THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



— <*> — 



[FIFTH SERIES.] 



MA Y 1888. 



XLIV. On the Numerical Relation between the Index of 

 Refraction and the Wave-length within a Refractive Medium, 

 and on the Limit of Refraction. By T. Pelham Dale, M.A.* 



TT1HE following equation (see Sir Geo. Airey's Treatise on 

 JL the Undulatory Theory, ed. 1877, p. 93) is proposed as 

 expressing the relation between wave-length and velocity of 

 propagation in an isotropic medium : — 



irh 



-\/(i-h* 



sin 



.... (a) 



irh 



v is here the velocity of propagation, h the distance between 

 the undulating particles, k the wave-length, m the absolute force 

 of attraction, supposed to follow the law of the inverse square. 



For our purpose t his may be put under the form 



7 . irh I irh ,~ N 



" = m T/T ^ 



It is convenient to reserve X to si gnify the wave-length in 

 free sether, and to use I for the wave-length within the medium. 

 The values of the wave-lengths in free sether are those given 

 in the text-book of Glazebrook and the tables of Lupton. 



Now, knowing the index of refraction for any fixed line by 

 observation of the index /u,, the corresponding value of I is 

 given by the equation 



l=± 

 V> 

 * Communicated b y the Physical Society : read February 11, 1888. 

 Phil. Mag. S. 5. Vol. 25. No. 156. May 1888. Z 



