THEORY OF THE DISPERSION OF LIGHT. 



259 



values of those variable terms), we shall have the following equations : 



-f q{(i smb} sin2 ^" 

 — w2 a = 2-{ + q{p cos b' 



+ q{Q cos il . „ 

 ^^ l2sin2^ 



+ /?{« J 



= 2 



— w2 13 cos b='X< 



sin 2 



'■ — p {a 



— g {(i cos & 



— 5- {|3 sin ft } 2 sin2 d ^ 

 + p' {j8 sin b} sin 2 ^ 

 + p' {|3 cos ft 

 + q {ex, 



2 sin2 ^ 



— w2 



w2 13 sin ft = 2-* 



^. I sin 2^1 



— ;>' {/3 cos ft J I 



.— /)' {|3 sin ft } 2 sin2 ^ J 



multiplicati^ 



1 2 sin2 ^ 1 



} sin 2 ^ J 



(25.) 



(26.) 



(27.) 



(28.) 



From the two last forms (27.) (28.) we obtain by multiplication and addition, 



r p' {j3 cos 2 ft 

 — w2|3 = 2J q {a cos ft 

 >_— q {a sin ft 

 And in like manner from (26.) and (29.) we deduce 



/{|32cos2& ■ 



(29.) 



- w2 (a2 + |32) = 2 



2 sin' 



in2 A 



(30.) 



+ J' {2 a|3 cos ft ^ 



In the case of elliptically polarized light ,we have 



a2 + i32 = 1 ; 



and it is thus obvious that when the quantities involved give the value of r? as here 

 expressed, viz. 



f y {|32 cos 2 ft} ^ 



-W2= 2 



2 sin' 



in^&X . . . . (31.) 



+ 5' {2a|3cosft} 



and when this value is substituted in (18.) (19.), and consequently in (6.), the formula 

 (5.) for elliptically polarized light is a particular solution of the differential equations 

 of motion of the system of molecules (14.). 



Deductions and Remarks. 



(10.) It is evident that in (31.) expressing the whole coefficient by a single letter, 

 we have the abridged form 



w2 = 2{H'2sin2^}, . (32.) 



* 2 l2 



