The second Ajax was another 3rd Rate 74 gun Ship of the Line and was launched on 3rd March 1798 on the Thames and commissioned in June of that year. 1953 tons; length 182ft; Beam 49ft. Armament: 28x 32 pounders; 30x 24 pounders;16x 9 pounders.
She was part of the 1801 Egyptian Operation and took Battle Honours at the Nile; likewise, at the Battle of Cape Finisterre in 1805 she received Battle Honours.
Ajax was part of Admiral Lord Nelson’s fleet of 27 ships of the line that on 21 October 1805 took on a combined French and Spanish fleet of 33 ships of the line at Cape Trafalgar. The Battle of Trafalgar saw 22 Franco-Spanish ships lost without a single British vessel being lost. Ajax received honours.
In February 1807 Ajax was part of the Dardanelles Operation near the Turkish island of Tenedos when, for some reason, she caught fire on 14 February, ran aground and blew up next day.