Graham is shown seated on the right at a circular, white-covered table, facing forward but glancing sideways rather than outward, with a place-setting for dinner in front of him. Holding a long pipe in his right hand, his left rests on his hip. He is dressed informally in grey, with a gold-brocade waistcoat, a fur-lined red velvet robe (with sleeves) loosely round his shoulders, a velvet turban cap, white stockings and slippers. Seated on the left in front of the table, with a place-setting under his left elbow, is a plainly attired man with his legs crossed, dressed all in black with a white collar and stockings, and black buckled shoes. His dress implies he is socially inferior to Graham but an educated man - perhaps a secretary or tutor - and it may be symbolic of this social difference that a salt-cellar lies on the table between them. He looks up out of the picture to the right, holds an open blank ledger towards the Captain, and has a decorated Chinese porcelain punch bowl and a spaniel at his feet. To his left, behind, dressed largely in white and standing under a hanging crown compass, a steward or cook uses a white napkin to hold a hot dish of roast fowl with gravy dripping from the front edge. The sails of another ship can be seen through the cabin's stern windows beyond. These have pier-glass mirrors between them and there is a shelf of richly bound books on far right of the picture, with an expensive carpet beneath the table: none of these are standard features and indicate a wealthy captain furnishing the cabin to suit his own tastes.

A black servant boy stands on the far right behind Graham, playing a pipe and tabor. Behind the table a standing man, presumably a hired singer, holds a sheet of music which bears the otherwise recorded song title 'Arragh my Judy' (one of that name being known, though the words are lost). Music unites the group, as does the very carefully plotted composition. On the left, the spaniel apparently joins in the singing. On the right a pug sits unnaturally upright on a chair, wearing Graham's wig, holding a scroll of paper like a baton under its front right leg and looking out over a paper propped on a glass in front. This is Hogarth's dog, placing the artist himself symbolically in the picture. The inclusion of servants and dogs, and the informality of the scene, suggests the painting tells a private rather than public story about Captain Graham and his circle. Lord George and the black servant both have pipes and the latter's attire echoes his master's. Similarly the pug's pose, in Graham's wig, appears to ape the formality of his official position. Only the pug and steward or cook on the left look directly out to the viewer: everyone else’s glance is oblique and remains within the picture. The cook's smile invites the spectator in, while he seems unaware that he is spilling gravy, though there is a napkin there to catch it. Hogarth has thus introduced elements of humour, but the painting has been tantalizingly enigmatic in its meaning ever since it became known.

This was only in 1888, when it was first lent for exhibition in Glasgow by the 5th Duke of Montrose, in whose family it remained since left by Captain Graham to his elder brother William, the 2nd Duke, in 1747. It only became famous from its general display in the National Maritime Museum from 1937, as part of its founding benefaction from Sir James Caird, who bought it from the 6th Duke in 1932. Until 2012, the Museum's usual speculation - repeated elsewhere - was that it might celebrate Graham's capture of French privateers off Ostend in 1745, while commanding the 24-gun 'Bridgewater' (or 'Bridgwater'), and be set in the cabin of the 60-gun 'Nottingham' which was his next command.

However, in September 2012, a paper called 'A Cure for the Captain' by Elizabeth Einberg appeared in a collection called 'A Window on that World. Essays presented …to Brian Allen' published by the Paul Mellon Centre, London (Yale UP). This at last gives a full and entertaining explanation of this longstanding puzzle. The story, in brief, is as follows.

In June 1741 Captain Graham, then commanding the 40-gun 'Lark', returned from a ten-month round trip convoying merchant ships to Turkey and back. He was exhausted and unwell on his return, but was immediately ordered to undertake other local duties off the Kent coast that he found uncongenial, though the exact details are not clear. The result was what we might now call a breakdown, in which he resigned his captaincy and went ashore for three years, stating his intention to go to Cheltenham and 'take the waters' there for his health. Whether he went is uncertain but Cheltenham was then a newly fashionable spa, whose mineral salts – which crystallized naturally at the wells – were also widely sold for drinking re-mixed with water elsewhere, or were sprinkled on food. A key feature of the composition is that - unusually for an informal male gathering of its time – it includes no alcoholic drink: the punch-bowl on the floor holds clear water, not punch; the single glass shown is of a size suitable for water and a salt-cellar is prominent on the table.

The Captain is also being served a roast fowl - that is, white meat not red - which known 18th-century doctors recommended as good for health, as some also did abstaining from alcohol. The fact that the bird is swimming in gravy and that the cook stands under the ship’s crown compass – hung in cabins for quick reference to the course being steered – also marks him out as a 'prince of cooks' in contemporary terms. The cheerful music being played (an Irish song title is visible on the sheet held by the red-haired singer) is also medicinal, since that was considered a remedy for 'melancholy' since ancient times; and the pet spaniel joins in, as dogs often do. Graham wears the turban cap favoured by the polite classes for keeping informal company 'in their own hair' (i.e. un-wigged) and his red Turkish-style robe, a trophy of his recent voyage, to keep himself warm – as doctors also recommended invalids should. His pipe is also apparently a Turkish chibouk. This is a long wooden or metal one, made in sections for travelling, which could be used for smoking tobacco or other medicinally soothing substances. Tobacco itself, hashish (marijuana) and opium were all variously considered such at the time.

