274 Mr. A. S. Percival : Method of 



Table IV. (Bispherical Lens.) 



First Surface. 



/- N ■ a -\ ■ 



(1.) sm <p 1 = sin 



(ii.) /P 1 =r 1 cos^ 1 '- 



fii\ sec 9 1 -{-fxa l sec t p 1 —a l sec <p x ' 



Second Surface. 



(1) sin 2 = - {(^i + ^- 5, 2 ) sin^i-^i'-^O+^i sm r '> 

 sin (0-, — 0i'+0 2 ~^i)~ r i s ' n (0i -^i) 



(2) ^P.: 



8111(^-0/-^) 



(3) tan0 o = r » nn »» ■ 



- r 2 cos 2 — / P 2 



(4) /C 2 or a 2 = — r 2 sin 2 cosec 2 . 



(5) ji? 2 =— r 2 s'm<f> 2 '. 



(H 



2 



3. 



(I.) VP., or i7=r„cos0 '+ 5—; — 2 2 



K J 2 2 r2 /- 2 sec0 2 + « 2 sec0 2 — jua 2 sec <p 



) p=?7 J x _ ( r 2 sec ^ 2 ) 3 -+ (a 2 seo <t> 2 r-(fia 2 Bec 2') 



2 I (r 2 sec 2 +a 2 sec0 2 — /i« 2 sec0 2 ') 3 



Plane Wave-Front : Incidence Normal: x and a x do not appea 



/- \ f-O ± t * r i • jU^COS-0/ 



(1.) /p —r, cos 0/-f — — , , or — L . — - 1 



v ' 1 1 ri /xsec^ 1 — sec X ' /*cos X ' -COS0! 



(1) sin 2 = — {(»*! + £ - r 2 ) sin (0 1 —0 1 ') + ?*! SU10/ j. 

 The remaining formulas remain unaltered. 



