274 



PROFESSOR POWELL ON THE ELLIPTIC POLARIZATION OF LIGHT 



(8.) On substituting the values of O and E, and arranging the terms, this is reducible 

 to the form 



'27r 



Hsinfy {vt- 



•oc)j-\- Kcosf ^(v^— a7)V 



where 



and 



j8 cos (p cos "4/ cos f— a sin <p cos •^' 

 — 13 sin p sin ^ cos f cos Q 

 -f |3 sin (p sin 4 sin ^ sin d 

 — a cos (p sin •»]/ cos 6 



=H, 



= K. 



j3 cos <p cos %// sin f 

 — 13 sin <p sin i^ sin |> cos & 

 — /3 sin (p sin -^ cos |> sin 6 

 — a cos 9 sin >!/ sin ^ j 



Then, since the intensity I at any part of the image is expressed by 



I=H2+K2, 



(9.) Squaring these quantities H and K, and taking the sum, after reduction, we 

 ultimately find for any value of %, or position of the analyzer, 



(/32 cos^ (p+a^ sin2(p) cos^-vl/ 

 + (|32 sin^ (p+a^ cos^^) sin^-vf^ 

 I=< —a|3 sin 2^ cos 2-^^008^ 



— a|3 cos 2(p sin 2'v^ cos f cos ^ 



— a|3 sin 2-^ sin f sin &. 



(10.) Or, in order to see the consequences of changing the position of the analyzer, 

 or the arc x» we must introduce it by substituting for p its value ^=%— i^, 



f (a2sin2 (%~'4.)+/32cos2(;^-'4/))cos2'a/ 



+ (a2 C0S2 (;^_^|.)+/32 sin2 {y^- ^))^\n^ y^ 



!=■{ — aj3cos2'\^sin 2(%— -v^) cosf 



— aj3 sin 2-4/ cos 2(x— -v//) cos f COS ^ 

 ^ — a/3 sin 2\J/ sin ^ sin ^. 



(11.) On expanding and reducing this becomes — 



(a2sin2;^-f (32 C0S2 ;)(;;) COS"* -v// ....]. 



4-(a^sin2;;^-j'-j32cos2;i,^) sin^-^/ .... 2. 

 + 2(a2cos2p(^^-/32sin2 5(i)sin2 2^|.. ... 3* 



I=S 



— -(a2— j32) sin2%sin2\//cos2'4/ ... 4. 



~aj3sin2%cos2 2'4/cosg' 5. 



+a/3cos2%sin2\//cos2'v}/cosf .... 6. 



— a/3 cos 2% sin 2-4/ cos 24/ cos f cos ^ . . 7* 



— a/3 sin 2% sin2 2%!/ cos g» cos & . . - . . 8. 

 — a/3 sin 2-4/ sing" sin ^ 9, 



