I notice the print when, as a student at St. Andrews, I was a regular of the, then many, antiquarian booksellers –this print was found in Billson of 15 Greyfriar Garden.
Interest was sparked on two counts, first it was a local view and secondly as a student of maritime matters I was mortified to learn of an incident, within cannon shot, of which I was so ignorant.
It is not engagement which was curious rather the aftermath as mentioned below...

The information below were from my notes taken at the archives at Kew.

The print above of an action on 27th May 1758 ,the during the Seven Years War 1754-1763, between the Marchall Belleisle Commanded by Francois Thurot and two British warships, the Solebay, commanded by Robert Craig and the Dolphin’s Prize, commanded by Benjamin Marlow.

The engagement left both sides badly damaged and each departed to repair.
It is the argument which took place after the battle between the two British captains which is of interest.
First we have Robert Craig’s instructions from the Admiralty :-

Adm 1/1606 Captain’s Letters, Robert Craig HMS Solebay, [Section 15]

HMS Solebay in Leith Road 21 April 1758
“…I received your Lordship’s order date 5th inst. To cruise with His majesties ship under my command and the Dolphin’s Prize off the Firth of Forth for the protection of trade of His Majesties subjects and the annoyance of the enemy, till further orders; and to send a boat ashore once in every three days for that purpose and particularly to raise as many men as possible for His Majesties service…”

ADM 52/1033 Master’s log Solebay

Thursday 25th May 8 weighed and with Dolphin left Aberdeen bay. 12 Girdleness latt 59.16 North
Friday 26th May At 4AM Scurdie ness NW by N 4 leagues At 6 Dolphin saw a sail to the SE coming right down upon us upon which we gave chase. At 7 up all hammocks and barricaded the tops, bunted the main sail.
Took the chase to be enemies ship of war.
At 8 Red Head NW by W 5 leagues
At ½ past began to engage.
At 9 the enemy standing to the North between us and the Dolphin upon which … after the enemy and give a broadside …we wear on stays: set studding sails set gibb stay sails: … got along the enemy and engaged within pistol shot Captain Craig was wounded, enemy shot ahead of us.
At ½ past 11 our starboard main yard arm was shot away by the quarter of the yard, main tops yard shot away, hanging to the mast in three pieces.
Saturday 27th Saw Cape Rock ahead about a musket distance. Killed 4 seamen and boatswain, 15 wounded 11 mortally.

Craig was amongst those badly wounded in the engagement as can be seen below:-
Leith 8th June
“..The musket shot I received from the privateer has passed through my lungs and lodged in my back, affected the nerves there, and in my left arm in such a manner, as it is impossible for me to come up in the ship: and that I humbly subject my case to their Lordships consideration to have the ship kept for me, or another when able to go to sea..”

There follows a series of requests for a position in a warmer climate:-
24th August Admiralty Office. He says he is as well as can be expected but wishes to serve in a warm climate- Med or West Indies he is staying at Blackheath till he hears from Admiralty.
21 September Admiralty Office Send surgeons certificate as to his wounds, and asks to be examined by Sick and Hurt Board – presumably for a pension.
Admiralty Office 25 October. Renews his application to be sent abroad to warm climate – says that for most part of winter will be confined to his room – asks for discharge from the Solebay for his servant Charles Mitchell along with himself –his discharge may have been discussed earlier.
26 December Seething Lane Again asking leave to go to Portugal or Italy “..To prevent, if possible a lingering death…” In the meantime it would appear that he has been disparaging Captain Marlow’s conduct:-

Sheerness 25th November 1758 Marlow writes to Craig whom he accuses “..I have repeated information from my friends that my character suffers extremely in the world from aspersions you have thrown out with respect to my conduct in our engagement with the Marchall Belleisle, tho I am conscious to my self that I stand exculpated in that affair, in the opinion of everybody present in the action, yet it is necessary for a full and ample vindication of my conduct that I should write this letter to you, to insist upon it that immediately on receipt of this acquaint me with what you have to charge me with on that occasion, that I may lose no time in asking their Lordships for court-martial, your answer to this will (unless it is an absolute confutation under your hand of these scandalous reports) be as well as this letter to you transmitted to the Lords Commissioner of the Admiralty” Ben. Marlow

There is a hint in these newspaper reports of the background to the row – but as will be seen the Admiralty sided with Marlow – who ended his career as an Admiral in 1779-80.

