326 Mr. T. P. Dale on the Index of Refraction and 



A convenient notation is Ia, X a , fi A , &c, for index and 

 wave-lengths of the line A &c. 



Now if V be the velocity of propagation in free asther, 



V 



whence from (/3) we have 



ttJiv , . ttIl 



— = k sm T' 



Calling -r- , 0, we have 



— — = k sin V ; 



for any other value ^ corresponding to index ^ we have 



7rlw 7 . Q 

 — — = k sin a 1} 



and 



7rh_n 



h 



or 



*l = \f (7) 



Hence if we can find a value of 6 for any one wave-length 

 and index, all the others can be found from the observed 

 wave-lengths and corresponding indices. 



The angle 6 can be readily found, if we know two indices, 

 one corresponding to any given wave-length, and the other 

 corresponding to double the wave-length, both within the 

 medium. 



For ^=6, 



then 



I 



TTh^Q 



2/~2' 



—j- = k sin 0=2k sin - cos -, 

 t Z 2i 



-2T = 2 * Sm 2 ; 



v e 



'. -= cos , 

 v 2 



^=cos* (S) 



Pi 2 w 





