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A story is told on the authority of his daughter, Lady Jane Hamilton, that this appointment was given him by Lord Spencer, at the instance of Mr. Dundas, afterwards Lord Melville (, i. 144n.); but as Lord Spencer was not at that time, nor for two years afterwards, first lord of the admiralty, the anecdote is clearly inaccurate in at least one of its most important details.

During the first two years of Duncan's command the work was limited to enforcing a rigid blockade of the enemy's coast, but in the spring of 1797 it became more important from the knowledge that the Dutch fleet in the Texel was getting ready for sea. The situation was one of extreme difficulty, for the mutiny which had paralysed the fleet at the Nore broke out also in that under Duncan, and kept it for some weeks in enforced inactivity. Duncan's personal influence and some happy displays of his vast personal strength held the crew of the Venerable to their duty; but with one other exception, that of the Adamant, the ships refused to quit their anchorage at Yarmouth, leaving the Venerable and Adamant alone to keep up the pretence of the blockade. Fortunately the Dutch were not at the time ready for sea; and when they were ready and anxious to sail, with thirty thousand troops, for the invasion of Ireland, a persistent westerly wind detained them in harbour till they judged that the season was too far advanced (Life of Wolfe Tone, ii. 425–35). For political purposes, however, the government in Holland, in spite of the opinion of their admiral, De Winter, to the contrary, ordered him to put to sea in the early days of October. ‘I cannot conceive,’ wrote Wolfe Tone (Life, ii. 452), ‘why the Dutch government sent out their fleet at that season, without motive or object, as far as I can learn. My opinion is that it is direct treason, and that the fleet was sold to Pitt, and so think Barras, Pleville le Pelley, and even Meyer, the Dutch ambassador, whom I have seen once or twice.’ This of course was scurrilous nonsense, but the currency of such belief emphasises De Winter's statement to Duncan, that ‘the government in Holland, much against his opinion, insisted on his going to sea to show they had done so’ (Arniston Memoirs, 250). Duncan, with the main body of the fleet, was at the time lying at Yarmouth revictualling, the Texel being watched by a small squadron under Captain Trollope in the Russell, from whom he received early information of the Dutch being at sea. He at once weighed, with a fair wind stood over to the Dutch coast, saw that the fleet was not returned to the Texel, and steering towards the south sighted it on the morning of 11 Oct. about seven miles from the shore and nearly halfway between the villages of Egmont and Camperdown. The wind was blowing straight on shore, and though the Dutch forming their line to the north preserved a bold front, it was clear that if the attack was not made promptly they would speedily get into shoal water, where no attack would be possible. Duncan at once realised the necessity of cutting off their retreat by getting between them and the land. At first he was anxious to bring up his fleet in a compact body, for at best his numbers were not more than equal to those of the Dutch; but seeing the absolute necessity of immediate action, without waiting for the ships astern to come up, without waiting to form line of battle, and with the fleet in very irregular order of sailing, in two groups, led respectively by himself in the Venerable and Vice-admiral Onslow in the Monarch, he made the signal to pass through the enemy's line and engage to leeward. It was a bold departure from the absolute rule laid down in the ‘Fighting Instructions,’ still new, though warranted by the more formal example of Howe on 1 June 1794; and on this occasion, as on the former, was crowned with complete success. The engagement was long and bloody; for though Duncan, by passing through the enemy's line, had prevented their untimely retreat, he had not advanced further in tactical science, and the battle was fought out on the primitive principles of ship against ship, the advantage remaining with those who were the better trained to the great gun exercise (, Histoire de la Marine Française sous la première République, 329), though the Dutch by their obstinate courage inflicted great loss on the English. It had been proposed to De Winter to make up for the want of skill by firing shell from the lower deck guns; and some experiments had been made during the summer which showed that the idea was feasible (, ii. 427); but want of familiarity with an arm so new and so dangerous presumably prevented its being acted on in the battle.

The news of the victory was received in England with the warmest enthusiasm. It was the first certain sign that the mutinies of the summer had not destroyed the power and the prestige of the British navy. Duncan was at once (21 Oct.) raised to the peerage as Baron Duncan of Lundie and Viscount Duncan of Camperdown, and there was a strong feeling that the reward was inadequate. Even as early as 18 Oct. his aunt, Lady Mary Duncan, wrote to Henry Dundas, at that time secretary of state for war: ‘Report