A conductance technique for measuring the temporal variations in the thickness of an isolated draining soap film is described. A ring-shaped surfactant-stabilised film, almost horizontal, is formed in the annular space between two vertical coaxial copper tubes; this film consists of a thin central lamella, of thickness a few microns, surrounded by a meniscus or Plateau border at each tube wall. Continuous drainage of the intralamellar liquid into the borders causes gradual thinning of the film, eventually leading to rupture. A voltage is applied across the two tube electrodes and the time evolution of the annular film thickness is inferred from continuous monitoring of the radial electrical resistance of the film over its lifetime. Drainage transients have, thus, been acquired for films stabilised with a variety of surfactants. The simple Reynolds model for drainage of viscous liquid between plane parallel rigid surfaces approaching without tangential motion, is generally found to underestimate the drainage rate of soap films by orders of magnitude. An alternative two-dimensional hydrodynamic swept-film-surface theory, accounting for film surface mobility, is presented. It postulates the existence of a small transition region linking the central lamella to the Plateau border, where the rate governing fluid flow and viscous dissipation occur. The resulting interfacial shear stress in the film is sustained by a small surface tension gradient along the transition region. From principles of slow viscous flow, a third-order differential equation is derived which, when combined with the integrated form of the continuity equation, yields the time evolution profile of the film thickness. Good agreement is obtained between theory and experiment over a wide range of experimental conditions : liquids with viscosities ranging from 1.09 to 75.5 mPas and four different surfactants were used.