47 



A paper was read, entitled, " Researches towards establishing a 

 Theory of the Dispersion of Light", No, IV. By the Rev. Baden 

 Powell, M.A., F.R.S., Savilian Professor of Geometry in the Uni- 

 versity of Oxford. 



In his former communications to the Royal Society the author 

 had instituted a comparison of the results of observation and of 

 theory with regard to the dispersion of light, in the instances of the 

 respective indices for the standard rays in fifteen different cases of 

 transparent media; and had found a sufficiently close agreement in 

 the cases which gave the lower numbers ; but there yet appeared to 

 be an increasing discrepancy as an advance was made towards the 

 higher. The theoretical formula employed in this investigation was 

 one derived from the undulatory hypothesis, by a process involving 

 some limitations, which rendered it only approximative. By pur- 

 suing the calculations to a greater degree of developement, or by 

 adopting methods of a more precise character, such as those of M. 

 Cauchy and of Mr. Kelland, the author was led to hope that a more 

 close coincidence might be obtained. The formulae of M, Cauchy, 

 however, involved calculations of so elaborate and overwhelming a 

 character, that he was induced to make trial of the method of Mr. 

 Kelland, applying it, in the first instance, to the case of the most 

 highly dispersive substance, namely, oil of Cassia, in which the 

 greatest discrepancy had before appeared. 



The object of the present communication is to state the results 

 obtained, together with the necessary data employed in the calcu- 

 lations ; and also to elucidate the general method, so as to render it 

 more easily applicable to other cases which may arise in the further 

 prosecution of the determination of specific indices. For this pur- 

 pose a general statement is given of Mr. KeUand's method, in whose 

 formulae, it is easy, knowing the value of the wave-length in air, 

 and taking the indices as given by observation for that particular 

 medium, to introduce the values of the wave-length in the medium. 

 Two of the constants are then determined for that medium ; and by 

 the aid of these, combined with the indices given by observation, 

 a value of the third constant is deduced for each ray : and the veri- 

 fication of the theory will result from the equality of the respective 

 values of this latter constant thus obtained. 



The author then gives tables exhibiting the comparison of observed 

 refractive indices with the results of Mr. KeUand's theory ; first, in 

 the case of sulphuret of carbon, at a temperature of 12° (centigrade) ; 

 next, of the same substance at 22° ; and lastly, of oil of Cassia : 

 from which it appears, that the accordance between the results of 

 observation and of theory is sufficiently within the limits of the 

 errors in the experimental data to satisfy all reasonable expectation. 



A paper was also in part read, entitled, " Experimental Re- 

 searches in Electricity." Twelfth Series. By Michael Faraday, Esq., 

 D.C.L., F.R.S., &c. 



A letter was read from Dr. Marshall Hall, in reply to a note con- 

 tained in the paper of Mr. Newport, published in the last volume of 

 the Philosophical Transactions. 



