Battle of Paoli During the American Revolution

Battle of Paoli During the American Revolution The Paoli Massacre occurred on September 20-21, 1777, during the American Revolution (1775-1783). In the late summer of 1777, General Sir William Howe embarked his army at New York City and sailed south with the goal of capturing the American capital of Philadelphia. Moving up the Chesapeake Bay, he landed at Head of Elk, MD and began marching north towards Pennsylvania. Acting to protect the city, General George Washington attempted to make a defensive stand along the Brandywine River in early September. Meeting Howe at the Battle of Brandywine on September 11, Washington was flanked by the British and forced to retreat east to Chester. While Howe paused at Brandywine, Washington crossed the Schuylkill River at Philadelphia and marched northwest with the goal of using the river as a defensive barrier. Reconsidering, he elected to re-cross to the south bank and began moving against Howe. Responding, the British commander prepared for battle and engaged the Americans on September 16. Clashing near Malvern, the fight proved brief as a massive thunderstorm descended on the area forc ing both armies to break off the battle. Wayne Detached In the wake of the Battle of the Clouds, Washington first retreated west to Yellow Springs and then to Reading Furnace in order to obtain dry powder and supplies. As the British were badly hampered by the rutted and muddy roads as well as the high water of the Schuylkill, Washington decided to detach forces led by Brigadier Generals William Maxwell and Anthony Wayne on September 18 to harass the enemys flanks and rear. It was also hoped to that Wayne, with 1,500 men that included four light guns and three troops of dragoons, could strike at Howes baggage train. To assist him in these efforts, Washington directed Brigadier General William Smallwood, who was moving north from Oxford with 2,000 militia, to rendezvous with Wayne. As Washington resupplied and began marching to re-cross the Schuylkill, Howe moved to Tredyffrin with the goal of reaching Swedes Ford. Advancing on Howes rear, Wayne encamped two miles southwest of the Paoli Tavern on September 19. Writing to Washington, he believed that his movements were unknown to the enemy and stated, I believe [Howe] knows Nothing of my situation. This was incorrect as Howe had been apprised of Waynes actions through spies and intercepted messages. Recording in his diary, British staff officer Captain John Andre commented, Intelligence having been received of the situation of General Wayne and his design for attacking our Rear, a plan was concerted for surprising him, and the execution entrusted to Major General [Charles] Grey. The British Move Seeing an opportunity to crush part of Washingtons army, Howe directed Grey to assemble a force of around 1,800 men consisting of the 42nd and 44th Regiments of Foot as well as the 2nd Light Infantry to strike at Waynes camp. Departing on the evening of September 20, Greys column moved down the Swedes Ford Road before reaching the Admiral Warren Tavern approximately one mile from the American position. In an effort to maintain secrecy, Andre reported that the column took every inhabitant with them as they passed along. At the tavern, Grey coerced a local blacksmith into serving as a guide for the final approach. Wayne Surprised Advancing around 1:00 AM on September 21, Grey ordered his men to remove the flints from their muskets to ensure that an accidental shot would not alert the Americans. Instead, he instructed his troops to rely on the bayonet, earning him the nickname No Flint.. Pushing past the tavern, the British approached around a set of woods to the north and quickly overwhelmed Waynes pickets who fired several shots. Alerted, the Americans were up and moving in a matter of moments, but were unable to resist the force of the British attack. Assaulting with around 1,200 men in three waves, Grey first sent forward the 2nd Light Infantry followed by the 44th and 42nd Foots. Pouring into Waynes camp, the British troops were able to easily spot their adversaries as they were silhouetted by their campfires. Though the Americans opened fire, their resistance was weakened as many lacked bayonets and could not fight back until they reloaded. Working to rescue the situation, Wayne was hampered by the chaos caused by the suddenness of Greys assault. With British bayonets slashing through his ranks, he directed the 1st Pennsylvania Regiment to cover the retreat of the artillery and supplies. As the British began to overwhelm his men, Wayne directed Colonel Richard Humptons 2nd Brigade to shift left to cover the retreat. Misunderstanding, Humpton instead shifted his men right and had to be corrected. With many of his men fleeing to the west through gaps in a fence, Wayne directed Lieutenant Colonel William Butlers 4th Pennsylvania Regiment to assume a position in nearby woods to provide covering fire. Wayne Routed Pressing forward, the British drove the disorganized Americans back. Andre stated, the Light Infantry being ordered to form to the front, rushed along the line putting to the bayonet all they came up with, and, overtaking the main herd of the fugitives, stabbed great numbers and pressed on their rear until it was thought prudent to order them to desist. Forced from the field, Waynes command retreated west towards White Horse Tavern with the British in pursuit. To compound the defeat, they encountered Smallwoods approaching militia who were also put to flight by the British. Breaking off the pursuit, Grey consolidated his men and returned to Howes camp later in the day. Paoli Massacre Aftermath In the fighting at Paoli, Wayne sustained 53 killed, 113 wounded, and 71 captured while Grey lost a mere 4 killed and 7 wounded. Quickly dubbed the Paoli Massacre by the Americans due to the intense, one-sided nature of the fight, there is no proof that British forces acted inappropriately during the engagement. In the wake of the Paoli Massacre, Wayne criticized Humptons performance which led to his subordinate preferred charges of negligence against his superior. A subsequent court of inquiry found that Wayne was not guilty of any misconduct but stated that he had made errors. Angered by this finding Wayne demanded and received a full court-martial. Held later that fall, it exonerated him of any blame for the defeat. Remaining with Washingtons army, Wayne later distinguished himself at the Battle of Stony Point and was present at the Siege of Yorktown. Though Grey had succeeded in smashing Wayne, the time taken for the operation allowed Washingtons army to move north of the Schuylkill and assume a position to contest a crossing of the river at Swedes Ford. Frustrated, Howe elected to move north along the river towards the upper fords. This forced Washington to follow along the north bank. Secretly counter-marching on the night of September 23, Howe reached Flatlands Ford, near Valley Forge, and crossed the river. In a position between Washington and Philadelphia, he advanced on the city which fell on September 26. Eager to rescue the situation, Washington attacked part of Howes army at the Battle of Germantown on October 4 but was narrowly defeated. Subsequent operations failed to dislodge Howe and Washington entered winter quarters at Valley Forge in December. Selected Sources British Battles: Paoli MassacreHistory of War: Paoli MassacrePaoli Battlefield

