The influence of viscosity and heat conduction in modifying the propagation of sound in circular tubes of moderate dimensions has been treated by Kirchhoff in his usual masterly style, but he passes over the case when the diameter is very large. In my book on the Theory of Sound, 2nd edition, § 348, I have given a full statement of Kirchhoff's theory, and have indicated the alterations required when the boundary is supposed to take the form of two parallel planes instead of a cylindrical surface. In any case the action of the wall is supposed to be such as to annihilate variation of temperature, and tangential as well as normal motion. In connexion with the problem of the propagation of sound over water I recently had occasion to extend the analysis to the case of a layer of very great thickness; and though, as the result showed, the solution fails to answer the question which I had then in view, it is of some interest in itself. In this case the practical question differs somewhat from that proposed by Kirchhoff, who assumes not only complete periodicity with respect to time, but also a quasi-periodicity with respect to x, the direction of propagation, all the functions being supposed proportional to emx, where m is a complex constant, and not otherwise to depend upon x.