The bewigged pug is a direct reference to the connection between Graham and Hogarth. The Captain lived near him in London, and was also MP for Stirlingshire (a family constituency) from that year, requiring his presence in Parliament when otherwise possible. Late in 1741 he was also in London attending his father, the 1st Duke, during his last illness, until his death there on 7 January 1742 – another reason for his own personal crisis. Graham was also a friend of London actors and others of artistic and literary interests. In particular, he and Hogarth were 'brothers' in that both were freemasons, and in 1734 had been jointly elected to act as 'masters of ceremony' at a particular masonic event. Graham was unable to be present but Hogarth's dog, in the captain's wig, represents their brotherly masonic connection and friendship, allowing for difference in social rank. The paper propped up is probably music or a list of rules and may bear a trace of Hogarth's signature (upside down). The dog itself holds the roll of white paper as a master of ceremonies at the time would have held his white staff of office, so Hogarth is in effect ‘presiding’ over what he shows, as one of the Captain’s London circle.

The sober-suited dining companion was long ago suggested to be the Scottish poet, David Mallet, of whom (unfortunately) no other portrait exists. This is none the less a convincing identification, since he had been tutor and Grand Tour travelling companion to the young Graham brothers, remained their lifelong friend and was otherwise well connected, notably as under-secretary to Frederick, Prince of Wales (d. 1751). In 1742 he married a wealthy second wife, who ensured he was always well turned-out, usually in black velvet as apparently shown. Here he holds out a blank journal or log-book towards the Captain, as if inviting him to resume his sea career as a successful commander.

In sum, the painting appears to be part of a campaign by Graham's friends, with Mallet perhaps the agent in its commission, to help the Captain recover his health and spirits, or a record of their efforts to that end after his father's death. Happily, they succeeded. Early in 1745 Graham was offered command of the 60-gun Cumberland, but turned it down in favour of the 24-gun Bridgewater, undoubtedly because - as a younger son - he needed to make his own fortune and the chances of taking enemy prizes in such a ship were better. The War of the Austrian Succession was then in progress (1742–49) and, serving in the Channel, he had great success off Ostend on 5 July 1745 (NS), when he took two Dunkirk privateers and recaptured a number of other British merchant vessels. From these he did well in both prize money and salvage payments.

Hogarth's picture was completed by the time Graham made his will in January 1745, before he returned to sea, in which he left it to his brother William, the 2nd Duke, naming it his ‘conversation piece drawn by Mr Hogarth’ (itself a respectfully friendly reference, rather than just ‘Hogarth’). The cabin shown is therefore unlikely to be in the Bridgewater or a later ship. It may be based on Graham’s previous one, the Lark, or one no larger, since it apparently lacks the stern gallery a 60-gunner would have had, and we know that Graham was seeking a small vessel at the time. The painting's likely date is therefore 1742-44.

Graham’s success off Ostend in 1745 quickly won him command of the Nottingham, 60 guns, which he this time accepted, and in which he also did well as senior officer of a small squadron in the Atlantic approaches, south of Ireland. In particular, he sank the large French privateer, 'Bacchus', but saved all her crew except the first lieutenant, who was killed in the action. Unfortunately, shortly after this exploit he was again taken ill and appears to have been landed at Bristol, where his ducal elder brother, William, collected him and took him to Bath for a cure. It was a vain effort, since he quickly died there on 2 January 1747, a week short of five years after their father. The cause is unknown but his apparently excitable temperament and uncertain earlier health suggests a chronic condition, perhaps ‘consumption' (tuberculosis).

He was much missed: ‘From a multitude of concurrent testimonies', wrote the 18th-century naval biographer, John Charnock, 'he appears to have been an officer who attained a great share of popularity, and was indeed, very deservedly, the idol of all seamen who knew him, as well on account of the high opinion entertained of his gallantry, as an invincible fund of good humour, which latter quality conciliated the affections of men in the same degree that the first related excited their admiration and esteem.’ (Biographia Navalis [1797] vol. 5, pp 22-24).

Whether the cabin setting of the picture was Hogarth's idea or suggested to him is unknown but, in either case, it may have been inspired by a similar work by Bartolommeo Nazari, a Venetian painter, which shows Lord Boyne and friends in the cabin of the ship taking them from Venice to Lisbon in 1732. Boyne was certainly known to Hogarth, who painted his portrait (and another one of Graham, now lost). It is very possible that Hogarth saw the large Nazari canvas but, even if not, it is known to have prompted an unusual number of smaller contemporary copies, of which he would have been aware. The Museum also has one of these (BHC2567).