AN INTERRUPTED MEDIUM. 539 



/i \ <* * (1 *) a i f fit 5 , , 1 1 



r= (1 *) -- j ^ - ^ - < - r cos'' (b + , - TT -- 2~3r r 

 J a + b 2 {a + b (a + b) cos * q> \ 



f -i IN f.'-r> 2 , 2 



r = z{ 1 (s 1) -- , + - tan 2 

 \ J a + l a(a + b) 



{? w 2 , , 1 



1 -- 5- + 7 - pr tan * m > 

 a + b a (a + b) ) 



If a b be not supposed small, there is another term, which is introduced thus : 



2 .'-,*+ &c. + 



4 sin 2 (p .- v (t r) 2 (a 5 cos 4 



(1 " 



8(1-*) sin 2 



2 sin 2 d) ma? (ab cos 4 + 1) 



^ 



-- r 



Thus the reflection increases with the angle of incidence, so far as this approxi- 

 mation proceeds. 



It is not difficult to work out the solution for the vibrations parallel to the 

 surface. 



Should the conclusions to be derived from the comparison of the two results 

 appear to give the law of elliptic polarization, I shall recur to the subject at some 

 future time. 



VOL. XV. PART IV. 7 F 



