Manchester Memoirs, Vol. xlii. (1898), No. 3. 



It appears that waves whose length (XJ exceeds a 

 certain limit «2/z) are partially transmitted. Moreover, 

 for sufficiently long waves we find 



^=.v/(i+i") . . . (90) 

 exactly as in § i. As the wave-length is diminished we 

 get a series of alternate intervals of total reflection and 

 partial transmission, respectively. But the intervals of 

 partial transmission become wider and wider as we pro- 

 ceed, so that our medium is transparent for relatively 

 short waves, except when the wave-length falls a little short 

 of an aliquot part of 2a. Moreover, in the middle of any 

 one of these intervals, of high order, we have Q — \ir and 

 sin ka—^Li, approximately.* It follows from (59) that the 

 coefficient of transmission is then nearly equal to unity. 



We have here perhaps an illustration of the theory of 

 refraction sketched by Sir George Stokes in the Wilde 

 lecture f At all events, we have constructed a one- 



* The angle 9 is now defined by the equation 



Q.O'ika — — ^'^ ^ , ?,m.ka = co?,6. 

 I -k^c^jir^ 



In the investigations of §§ 2, 3 we have only to write m-I{i — k'^c'^l'^'^] for y. 



throughout. The results, such as (30), (31), and (59), from which ^ has 



been eliminated, will remain unaltered. 



t Manchester Memoirs, vol. xli. (1897), No. 15. 



