The paper gives a new derivation of the rms displacement and slope of the surface of a spherical drop in the presence of thermally excited capillary waves. Calculations for a spherical surface have the advantage, over similar calculations for a plane surface, that they avoid the difficulty of having to choose an arbitrary upper limit for the wavelength. Expressions are obtained for time and distance correlation functions of the vertical displacement, of the difference in vertical displacement between different times or locations, of vertical velocity, and of the difference of vertical velocity between separate times or locations on the surface. The correlation function for the difference in vertical velocity between two points on the surface rapidly attains a constant, nonzero value as the separation of the points increases. The limiting value of the velocity difference is related to the speed of motion along the reaction coordinate when the process of accommodation into the bulk liquid is treated by transition-state theory. This leads to an estimate of the physical length of the critical region of the reaction coordinate that must be traversed If accommodation is to occur.