What Is a Rational Number Definition and Examples

What Is a Rational Number Definition and Examples SAT / ACT Prep Online Guides and Tips Have you heard the term â€Å"rational numbers?† Are you wondering, â€Å"What is a rational number?† If so, you’re in the right place! In this article, we’ll discuss the rational number definition, give rational numbers examples, and offer some tips and tricks for understanding if a number is rational or irrational. What Is A Rational Number? In order to understand what rational numbers are, we first need to cover some basic math definitions: Integers are whole numbers (like 1, 2, 3, and 4) and their negative counterparts (like -1, -2, -3, and -4). Fractions are numbers that are expressed as ratios. A fraction is a part of a whole. Fractions have numerators, which are the numbers on the top of the fraction that show the parts taken from the whole. Fractions also have denominators, which are the numbers on the bottom of the fraction that show how many parts are in the whole. Okay! Now that we know those terms, let’s turn to our original question. What is a rational number? A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers. The denominator in a rational number cannot be zero. Expressed as an equation, a rational number is a number a/b, b≠ 0 where a and b are both integers. This equation shows that all integers, finite decimals, and repeating decimals are rational numbers. In other words, most numbers are rational numbers. Here’s a hint: if you’re working with a number with a long line of different decimals, then your number is irrational! If you’re working with an integer or a number with terminal or repeating decimals (like 1.333333), then your number is rational! Rational Number Examples Now that we know the rational number definition, let’s use that definition to examine some numbers and see if they’re rational or not. Let’s start with the number 6. The number 6 is an integer. It’s also a rational number. Why? Because 6 can also be expressed as 6/1. When expressed as 6, both the numerator and the denominator are integers. The denominator doesn’t equal 0. What about the number -6? -6 can be written as -6/1. Or 6/-1. Either way, -6 is a rational number, because it can be expressed as a fraction where the numerator and denominator are integers and the denominator doesn’t equal 0. What’s an Irrational Number? The opposite of rational numbers are irrational numbers. In simple terms, irrational numbers are real numbers that can’t be written as a simple fraction like 6/1. Take Ï€. Ï€ is a real number. But it’s also an irrational number, because you can’t write Ï€ as a simple fraction: Ï€ = 3.1415926535897932384626433832795 (and counting) There’s no way to write Ï€ as a simple fraction, so it’s irrational. The same goes for √2. The √2 equals 1.4142135623730950...(etc). You can’t make √2 into a simple fraction, so it’s an irrational number. Famous Irrational Numbers There aren’t any famous rational numbers, because the vast majority of numbers are rational. There are a few famous irrational numbers. Here are some ones you might have seen: e: The number e (Euler's Number) is another famous irrational number. People have also calculated e to lots of decimal places without any pattern showing. The first few digits look like this: 2.7182818284590452353602874713527. Ï€: People have calculated Pi to over a quadrillion decimal places and still there is no pattern. The first few digits look like this: 3.1415926535897932384626433832795 √: Many square roots, cube roots, etc are also irrational numbers. Examples: √3 = 1.7320508075688772935274463415059 (etc) √99 = 9.9498743710661995473447982100121 (etc) Not all square roots are irrational numbers, though! If your square root results in a whole number (like √4 or √9), then you actually are working with a rational number! That’s not the only thing you have to be careful about! Sometimes, multiplying two irrational numbers will result in a rational number. For example, √2 * √2 = 2 2 is a rational number. Main Takeaways Rational numbers are numbers that can be expressed as simple fractions. Irrational numbers are numbers that can’t be expressed as simple fractions. What's Next? Want to know the fastest and easiest ways to convert between Fahrenheit and Celsius? We've got you covered! Check out our guide to the best ways to convert Celsius to Fahrenheit (or vice versa). Are you learning about logarithms and natural logs in math class?We have a guide on all the natural log rules you need to know. Did you know that water has a very special density? Check out our guide to learn what the density of water is and how the density can change.