98 Professor Airy on the 



the latter being = j x that of the former. Let the vibration per- 



. 2ir 



pendicular to AP t be c.sin -^ (vt-x) or c.sin£ (for brevity): and 

 let the vibrations be 

 In Oov p . sin f+t/, or p cos v . sin £+^ sin v . cos £, or wsm^ + x cos £. 



In o L o 2 , lip . sin £ + v — 90°, 

 or - Ap.cos £ + v, or Ap sin u.sin £-^> cos u.cos £, or kx sin £-Au>cos£. 

 In Ee„ y.sin f+x, or 5- cos X -sin £ + ?.sin X - cos£ or y.sin f + s.cos£. 



In e,e s , fsin £ + x + 90°, 



or f.cosf+x or- | sin x .sin£ + | cos x .cos£, or -|sinf + f cos£. 



Resolving these in directions parallel and perpendicular to AP„ 

 and comparing them with the vibration from the original polari- 

 zation, 



cos <Th£ (w sin I + « cos £) + sin a + <£ (Ax sin I - kw cos £) 



+ cos^+0 (y sin ? + s cos + sin a + ( - ^ sin j; + 3 cos f) = c sin ?, 



sin ^+4> (w sin £ + z cos £) - cos a+<£ (Ax sin %-kw cos {•) 

 + sin «T0 (y sin £ + s cos £) - cos <h^"(- - sin £ + | cos £)=0. 



Or (since these equations ought to hold for all values of £) 



equating separately the coefficients of sin £ and cos £, 



sina + _ /,^ 



cos a + c£.w> + &.sin a + <p.x +cos a + <p.y — ■ — j ( » - c \ l )> 



COS 



silla + / 9 \ 



a + ^).X— A sin C + 0.I0 + COS a + 0.X -+- ^ — y — " V-* 1 ' 



