There are slides devoted to this topic: Lecture 6a, pp. 8-10.
Visit the NNDB entry for Lord Kelvin, the confident scientific polymath who invented the first tide predictor, to read about the Baron’s life and work.
To learn more about the development of tide prediction, read the brief “History of Tidal Analysis and Prediction” article written for the National Oceanic and Atmospheric Administration (NOAA), which discusses Kelvin’s contributions to the science as well as those who developed on his ideas. Afterwards, learn about tide predicting machines and how they work by reading the “Tide Predicting Machines” page. If you’re confused by some of the mathematical language in that article, you can read more about tidal machine development in the NOAA’s article “Old Brass Brains: Mechanical Prediction of Tides,” which explains how the machines work in laymen’s terms.
Check out this JAVA simulation of Kelvin’s tide predicting machine, featured on the American Mathematical Society website, which allows the user to program the machine for seven different ports and see the charted results.