201 



observations on several other media, especially phosphorus, a sub- 

 stance at the very summit of the scale, for which I had long been 

 extremely desirous to obtain some determinations of indices*. 



Among these results only two sets are in a form in which they can 

 be made available for comparison with theory. These are the indices 

 for the standard rays in bisulphide of carbon, and for solution of phos- 

 phorus in that medium, which I have now calculated theoretically. 



The results (given in the sequel) in both cases indicate discre- 

 pancies between theory and observation too great to be due to any 

 reasonable allowance for error ; and we are confirmed in the con- 

 clusion before arrived at, that, for highly dispersive substances, the 

 theory, IN ITS PRESENT STATE, is defective. 



But these comparisons are all made by means of the same formula 

 employed in my former researches, viz. that derived from Cauchy's 

 theory by Sir W. R. Hamilton, which he communicated to me, and 

 which I explained in a paper in the Philosophical Magazine f. 



Considering the unsatisfactory condition in which the question 

 was left when tried by the test of the higher media in my former 

 inquiries, it is a matter of some surprise that in the long interval 

 since the publication of those results no mathematician has been in- 

 duced to revise the theory. Some criticisms indeed were advanced 

 by Mr. Earnshaw^;, and others by Prof. Mosotti and the Abbe' 

 Moigno, bearing on the general principle. Sir W. R. Hamilton's 

 formula in particular was founded on certain assumptions con- 

 fessedly but approximate. It remains then a promising field for 

 inquiry to analysts, whether a better formula might not be deduced, 

 or other improvements made in the general theory, by which a 

 method applying so well to lower cases might be made equally 

 successful for the higher. 



Results of calculation, for Ether, Hydrate of Pheny I, Oils of Spike- 

 nard, Lavender and Sandal-wood, Benzole, Bisulphide of Carbon, 

 and Solution of Phosphorus in that medium. 



Three indices assumed from observation, viz. /u , p. and p. , give 

 the medium constants, viz. 



* See Phil. Mag. July 1859. t Vol. viii. N. S. March 1836. 



J See Phil. Mag. April 1842 and August 1842. 



See British Association Reports, 1849, Sect. Proc. p. 8. 



