



Be E a plane, applied ± on the bisectrix .'.(>; if now one measures 



