Maxwell's Electro-magnetic Theory of Light. 385 



2 { (Dr'P) Tsin 3 ^ dG+ (D 2 -'P) I cos 2 sin dO \ 

 m < J J J 



9. Substituting this value in (11), we obtain 



Performing the operation denoted by T)iD 2 on the whole expres 

 sion, we get 



Let P = A ie vr v ~ (15). 



Then since D X P = ( ^ i H ) P, with a similar expression 



\ T mr T! / 



for D 2 P, we obtain as the condition that (15) should be a solution 

 of (14) 



4 2 \ 



5 ,+ 



27T<y 4>7T' 47T 2 27T7 4 TT 2 



1)17 T 2 T 2 2 1UT T 2 



Also /c = , where V is the velocity of propagation of electrical 







disturbances in vacuo. Substituting this and simplifying we obtain 



_,_^ .i _, ir 



.. (16). 



2 22 



Here u is the refractive index of the medium, and 



m?r 



For transparent media, 7 will be small, and the above equation 

 may be written 



