The results of an experimental study of the non-Boussinesq lock-exchange problem are described. The experiments were performed in a rectangular channel using water and either a sodium iodide solution or a sodium chloride solution as the two fluids. These combinations of fluids have density ratios (light over heavy density) in the range 0.61 to 1. A two-layer hydraulic theory is developed to model the experiments. The theory assumes that a light gravity current propagates in one direction along the top of the channel and a heavy gravity current propagates in the opposite direction along the bottom of the channel. The two currents are assumed to be connected by either a combination of an internal bore and an expansion wave, or just an expansion wave. The present results, previous experimental results and two-dimensional numerical simulations from a companion paper are compared with the theory. The results of the comparison lead to the conclusion that the theory without the internal bore is the most appropriate.