( 372 ) 



valiios of i(^ Iviii.u' hotwppii O and , : il Ix'conics posilivc, liowoAor tor 



- <^ ,( <^ -r >vliilsl llio absolute valiu's of // are CMiiial for Iwo i)oles, 

 2 ^ ^ 



lying' syninietrically with regard to tiie plnne H<>. 'V\\q same thing 

 liolds good tbr th(^ c-xtinclion on |thines, lyijig syninietrically with 

 reo-ard to tiie i)lanc ()l\ so that the isogyres (h-awn n|K)n tiie globe 

 will lie syninietrically with respeet to the planes l{( >, OP and also 

 UP. Just as the symmetry with regard to IK) and OP is accom- 

 panied by a change of sign, so also for the i>lane IIV. 



The extinction with i-egard to the variable zone-axis OZ is easy 

 to reduce to that with respect to the acute bisectrix, as the latter 



is yielded by /_ ONc = ^ Qc — ^^ — y — y' ■ 



cot 2y =: cot {jt — 2y') = — cot 2//'. 

 from which follows according to (3) 



A 



cot 2ii' = : B sin .v (6) 



sin .^' 



in which : 



cos^ ft -\- sin"^ n cos^ y 



.4 = 

 B = 



sin 2(1 sin y 

 sin^ fi 



sin 2;i sin y 



For the determination of the greatest extinction \vitli regard to 

 the acute bisectrix with x = constant and a variable angle «, we 

 may set about as follows'). If we caW ^ AN O = i^\ ^Bi^O = ly', 

 we find from the triangles ANO and JJXO 

 sin /^ AON _ 



til If? = - 



sin ON cot V— cos ONco^ /^ xWN 



sin V cos a 



cos X COS V — sin x sin V sin a 

 and 



sin V cos a 



COS V cos X, -\- sin V sin x sin a 

 No\v 2y' = ip — xp' 



— 2 sin'' Vsin a cos a sin x 

 'y y = ty ( ip — If' ) = .;7„2 p^.^,. ^^_^^o.?^ Vcos"" x—sin^ Vsin"" (( sin' x ' 

 which gives : 



I) A. Harker, Mia. Mag. XllI, 1903, p. 66—67. 



