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 University 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 formulæe 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. Kelland's method, in whose formulæ, 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. Kelland'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.
