The violent and erratic motion often exhibited by pendent drops during diffusion of a solute across their interfaces has been investigated qualitatively and quantitatively. The qualitative tests indicate that a local lowering of interfacial tension by the solute is a necessary condition for this phenomenon. A mechanism is proposed to account for transient non-uniformity of interfacial tension during diffusion. It is based on two assumptions regarding the course of the diffusion in the region of the interface and the existence of convection currents or similar disturbances in the liquids. The change in energy producing one series of oscillations of a drop is estimated with a view to comparison with the energy dissipated, as determined in part II.