DISPERSION. 51 



is convergent, and that all the terms after the third may be 

 neglected. Hence, since 



7 S 



= = 



the velocity in vacuo being unity, we have 



an equation expressing the refractive index 'in terms of the 

 time of vibration, or of the wave-length in vacuo. 



(65) The constants in this formula, A lt A 2 , A 3 , will be 

 determined, when we know three values of ju, with the cor- 

 responding values of s, or of the wave-length in vacuo ; and 

 the formula may be then applied to calculate the values of fj. 

 corresponding to any other values of s, which may be thus 

 compared with the results of observation. The comparison 

 has been made by Professor Powell, and by M. Cauchy him- 

 self, by means'of the observations of Fraunhofer on the refrac- 

 tive indices of water and several kinds of glass, and the 

 agreement of the calculated and observed results is within the 

 limits of the errors of observation. 



But the truth of a formula, expressing the relation be- 

 tween the refractive index and the wave-length in vacuo, can 

 only be satisfactorily tested in the case of highly-dispersive 

 media ; and for such media no observations of sufficient accu- 

 racy hitherto existed. To supply this want, Professor Powell 

 undertook the laborious task of determining the refractive in- 

 dices corresponding to the seven definite rays of Fraunhofer, 

 for a great number of media, including those of a highly dis- 

 persive power, and of comparing them with the theory of 

 M. Cauchy. The result of the comparison is, on the whole, 

 satisfactory. 



(66) It is an interesting consequence of the preceding for- 



E2 



