250 PROFESSOR POWELL'S RESEARCHES TOWARDS ESTABLISHING 



rays, here depend on nothing but the lengths of their periods or waves simply as 

 such ; and the intervals between them are precisely proportional to the differences of 

 these lengths. These lengths decrease from the red to the blue end of the spectrum. 



We might search for some empirical law which should connect these two serieses 

 of data, the one being some inverse function of the other ; but it would be more 

 satisfactory should such a formula be supplied by any theory of light. 



I shall not I trust be considered as assuming a controversial tone, if I observe that 

 no researches directly suggesting any such formula have been published except those 

 of M. Cauchy, on the hypothesis of undulations. In these, indeed, such a formula is 

 not actually developed. But in a paper in the London and Edinburgh Journal of 

 Science*, in the former part of which I have offered a brief abstract of M. Cauchy's 

 peculiar theory of undulations, some remarks upon it are given, including the de- 

 duction of a formula in which the relation between the length of a wave and the velo- 

 city of its propagation is precisely expressed ; this last quantity being in fact the 

 same as the reciprocal of the refractive index. 



Without entering any further into theoretical considerations, it will be admitted 

 that such a formula, (from whatever source derived,) if found to supply anything like 

 a representation of the law of nature, or a clue to guide us through the seeming dis- 

 order which prevails among the experimental results, would be entitled to attention. 



It has therefore been my object, without reference to the support of a theory, to 

 examine by means of this formula the relation between the index of refraction and the 

 length of the period or wave for each definite ray throughout the whole series of nume- 

 rical results which we at present possess. And it will become a matter of increasing 

 interest to pursue observations on the indices of definite rays for a greater range of 

 transparent media. 



The present paper will be occupied with the discussion of the data already known; 

 and before proceeding to that discussion I will merely add, that whatever degree of 

 interest may attach to the inquiry, the merit is due to Professor Airy, in whose sug- 

 gestion it originated. 



General Observations on the Formula. 



In the investigations in the paper above referred to, on substituting for the velocity 



s I 



of a wave expressed by -r its equivalent — , the formula at once presents the relation 



between the index ^ and the length of a wave X. H, r, and 71 are quantities depen- 

 dent on the nature of the medium ; r, by hypothesis, always being a sensible fraction 

 of "K : thus the formula becomes 



^ = n 



sm 



(^") 



* Nos. 31 et seq. 



