Mr. Earnshaw on the Theory of the Dispersion of Light. 305 



for a very extensive range of substances, the indices of refrac- 

 tion as found both by experiment and by theory. The near 

 agreement of results, as there exhibited, is such as cannot fail 

 to impress the reader, who is content with a general view of 

 them, with most favourable sentiments respecting the theory 

 from which they are derived. I have however dipped deeper 

 into the matter, and by executing the calculations of several 

 cases have arrived at results which 1 desire now to set before 

 your readers, chiefly with a view of eliciting from some one 

 such an explanation as shall induce me to assent to the opi- 

 nion of Professor Powell, that "the theory of undulations sup- 

 plies at once both the laws and the explanation of the phae- 

 nomena of dispersion." 



The first method of calculation is the one which was made 

 use of by Professor Powell in three papers printed in the 

 Transactions of the Royal Society, under the title "Researches 

 towards establishing a theory of the Dispersion of Light," and 

 distinguished as Nos. I. II. III. The formula employed is 

 equivalent to the following : — 



"iM :"' 



This equation being directly furnished by theory, it is a 

 matter of intense interest to see how far its truth is supported 

 by experiment. I have not however met with any calcula- 

 tions founded upon it, except in the papers just referred to, 

 and therefore it is that in my remarks upon it I shall be under 

 the necessity of referring to an inadvertence in those papers 

 which I should otherwise gladly have left unmentioned. After 

 comparing the results of theory with those furnished by expe- 

 riment, Professor Powell comes to the conclusion that " the 

 refractive indices are related to the lengths of waves, as nearly 

 as possible, according to the formula deduced from M. 

 Cauchy's theory." Now, if I mistake not, in all those papers, 

 the author, by forgetting to reduce Fraunhofer's values of A in 

 air to the proper medium, did in fact employ a formula which 

 differs from the correct one furnished by theory ; for, rectify- 

 ing the oversight, the true formula supplied by M. Cauchy's 

 theory is the following : — 



sm C — 1 



