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 but, as Stokes observed : "If we reflect on the state of the subject as Fresnel found it, and as he left it, the wonder is, not that he failed to give a rigorous dynamical theory, but that a single mind was capable of effecting so much."

In a second supplement to his first memoir on Double Refraction, presented to the Academy on November 26th, 1821, Fresnel indicated the lines on which his theory might be extended so as to take account of dispersion. "The molecular groups, or the particles of bodies," he wrote, "may be separated by intervals which, though small, are certainly not altogether insensible relatively to the length of a wave." Such a coarse-grainedness of the medium would, as he foresaw, introduce into the equations terms by which dispersion might be explained; indeed, the theory of dispersion which was afterwards given by Cauchy was actually based on this principle. It seems likely that, towards the close of his life, Fresnel was contemplating a great memoir on dispersion, which was never completed.

Fresnel had reason at first to be pleased with the reception of his work on the optics of crystals: for in August, 1822, Laplace spoke highly of it in public; and when at the end of the year a seat in the Academy became vacant, he was encouraged to hope that the choice would fall on him. In this he was disappointed. Meanwhile his researches were steadily continued; and in January, 1823, the very month of his rejection, he presented to the Academy a theory in which reflexion and refraction are referred to the dynamical properties of the luminiferous media.