50 DISPERSION. 



Accordingly, the velocity of propagation is a function of the 

 wave-length, and varies with the colour. 



(63) In a vacuum, and in media (such as atmospheric air) 

 which do not disperse the light, the coefficients #2, #3, &c., 

 are insensible, and we have 



that is, the velocity of propagation is independent of the wave- 

 length, and the same for light of all colours. 



In other media we may, as a first approximation, neglect 

 the third and following terms of the series, and we have 



Hence, if Fi, F 2 denote the velocities of propagation for two 

 definite rays of the spectrum, and k i9 k^ the corresponding 

 values of k, 



The truth of this formula has been verified by M. Cauchy, by 

 introducing in it the values of the refractive indices and 

 wave-lengths in certain media, as determined by Fraunhofer 

 for the seven definite rays. 



(64) The general formula, above given, is unsuited to a 

 comparison with observation in its present form, inasmuch as 



the variable k( = j is not independent of F. This diffi- 

 \ A / 



culty is overcome by M. Cauchy by inverting the first series. 

 The result is of the form 



tf = A l s*+Az s 4 +A 3 s 6 + &c. 

 M. Cauchy has shown that this series, as well as the former, 



