Complex sentence: The analyzer used rolling sphere integrators to compute the Fourier coefficients of the height of the tide as a function of time, and the harmonic synthesizer used a system of cords and pulleys to generate and sum the harmonic partials for prediction of future tides.
Split into simpler sentences: The analyzer used rolling sphere integrators to compute the Fourier coefficients of the height of the tide as a function of time. The coefficients were input to the synthesizer that used a system of cords and pulleys to generate and sum the harmonic partials for prediction of future tides.