Thermometrical navigation : being a series of experiments and observations, tending to prove, that by ascertaining the relative heat of the sea-water from time to time, the passage of a ship through the Gulph Stream, and from deep water into soundings, may be discovered in time to avoid danger, although (owing to tempestuous weather,) it may be impossible to heave the lead or observe the heavenly bodies. Extracted from the American philosophical transactions. Vol. 2 & 3. With additions and improvements

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Williams probably acquired his interest in the Gulf Stream from Benjamin Franklin, his great-uncle and the first to understand the nature of the Gulf Stream. Like his uncle, Williams observed its action during his trips across the Atlantic as a diplomat. in this work, he investigates how ships approaching the American coast can take advantage of the temperature differntial of the Stream to establish their position in any weather, without celestial sightings. This was an important navigational aid in the stormy north Atlantic, and one of great use to mariners.