The instability of a two-dimensional moving contact line is studied for a thin liquid film flowing down an inclined plane, leading to the formation of rivulets. A fluorescent imaging method was developed to facilitate accurate measurement of the spacing between rivulets, tip velocity, three-dimensional shape and dynamic contact line. A fluid circulation system produced steady films at constant volumetric flux, in contrast to time-varying films at constant total volume, as in previous measurements. Comparisons are made with the existing data for constant-volume films, and with theoretical predictions for the wavelength of the rivulets formed at constant inlet flow rate. Data were also obtained for rivulet shapes, tip speeds and contact angles as functions of the angle of inclination of the plate and liquid Reynolds number.