The following investigation was made in consequence of certain peculiarities in the earlier results of some recent measurements of ripples by Prof. Michie Smith, in my Laboratory, which will, I hope, soon be communicated to the Society. These seemed to suggest that viscosity might have some influence on the results, as might also the film of oxide, &c, which soon gathers on a free surface of mercury. I therefore took account of the density, as well as of possible rigidity, of this surface layer, in addition to the surface tension which, was the object of Prof. Smith's work. The later part of the paper, where Cartesian coordinates are employed, runs somewhat on the lines of an analogous investigation in Basset's Hydrodynamics. My original object, however, was different from his, as I sought the effects of viscosity on waves steadily maintained by means of a tuning-fork used as a current interruptor; not on waves once started and then left to themselves. Besides obtaining his boundary conditions in a singular manner, I think that in his § 521 Mr Basset has made an erroneous investigation of the effects of very great viscosity.