Of a numerous family only two sons survived Ludlam; of these the elder, Thomas Ludlam (1775–1810), after serving an apprenticeship to a printer, entered the service of the Sierra Leone Company, and going out to the colony became a member of the council, and twice governor for the company.
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In 1795 John Playfair published a different formulation of Euclid's parallel postulate, which is now called Playfair's axiom; though the axiom bears Playfair's name, he did not create it, but credited others, in particular William Ludlam, with the prior use of it.