Caledonian Mercury Tuesday 30th May 1758 We are now told, it was the Solebay that first attacked the French Privateer off the Red-Head about 9 ‘oclock, and a little after the Dolphin came up to her assistance. The Solebay had her Main-top-yard, her Main-yard, and Main-top gallant yard shot away; the Mizzen-mast, shot almost through, her main-stays, Spring-stay, and Main-top mast shot away, and all her sails cut to pieces. She had five killed, viz. James Nichols, Boatswain, a Welshman; John Ker from Stornoway; John White of Leven; William Duncan and Hugh Craig both of Leith. James Black is since dead of his wounds; and there are two or three who, it is thought, cannot recover. There were in all fourteen wounded.
Captain Craig still continues without hopes of recovery. The Dolphin had one killed and fourteen wounded.

Caledonian Mercury Thursday 1st June 1758
To the publisher of the Caledonian Mercury. Sir, “Upon Friday morning, the Dolphin Captains Marlow, and Solebay, Captain Craig, about 7 o’clock saw a sail of the Red-head, which they made for: about 8 o’clock, Captain Marlow in the Dolphin, came close along-side her and hailed her, as she had then hoisted English colours flying, whereupon the enemy immediately hoisted French colours, and retuned answer a whole broadside, which the Dolphin returned very smartly, and continued close alongside, for the space of an hour and a half, before the Solebay could come up to fire one gun, in which time the Dolphin sustained very considerable loss. After the Solebay came up, they both continued in close action till 12 o’clock, when the enemy thought proper to sheer off, leaving our ships in such a shattered condition, that we could not come up with her. ...”

Caledonian Mercury Saturday 22nd July 1758
A gentleman from Gottenburg informs us, That he was at Gottenburg, when the Belleisle Privateer came in to be refitted: and that one evening, in a Mason-lodge, the Captain (Thurot) acquainted them with particulars of his engagement with the Solebay and Dolphin Men of War, when he acknowledged that he had lost 80 men: and further added, That if he had no more than a single sixpence in the whole world, he would share it with Captain Craig of the Solebay, whose bravery he extolled even to the skies; and swore that nothing would gave him greater pain than to hear of his death. In many encomiums he passed on the gallant behaviour of the Solebay, he said They engaged him so desperately, that he believed the were rather D[evi]ls than men; and that he would sooner engage some other ships of 50 guns, than Captain Craig and his crew with twenty.

It appears that Captain Craig failed to give satisfaction, and Captain Marlow asked, and received a Court Martial to vindicate his conduct which it does: -

ADM 1/5298 Court Martial held aboard HMS Tonnington Sheerness harbour 30th & 31st March 1759 “… the court is of the opinion that the charge is not in whole nor in no part proved against Captain Marlow, it, and do acquit Captain Marlow with honours of the whole and every point of the charge, and he is hereby honourably acquitted …”
For more on Marlow see link

Captain Francois Thurot,Marchall Belleisle ,[his ship's proper name] was to be killed in the next action of the Ils of Man :-

ADM 1/1760 Letters of Captain John Elliot HMS Aeolus 1759.

Aeolus in Ramsay Bay 29th February 1760

"Sir, Please to acquaint the Rt. Hon. My Lords Commissioners of the Admiralty that on the 21st inst. I received information at Kinsale from His Grace the Lord Lt. of the Island that there were three ships of the enemy’s on Carrickfergus. A copy of which I sent their Lordships that day. The same evening I sailed with His Majesties ship under my command together with the Pallas and Brilliant in quest of them, I made the entrance of Carrickfergus on the evening of the 26th, but could not get in the wind being contrary and very bad weather, on the 28th at 4 in the morning we got sight of them and gave chase about 9 I got up alongside their commodore off then isle of Man and in a few minutes after the action became general and lasted about an hour and half, when they all three struck their colours. They are the Marshall Bellisle of 44 guns and 545 men including troops, Monsieur Thurot commander who is killed, the La Blonde of 32 guns and 400 men commanded by captain La Kayee and the Terpsichore of 26 guns and 300 men commanded by Captain Desrevaudais. I put into this road to repair the ships who are all much disabled in masts and rigging. The Marshall Bellisle in particular who lost her bowsprit, mizzen mast and main yard, in the action and it’s with great difficulty we prevented her sinking. It is with greatest pleasure I acquaint their Lordships that the officers and men of His Majesties ships behaved remarkably well on the occasion… I shall use the greatest dispatch in getting the ships refitted and purpose returning to Plymouth or some other port in England as soon as able, if I don’t receive their Lordships directions before the ship are got ready Enclosed is the state and condition of His Majesties ships with an account of the killed and wounded.
In His Majesty’s ships. Killed Wounded Aeolus 4 killed 15 Wounded Pallas 1 killed 5 Wounded Brilliant 11 Wounded NB. I find it impossible to ascertain the numbers of the enemy killed and wounded, but by the best accounts I get they amount to about 300."