the Wave-length within a Refractive Medium. 327 



Now ix and /j, x can be found either by observation or inter- 

 polation. If H be the line chosen, then, practically, the index 

 of a wave-length twice as long in the medium will not be far 

 from A ; this we may call /ul 2 b. and speak of it as the index of 

 the octave below. 



It is evident that if k remain constant, — ^ — continually 



approaches k as diminishes. Now if I be increased and h and 

 in remain constant, diminishes ; hence there must be a limit 

 of refraction in the case of waves of very great length. This 

 limit, denoted by v, is evidently found by the equation 



(0 



Since v=/n - .— , 



This is in effect the limit found by Cauchy in a somewhat 

 modified form. 



sin 



¥ 

 sin 0' 



it follows on substitution of -y- for and - for L and di- 

 t fi 



viding out, that 



sin#=— sin t (£) 



Combining this with the equation above, 



6: 



\i 



(v) 



we can find a value of 6 which satisfies both these equations 

 from any two values of wave-length and corresponding index. 

 And from this value of the corresponding values of to any 

 other index and wave-length can be found. 



In practice this equation can be solved by trial without 

 much trouble, especially when a large number of indices of 

 substances of similar refractive power have to be investigated, 

 when a table may be made once for all, and from this may 

 be found by inspection. 



The wave-lengths made use of in this paper are generally 

 those corresponding to lines A and H. These are both within 

 the visible spectrum, yet far enough apart to render errors of 

 observation of little consequence. In the case of the liquids 

 examined I am altogether indebted to Dr. Gladstone, who fur- 

 nished me with those contained in Table III. for the purposes 

 Z2 



