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 course of 1781 and 1782, while on the North American station, to act as judge advocate in several courts-martial, and was led to study the laws and methods of procedure in such courts. He followed out these lines of study during the peace, while still purser of the Santa Margarita, and in 1790, according to his own statement, laid a new code of signals before the admiralty. It caught the attention of Lord Hood [see ], then first sea lord, and when in the Russian armament of 1791, he hoisted his flag in command, he made McArthur his secretary. He was desirous of trying McArthur's signals; but as there was some delicacy about introducing a new code to supersede that of Lord Howe, McArthur is said to have recast his, remodelling it on the basis of Howe's. After approval by Howe, it was tested and used in the experimental cruise of 1792; and ‘from that period,’ McArthur wrote in 1807, ‘it has been universally adopted in the service, and is, it is believed, continued with little or no variation in form or substance at the present day.’ But in this McArthur was certainly wrong, for Sir Home Popham's [q. v.] code had been generally adopted some years before 1807. As early as 1799 McArthur claimed to be the real author of the code known by the name of Lord Howe (Naval Chronicle, i. 509, ii. 70; Thoughts on several plans combining a system of Universal Signals); it appears probable, however, that his share in it was little more than seeing it through the press.

In 1793, when Hood went out as commander-in-chief in the Mediterranean, McArthur was again his secretary, being appointed also purser of the Victory. His duties at this time were extremely onerous and important. In addition to the ordinary work of secretary, the occupation of Toulon and the intimate association of the Spanish and Italian forces threw on him the conduct of a correspondence in the three foreign languages, without, he says, any assistance; he had also to act as Hood's interpreter, and as Hood's representative in the disbursements of public money, both to the British forces and to those of the allies. For some time there was no English commissary-general, and he had to act in that capacity. He was also prize agent for the fleet; and though his duties as purser of the Victory were performed by a deputy, the responsibility, pecuniary and otherwise, rested on him. When Hood, after returning to England, was ordered to strike his flag, McArthur went back to the Mediterranean as simple purser of the Victory. As soon as the ship joined the fleet, Rear-admiral Man hoisted his flag on board, and in the action of 14 July 1795 [see ] McArthur volunteered to observe the signals, ‘the admiral's secretary, whose proper duty it was, professing his want of experience in the duty and giving a preference to being stationed at one of the quarter-deck guns.’ He was afterwards secretary to Sir Hyde Parker (1739–1807) [q. v.], and returned to England with him early in 1796.

In 1803, when Lord Nelson was going out to the Mediterranean, he offered to take McArthur as his secretary. McArthur, however, declined, ‘as Lord Hood's accounts with the treasury were then pending before the auditors.’ This was the official reason, but he was probably more directly influenced by the pressure of his literary engagements. When quite a young man he had published ‘The Army and Navy Gentleman's Companion, or a new and complete Treatise on the Theory and Practice of Fencing’ (1781, 4to). In 1792, while secretary to Lord Hood, he brought out ‘A Treatise of the Principles and Practice of Naval Courts-martial’ (1 vol. 8vo), which in the second edition bore the title of ‘Principles and Practice of Naval and Military Courts-martial’ (1805, 2 vols. 8vo); in this form it ran through many editions, and was long the standard work on the subject. In 1799, in conjunction with James Stanier Clarke [q. v.], he commenced the publication, in monthly numbers, of the ‘Naval Chronicle,’ which ran to forty half-yearly volumes, and was mainly devoted to accounts of the current naval transactions and to biographical notices of the principal naval officers of the day, often from notes supplied by the subjects themselves. So far as it treats of contemporary events or persons, it is of very high authority. But McArthur's most important work, also in conjunction with Clarke, was the ‘Life of Lord Nelson,’ 1809, 2 vols. 4to, to which, it was understood, he contributed the naval material, while Clarke supplied the literary skill. On 22 July 1806 the university of Edinburgh conferred on him the degree of LL.D.

He was also the author of ‘Financial and Political Facts of the Eighteenth Century’ (1801, 8vo), which, with the change of ‘century’ into ‘and present centuries,’ ran through several editions; and of ‘A Translation from the Italian of the Abbé Cesarotti's Historical and Critical Dissertation respecting the Controversy on the Authenticity of Ossian's Poems: with Notes and Observations by the Translator’ (1806, 8vo), in which he describes himself as ‘one of the committee of the Highland Society of London appointed to superintend the publication of Ossian in the original Gaelic.’ He was at this time living