In a series of papers inserted in the Philosophical Transactions (1835,1836,1837), and afterwards, in a more correct and complete form, in my Treatise ‘On the Undulatory Theory applied to the Dispersion of Light’ (1841), I endeavoured to investigate the great problem of the explanation of the unequal refrangibility of light on the principles of the undulatory theory, as proposed by M. Cauchy about 1830, by numerical comparison with the indices observed, more especially in cases of the most highly dispersive media then examined. The general result then arrived at was, that while the theory applied perfectly through an extensive range of media of low and moderate dispersive power, it did not apply well to those of higher; and to the highest in the scale (which of course formed the true test of the theory) it did not apply within any allowable limits of accuracy. Since that time little has been done towards prosecuting the subject.