Question: John Hamilton-Leslie fought on the side of a King of Great Britain and Ireland who was the ruler of the Duchy and Electorate of Brunswick-Luneburg in what empire?

full_context: Document 1: John Murray of Broughton: Sir John Murray of Broughton, 7th Baronet Stanhope (c. 1718 – 6 December 1777), was a Jacobite, who served as secretary to Prince Charles Edward Stuart ('Bonnie Prince Charlie') during the Jacobite Rising of 1745. He later earned the hatred of the Jacobites by turning King's evidence.
Document 2: Charles Edward Stuart: Charles Edward Louis John Casimir Sylvester Severino Maria Stuart (31 December 1720 – 31 January 1788), commonly known in Britain during his lifetime as The Young Pretender and The Young Chevalier, and often known in retrospective accounts as Bonnie Prince Charlie, was the second Jacobite pretender to the thrones of England, Scotland, France and Ireland (as Charles III) from the death of his father in 1766. This claim was based on his status as the eldest son of James Francis Edward Stuart, himself the son of James VII and II. Charles is perhaps best known as the instigator of the unsuccessful Jacobite uprising of 1745, in which he led an insurrection to restore his family to the throne of Great Britain. The uprising ended in defeat at the Battle of Culloden, effectively terminating the Jacobite cause. Jacobites supported the Stuart claim because they hoped for religious toleration for Roman Catholics and because they believed in the divine right of kings. Charles's flight from Scotland after the uprising has rendered him a romantic figure of heroic failure in some later representations. In 1759 he was involved in a French plan to invade Britain, which was abandoned after British naval victories.
Document 3: Charlotte of Mecklenburg-Strelitz: Charlotte of Mecklenburg-Strelitz (Sophia Charlotte; 19 May 1744 – 17 November 1818) was by marriage to King George III the Queen of Great Britain and Ireland from her wedding in 1761 until the union of the two kingdoms in 1801, after which she was Queen of the United Kingdom of Great Britain and Ireland until her death in 1818. She was also the Electress of Hanover in the Holy Roman Empire until the promotion of her husband to King of Hanover on 12 October 1814, after which she was also queen consort of Hanover.
Document 4: Prince George of Denmark: Prince George of Denmark and Norway, Duke of Cumberland (Danish: "Jørgen" ; 2 April 165328 October 1708), was the husband of Queen Anne, who reigned over Great Britain from 1702.
Document 5: George I of Great Britain: George I (George Louis; German: "Georg Ludwig" ; 28 May 1660 – 11 June 1727) was King of Great Britain and Ireland from 1 August 1714 until his death, and ruler of the Duchy and Electorate of Brunswick-Lüneburg (Hanover) in the Holy Roman Empire from 1698.
Document 6: Jacobite rising of 1715: The Jacobite rising of 1715 (Scottish Gaelic: "Bliadhna Sheumais" ] ) (also referred to as the Fifteen or Lord Mar's Revolt), was the attempt by James Francis Edward Stuart (also called the Old Pretender) to regain the thrones of England, Ireland and Scotland for the exiled House of Stuart.
Document 7: James Scott, Earl of Dalkeith: Sir James Scott, Earl of Dalkeith KT (23 May 1674 – 14 March 1705) was an English nobleman and politician. He was the son of James Scott, 1st Duke of Monmouth and Anne Scott, 1st Duchess of Buccleuch. He was also the grandson of Charles II of England, Scotland and Ireland. On 2 January 1693/94 he married Lady Henrietta Hyde (born in Hindon, Wiltshire, c. 1677, died 30 May 1730), daughter of Laurence Hyde, 1st Earl of Rochester and Henrietta Hyde, Countess of Rochester. They had six children:
Document 8: John Hamilton-Leslie, 9th Earl of Rothes: John Hamilton-Leslie, 9th Earl of Rothes (1679–1722) was a Scottish nobleman who fought on the side of George I during the Jacobite rising of 1715.
Document 9: George III of the United Kingdom: George III (George William Frederick; 4 June 1738 – 29 January 1820) was King of Great Britain and Ireland from 25 October 1760 until the union of the two countries on 1 January 1801, after which he was King of the United Kingdom of Great Britain and Ireland until his death. He was concurrently Duke and prince-elector of Brunswick-Lüneburg ("Hanover") in the Holy Roman Empire until his promotion to King of Hanover on 12 October 1814. He was the third British monarch of the House of Hanover, but unlike his two predecessors, he was born in Britain, spoke English as his first language, and never visited Hanover.
Document 10: George II of Great Britain: George II (George Augustus; German: "Georg II. August" ; 30 October / 9 November 1683  – 25 October 1760) was King of Great Britain and Ireland, Duke of Brunswick-Lüneburg (Hanover) and Prince-elector of the Holy Roman Empire from 11 June 1727 (O.S.) until his death.
Document 11: Jacobite rising of 1745: The Jacobite rising of 1745 (Scottish Gaelic: "Bliadhna Theàrlaich" ] , "The Year of Charles") was the attempt by Charles Edward Stuart to regain the British throne for the exiled House of Stuart. The rising occurred during the War of the Austrian Succession, when most of the British Army was on the European continent. Charles Edward Stuart, commonly known as "Bonnie Prince Charlie" or "the Young Pretender", sailed to Scotland and raised the Jacobite standard at Glenfinnan in the Scottish Highlands, where he was supported by a gathering of Highland clansmen. The march south began with an initial victory at Prestonpans near Edinburgh. The Jacobite army, now in bold spirits, marched onwards to Carlisle, over the border in England. When it reached Derby, some British divisions were recalled from the Continent and the Jacobite army retreated north to Inverness where the last battle on Scottish soil took place on a nearby moor at Culloden. The Battle of Culloden ended with the final defeat of the Jacobite cause. Charles Edward Stuart fled with a price on his head before finally sailing to France.
Document 12: Sophia of Hanover: Sophia of the Palatinate (commonly referred to as Sophia of Hanover; 14 October 1630 – 8 June 1714) was the Electress of Hanover from 1692 to 1698. As a granddaughter of James VI and I, she became heir presumptive to the crowns of the Kingdom of England and the Kingdom of Ireland under the Act of Settlement 1701. After the Acts of Union 1707, she became heir presumptive to the unified throne of the Kingdom of Great Britain. She died less than two months before she would have become queen, and her claim to the throne passed on to her eldest son, George Louis, Elector of Hanover, who ascended as George I on 1 August 1714 (Old Style).
Document 13: George IV of the United Kingdom: George IV (George Augustus Frederick; 12 August 1762 – 26 June 1830) was King of the United Kingdom of Great Britain and Ireland and of Hanover following the death of his father, George III, on 29 January 1820, until his own death ten years later. From 1811 until his accession, he served as Prince Regent during his father's final mental illness.
Document 14: James Hamilton, 4th Duke of Hamilton: Lieutenant General James Hamilton, 4th Duke of Hamilton and 1st Duke of Brandon {'1': ", '2': ", '3': 'KG KT', '4': "} (11 April 1658 – 15 November 1712) was a
Document 15: George William, Duke of Brunswick-Lüneburg: George William German: "Georg Wilhelm" (Herzberg am Harz, 26 January 1624 – 28 August 1705, Wienhausen) was Duke of Brunswick-Lüneburg. He ruled first over the Principality of Calenberg, a subdivision of the duchy, then over the Lüneburg subdivision. In 1689, he occupied the Duchy of Saxe-Lauenburg and passed it on to his successors. George William was the father of Sophia Dorothea of Celle, wife of George I of Great Britain.
ground_truth: Holy Roman Empire