Question: What was the importance to the American Revolution of the battle named after the capital of the county where Princeton is also located?

The Battle of Trenton was a small but pivotal battle during the American Revolutionary War which took place on the morning of December 26, 1776, in Trenton, New Jersey. After General George Washington's crossing of the Delaware River north of Trenton the previous night, Washington led the main body of the Continental Army against Hessian mercenaries garrisoned at Trenton. The battle significantly boosted the Continental Army's flagging morale, and inspired re-enlistments. After a brief battle, almost two - thirds of the Hessian force was captured, with negligible losses to the Americans. <SEP> As of the 2010 United States Census, the municipality's population was 28,572, reflecting the former township's population of 16,265, along with the 12,307 in the former borough. Princeton is a municipality with a borough form of government in Mercer County, New Jersey, United States, that was established in its current form on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township. <SEP> the death of general mercer at the battle of princeton, january 3, 1777 is the title of an oil painting by the american artist john trumbull depicting the death of the american general hugh mercer at the battle of princeton on january 3, 1777 during the american revolutionary war. the painting was trumbull’s first depiction of an american victory. it is one of a series of historical paintings on the war, which also includes the "declaration of independence" and "the capture of the hessians at trenton, december 26, 1776". <SEP> on february 8, 1847, doniphan continued his march with 924 men mostly from missouri; he accompanied a train of 315 wagons of a large commercial caravan heading to the state capital. meanwhile, the mexican forces in the state had time to prepare a defense against the americans. about 20 miles (32 km) north of the capital where two mountain ranges join from east to west is the only pass into the capital; known as sacramento pass, this point is now part of present-day chihuahua city. the battle of sacramento was the most important battle fought in the state of chihuahua because it was the sole defense for the state capital. the battle ended quickly because of some devastating defensive errors from the mexican forces and the ingenious strategic moves by the american forces. after their loss at the battle of sacramento, the remaining mexican soldiers retreated south, leaving the city to american occupation. almost 300 mexicans were killed in the battle, as well as almost 300 wounded. the americans also confiscated large amounts of mexican supplies and took 400 mexican soldiers prisoners of war. american forces maintained an occupation of the state capital for the rest of the mexican–american war. <SEP> New Jersey's 15th Legislative District is one of 40 in the New Jersey Legislature, covering the Hunterdon County municipalities of East Amwell Township, Lambertville City and West Amwell Township; and the Mercer County municipalities of Ewing Township, Hopewell Borough, Hopewell Township, Lawrence Township, Pennington Borough, Trenton City and West Windsor Township.