It's time to do a little backtracking with Scorpions in a Bottle. I began my account of the Hudson Campaign in media res, as it were, with Burgoyne facing disaster in October 1777, just before the timeline's point-of-divergence. The present section is the prequel, showing Burgoyne setting out from Canada in high spirits and certain of victory. With this section done, the third chapter of Scorpions, "The Rebellion Ends", is now complete.
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As the year 1777 dawned, the North ministry found itself facing unexpected difficulties. The campaign in America, initially completely successful, had ended in disappointment. Instead of capturing Philadelphia, and thus ending the Rebellion, Lord North and his ministers heard of the setbacks in Trenton and Princeton. It was recognized that a simple show of force would be insufficient to put down the Rebellion. It would be necessary to employ as much military strategy as a comparable engagement with a European power would merit.
Fortunately for Lord North, the hour had brought forth the man. General John Burgoyne had returned to London several months before the evacuation of Boston, and so was able to bring firsthand knowledge of conditions in America to the North ministry, along with a first-rate military intelligence to analyze the situation and recommend a course of action. Burgoyne recognized that the Americans’ greatest strength, the vast extent of the area under their control, could also be their greatest weakness. Provided that sufficient forces could be brought to bear, the thinly-settled territory could easily be split asunder, and the centers of the Rebellion isolated from each other. Once this was done, the rebellious areas could be overcome piecemeal.
The optimal strategy, as Burgoyne well understood, was to build on the army’s strengths. The strong positions in Canada and New York City provided a ready-made platform from which to seal New England off from the remaining colonies. Burgoyne himself would lead one army south from Quebec, while a second traveled east from the Iroquois country, and Howe led a third north up the Hudson from New York. All three armies would meet at Albany, securing control of New York province and leaving New England isolated. This plan was approved by Lord Germain, and Burgoyne sailed to Canada to take command of an army of some 7,000 men, including regiments of Hessian soldiers, French Canadian militia, and Indian auxiliaries. 
General Howe, who had remained in America, also initially favored a pincer attack on Albany, but by the spring of 1777 he had decided instead to carry out an amphibious attack on Philadelphia, leaving Clinton in command of a small force in New York City with orders not to leave the vicinity of the city. Although Lord Germain sent Howe a letter saying he expected Howe to move up the Hudson, Howe chose to regard this as a suggestion rather than an order, and proceeded with his attack on Philadelphia. In June 1777, as Burgoyne was moving his army south down Lake Champlain, Howe was preparing to embark his troops for the move on Philadelphia. Howe finally set sail on July 23, making landfall at the head of Chesapeake Bay on August 24.
Burgoyne was aided by a leadership dispute among the Americans. General Horatio Gates sought command of the Northern Department for himself, and he spent much of 1777 intriguing to replace General Philip Schuyler. The two traded command of the area several times, depriving the rebel forces of consistent leadership. During his periods of command, Gates’ natural indolence left the rebels unprepared in spite of their knowledge of Burgoyne’s impending attack. In late June Burgoyne’s forces easily drove the rebels out of Fort Ticonderoga, at the south end of Lake Champlain.
Once Burgoyne began moving south from Lake Champlain, he found that he had run out of easy victories. For the next four weeks, his men faced a grueling struggle to advance though a wilderness festooned with rebel booby-traps. A detachment of Hessian soldiers was repulsed on a foraging expedition to Bennington, New Hampshire on August 14, losing several hundred men. Meanwhile, Lt. Col. Barry St. Leger’s force, moving east down the Mohawk Valley, was halted at Fort Stanwix and forced to turn back. By September, Burgoyne’s provisions were dwindling, and most of his Indian allies had deserted him.
Had Burgoyne continued to face General Schuyler, all might have been lost. Fortunately, the capture of Fort Ticonderoga allowed Gates to regain command of the rebel army, and once again his indolence proved vital to Burgoyne’s success. After taking command of the rebels, Gates was content to rely on his predecessor’s preparations. They were sufficient to halt Burgoyne, but not to defeat him.  An attack by Burgoyne on September 12 ended in stalemate for the two opposing armies. As was often the case in the Hudson campaign, Burgoyne’s chief strength was the weakness of his enemies: a quarrel between Gates and General Benedict Arnold deprived the rebel commander of his most energetic and able subordinate. For the next three weeks, Burgoyne dug in and prepared to receive a rebel counterattack. It was only gradually that Burgoyne realized that Gates had no intention of launching his own attack, and was content to sit and wait at Saratoga while Burgoyne’s army slowly melted away. Burgoyne on October 7 chose to launch another attack on the rebel positions. Had he faced only Gates, the attack would almost certainly have succeeded in dislodging the rebels. Unfortunately for Burgoyne, Arnold had chosen to remain with the rebel army in spite of his quarrel with Gates, and his quick thinking and daring leadership allowed the rebels to repulse Burgoyne’s advance, and even threatened to drive the British army from its fortified redoubts. It was only nightfall, and Arnold’s incapacitation after being wounded in the leg, that prevented a complete rout. 
1. Wesley Van Luvender. The Military Thought and Action of John Burgoyne (New York, 1944), pp. 117-23.
2. Robert Sidney. Horatio Gates: The Man Who Lost the Rebellion (New York, 1970), pp. 45-59.
3. Bamford Parkes. Benedict Arnold: The Rebel Genius (New York, 1965), pp. 210-22.