( 371 ) 



becomes = "- for ;ill values of k, iiiul tlie same thing' takes place 



with « = for all values of ,v\ ('Onsequeiitly on all planes parallel 

 to the acute or to the obtuse bisectrix the extinction with respect 

 to these bisectrices is straight. If the direction of the mean 



index of refraction {^JR) becomes zone-axis, with a = , a certain 



particularity shows itself. For this . value of n (4) assumes the 

 following form : 



1 / 1 — sin'* V 1 sin x 



cot 2ir— -r-^ r^-j7 — • h "r^^r 



Sin 2« \^ .si?r V sm x sin' V 



(2a=7Ti 



1 / cos^ V sin X , 



+ ^7^A ■ • • ■ (5) 



sin 2a \ sin'' V . sin x siji' V 



(2«=:t) 

 Jt 



For .1' = becomes y = ~. 



Li 

 Jt 



For .y = ^ V (5) changes into 



' Li 



1 / cosV cos V\ 



cot 2.V = -^-— — — + 



sin 2a \ sin'' V si7i^ VJ 



// becomes indefinite; the pole JSf of the plane at this moment 

 coincides with an optical axis. 



Jt n 1 "^ 



Finally for .i; =z - u becomes= . ho the extinction is - for a 



' 2 ^ 2 



Jt - 



value of .V between 0° and V, next becomes indefinite and re- 



2 



mains 0° for x = V to -, as the sign for cot %i shows 



9 9 ° ■' 



Jt ^^ Jt 



2'' 



As to the values of // in general, the following may be observed. 



Jt 

 In (4), if — ^y^^ is assumed, is always 



Li 



1 2> 1 — si'>^'^ V sin'' « ]^ 

 1 > 1 — sm' V cos' « > 



For a given value of a cot2y keeps the same sign, if 6' varies 



betweeii and jt ; it gets, however, negative values for ,v between 



and — Jt. If we confine ourselves to a variation of ;v between the 



Jt 

 limits and - , then the sign of cot 'ly becomes negative for the 



Li 



