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Hessians were mercenaries hired by the British to fight against the American Patriots in the Revolutionary War.

One of the most famous incidents involving these German mercinaries was the Battle of Trenton, where about 900 Hessians were captured out of a force of 1,400. Washington's army crossed the Delerware river on Christmas Night of 1776 to carry out a surprise attack.

About 30,000 of these mercenaries were hired and they came to be called Hessians because 16,992 of the total 30,067 men came from Hessen-Kassel. The rest came from Anhalt-Zerbst, Anspach-Bayreuth, Brunswick-Lüneburg, Hesse-Hanau, Nassau, and Waldeck and other German states.

In early 1776, George III hired units from the various houses or states of Germany. Several of these rulers, needing hard currency and being "between wars", were only too happy to oblige.

The troops were not mercenaries in the modern sense of professionals who fought for money. As in most armies of the 18th century, the men were mainly conscripts, debtors or the victims of impressment. Pay was low - some soldiers apparently got nothing but their daily food. The officer corps were usually career officers who had served in earlier European wars. The revenues realized from their service went back to the German royalty.

Hessians composed approximately one third of the British forces in the conflict. They included jaegers, hussars, three artillery companies and four battalions of grenadiers. Most of the infantry were chasseurs (sharpshooters), musketeers and fusiliers. They were armed mainly with smoothbore muskets. Artillery used 3-pound guns.

Initially, the average regimental was made up of 500-600 men. Later in the war, the regiments had only 300-400 men.

About 18,000 Hessian troops arrived to North America in 1776. They first landed at Staten Island on August 15 and their first engagement was in the Battle of Long Island. Some Hessians fought in every campaign, although after 1777 they were mainly used as garrison troops. Only two regiments fought at Yorktown in 1781.

In addition to firepower, American rebels used propaganda against Hessians. They enticed Hessians to desert to join the German-American population. In April 1778, one letter promised 50 acres of land to every deserter. Benjamin Franklin wrote an article that claimed that a Hessian commander wanted more of his soldiers dead so that he could be better compensated.

17,313 Hessians returned to their homelands. Of the 12,526 of those who did not, about 7,700 died - around 1200 Hessians were killed in action and 6,354 died from illness or accident. Approximately 5,000 settled in North America, both in the United States and Canada - some because their commanders refused to take them back to Germany because they were criminals or physically unfit.

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In mathematics, the Hessian matrix of a function f of several real variables is the (symmetric) matrix of all second partial derivatives. See symmetry of second derivatives