Mr Stokes said it was well known to all engaged in optical researches that Fraunhofer had most accurately measured the wave lengths of seven of the principal fixed lines of the spectrum. Now he found that by a very simple species of interpolation, which he described, he could find the wave length for any point intermediate between the two of them. He then exemplified the accuracy to be obtained by his method by applying it to the actually known points, and shewed that in these far larger intervals than he ever required to apply the method to the error was only in the eighth, and in one case in the seventh, place of decimals. By introducing a term depending on the square into the interpolation still greater accuracy was attainable. The mode of interpolation depended on the known fact that, if substances of extremely high refractive power be excepted, the increment Δμ, of the refractive index in passing from one point of the spectrum to another is nearly proportional to the increment Δμ-2 of the squared reciprocal of the wave length. Even in the case of flint glass, the substance usually employed in the prismatic analysis of light, this law is nearly true for the whole spectrum, and will be all but exact if restricted to the interval between two consecutive fixed lines. Hence we have only to consider μ as a function, not of λ, but of λ-2, and then take proportional parts.