Laplace's improvements in theory were substantial, but they still left prediction in an approximate state. This position changed in the 1860s when the local circumstances of tidal phenomena were more fully brought into account by William Thomson 's application of Fourier analysis to the tidal motions as harmonic analysis. Thomson's work in this field was further developed and extended by George Darwin, applying the lunar theory current in his time. Darwin's symbols for the tidal harmonic constituents are still used.