For the British Crown, such frontiers were smudges on the edge of the map. What truly mattered was protecting Britain’s trade with the European continent against French interference. So, when French colonists built forts in the contested borderland of the Ohio Valley, near Pittsburgh, King George III went through the motions of shooing them away. This task was unimportant enough, however, to fall to an American-born major who’d been in uniform less than a year, a twenty-one-year-old named George Washington.

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Sending Washington wasn’t exactly sending the big guns. When he ordered the French to leave, they refused. He returned the next year to build a fort. As he prepared to do so, though, the Seneca leader Tanaghrisson approached Washington, warned him that the French were near, and proposed an ambush. Washington went along, and the two managed, with their combined forces, to capture a French unit. But things spun out of his control when Tanaghrisson drove a hatchet into the French commander’s skull and his men began killing the wounded. In another fates-or-hobgoblins moment, a discombobulated Washington had started a war.

A huge one. In the United States, it’s known as the French and Indian War, but that was just the American portion of the conflict. The Seven Years’ War drew in all the great Western powers. It reached Europe, Africa, and Asia, leading Winston Churchill to call it “the first world war.” As in the later World Wars, Britain’s side won. Lagos, Le Havre, Quebec, Quiberon Bay—“Our bells are worn threadbare with ringing for victories,” Horace Walpole wrote.

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George Washington, trudging through a muddy Pennsylvania forest, had inadvertently set cannons roaring from Prague to Manila. This surely confirmed the colonists’ sense of their own importance. But it also revealed them to be cogwheels in a vast imperial machinery, one they neither controlled nor comprehended.

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For a war of independence, it is bizarre how many foreigners featured in the American Revolution. The greatest American hero after Washington was the Marquis de Lafayette, who arrived, in 1777, barely speaking English. Washington and Lafayette’s war-ending triumph over Lord Cornwallis at Yorktown, in 1781, owed much to Comte de Rochambeau’s French soldiers and Comte de Grasse’s French ships. About a quarter of the British Army troops, meanwhile, were actually German—the hated Hessians.

There’s a reason for this. Once the colonists showed they could win battles, Britain’s many enemies piled on. The result was “a Russian doll of a war, with conflicts nested in other ones, far beyond the thirteen colonies,” Pearsall writes. There is no one name for the connected conflicts, which include the Anglo-French War of 1778-83, the Anglo-Spanish War of 1779-83, the Fourth Anglo-Dutch War, and the Second Mysore War. Pearsall suggests “the Nine Years’ War.”

How central were the thirteen colonies here? Burnard and O’Shaughnessy point out that, whereas Britain regularly sent nobles to govern the Caribbean colonies—and dukes and earls to Ireland—the men appointed to administer the thirteen colonies more often lacked titles and were paid less. The Massachusetts governor during the Boston Tea Party, Thomas Hutchinson, was a local merchant.

Hence the Hessians. George III made do with mercenaries from German lands because he needed British troops to protect a place that mattered more: Ireland.

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Lord Cornwallis encountered these imperial priorities in 1778, when he was briefly ordered to leave America along with four thousand troops during a panic that the French might invade Jamaica. He ran fully aground on the same priorities in 1781, when rebel forces surrounded him at Yorktown. Cornwallis needed reinforcements, and one reason too few came was that Britain had sent ships to the Indian Ocean, where it was fighting the Sultan of Mysore, Hyder Ali. The battles in southern India “were on a scale that far surpassed those of America,” Burnard and O’Shaughnessy write, and they burned through British resources. Pearsall deems Hyder Ali the unsung hero of Yorktown.

Cornwallis laid down his arms in October, 1781. Yet a puzzle for schoolchildren is: If the war basically finished with Yorktown in 1781, why wasn’t the peace treaty ratified until 1784? In fact, only the American fighting had ended. Major engagements lay ahead: Britain’s triumphant defense of Jamaica against France in the Battle of the Saintes, in 1782; the exhaustion of the Franco-Spanish siege of Gibraltar, in 1783. Combat in southern India raged until 1784.

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Bayly, unimpressed by the thirteen colonies’ influence, argued that the main engine of political modernity wasn’t a revolution in ideas but one in arms. By the eighteenth century, developments in military technology and state organization had made wars punishingly expensive. That’s why Britain, after the Seven Years’ War, needed to hike taxes, setting off the American Revolution. And it’s why France, after the American Revolutionary War, had to do the same, which led to the calling of the Estates General, the revolt of the Third Estate, and the monarchy’s fall.