They performed several experiments: the electrolysis of water, dosing, titration, verifying the laws of circuits in electricity and biology experiments.
So anyone looking at this sequence would immediately decide to get their hydrogen from that sodium hydroxide production not from the electrolysis of water.
The process reverses electrolysis, which many may recall from a high school experiment that involved placing two electrodes in water, passing an electric current through them and collecting the hydrogen and oxygen that bubbled off.