High Quality Content by WIKIPEDIA articles! HMS Ajax was an Ajax class 74-gun third rate ship of the line of the Royal Navy. She was built by John Randall Co of Rotherhithe and launched on the Thames on 3 March 1798.Ajax participated in the Egyptian operation of 1801, the Battle of Cape Finisterre in 1805 and the Battle of Trafalgar, before she was lost to a disastrous fire in 1807 during the Dardanelles Operation.