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Yorktown, Virginia. Siege and Battle of Yorktown. This was essentially the final military act of the American Revolutionary War. 9,000 British soldiers (including German mercenaries) faced a land and sea attack by 8,000 American regulars and 3,000 militia, as well as 8,000 French soldiers on

Yorktown, Virginia. 3:00 PM. The French are the first to open fire. The first American salvo is fired by George Washington himself.

Yorktown, Virginia. Franco-American troops begin siege operations with trenches and siege guns.

Yorktown, Virginia. Allied troops are ready to launch the attack: 8,850 Americans and 7,800 French. The besieged Englishman Cornwallis can count on 7,000 soldiers.

Graves’ English fleet returns to New York harbor with 14 ships in need of repair.

Chesapeake, off Yorktown. The second French fleet from Newport also arrives. De Grasse now has 35 warships. It is the largest military fleet North America has ever seen.

Yorktown, Virginia. American ground troops have arrived. The French will arrive in two days. De Grasse’s French fleet is off the Chesapeake.

Chesapeake, off Yorktown. 6:30 PM. The Battle of the Chesapeake is over. The British lose 336 sailors killed or wounded, the French 209. But the real damage is material: six British ships disabled (Shrewsbury, Montagu, Intrepid, Princessa, Terrible, Ajax), and four French ships (Pluton, Diademe,

Chesapeake, off Yorktown. 5:15 PM. The two fleets are now in full contact. The British ships Diademe, Esprit, Terrible, Europe, and Montagu also intervened, suffering losses. The Royal Oak, London, Bedford, Resolution, Centaur, and Monarch, however, escaped almost unscathed.

The allied American and French ground troops, 9,000 in all, left the banks of the Hudson River heading south, toward Yorktown, where they were also expected to find support from the French war fleet against the English.

5:30 AM. Spartanburg, South Carolina. First contact between the American militia’s scouts and the British Army’s advanced guard. Within hours, the battle will escalate to a nearby battle in the open field at Cowpens. The overwhelming American victory will force the British to retreat into

Caribbean (West Indies). 250 miles west of St. Vincent, the English convoy, escorted by the 64-gun gunboat Ramillies, is attacked by the French. Sixty-one ships fall into French hands. Only three survive. Three thousand prisoners are taken, and the financial damage is enormous (one and

George Washington loses the battles of Brandywine and Germantown in defense of Philadelphia

Battle of Brandywine Creek, Pennsylvania. German Hessians of William Howe’s British army defeat George Washington’s Americans, capturing 400 and killing nearly as many. The British lose 93 soldiers.

New York, United States of America. British troops under General Howe attack New York.

Battle of Quebec City, Canada. American rebels attempt to attack the British in Quebec City, effectively launching an American invasion of Canada. The attempt fails, and the British capture more than 400 soldiers.

Quebec City, Canada. While Montgomery takes Montreal, Arnold and his 600 exhausted rebels dare to besiege Quebec City and demand its surrender. British General MacLean is undaunted and fires cannon fire at the first two American messengers.

Montreal, Canada. The city surrenders to American General Montgomery.

American Revolution. The number of Germans employed in the war by the British amounted to 29,166, including 12,500 from Hesse-Cassel, 4,000 from Brunswick, 900 from Hesse-Hanau, 750 from Waldeck, 1,285 from Ansbach-Bayreuth, and 1,160 from Anhalt-Zerbst. Offers from Bavaria and Württemberg were rejected due to

London. The English fleet leaves the Thames, heading for America to support theloyalists , against therebels (called insteadpatriots (from the Americans). It consisted of eight British regiments, 5,000 German Brunswickers for Canada, 12,000 Hessians, 3,500 Highlanders (both German corps), and 1,000 volunteers from the Guards.

Battle of Bunker Hill: 1:00 PM. British troops land on the Bunker Hill peninsula.

Battle of Bunker Hill: morning. British battleships assembled in Boston Bay open fire on the rebels. These include the Falcon, the Lively, the Somerset with its 64 guns, two floating batteries, and shore-based guns. The broadsides arrive forty at a time.

The English abandon Boston

Alexander Cummings invents the first “flush toilet” (although the first attempt dates back to 1596: Sir John Harrington) (contrary to urban legend, inventor Thomas Crapper had nothing to do with the invention)

Asia produces 80% of the world’s gross domestic product. India and China alone produce about 65% of the total. Europe is still negligible on the global scale. In a few decades, everything will change. By 1950, the United States and Western Europe will account for

Thomas Young, English, the youngest of 10 children of a Quaker family from Somerset; by the age of 14, he had already learned seven languages, including Hebrew, Persian, and Arabic; having become a doctor, he made important contributions to the understanding of the functioning of

Laplace proves that the irregularities of i (orbital inclination) and e (orbital eccentricity) are limited

John Harrison, now eighty years old, after demonstrating to King George III the accuracy (0.3s per day) of the H-5 clock, received recognition from Parliament which, bypassing the authority of the Longitude Board, donated him 8,750 pounds (of the 10,000 that the Board still owed

Joseph Priestley, inspired by a meeting with Benjamin Franklin in London years earlier, devoted himself to the study of “fixed air” (now known as carbon dioxide). His studies, begun in 1767, culminated in 1772 with the publication of “Instructions for Impregning Water with Fixed Air”

Euler discovers that the formula x2 + x + 41 with x = 0 … 39 generates only prime numbers. The same result is achieved with, in place of 41, the numbers q = 2, 3, 5, 11, 17, producing prime numbers up to q-2.

Pope Clement XIV opens the Vatican Museums to the public

The Sacred Congregation of Rites, at the urging of Ferdinand IV of Bourbon, King of Naples, proclaimed those tortured at Otranto in 1480-1481 by Ahmed Pasha Gedik “the Toothless” “servants of God, confessors of the faith, and glorious martyrs of Jesus Christ.” A full consecration

The Endeavour, commanded by Cook, ran aground on the Great Barrier Reef in North Queensland, Australia. The crew worked hard for days to lighten the ship, pump out water, and patch the leaks, finally refloating the vessel. This feat was also successful because the crew

Tsunami at Ishigatei Island, Japan, with an 85m high wave

Clairut, D’Alambert, and Euler ready to discard Newton’s theory by mistake of orbits of planets and the Moon

John Harrison completes the H-5 (sea-clock), a more sober version of the H-4, also portable.

Samuel Adams, a radical American independence activist, was the first to speak of total independence from England. In 1775, along with John Hancock, he was among the first to be alerted by the Minuteman to the arrival of British Redcoats in Boston. The two escaped

Ludwig Van Beethoven

The philosopher Georg Wilhelm Friedrich Hegel was born in Stuttgart.

French diplomat manages to smuggle Eugenia caryophyllata seedlings, the plant from which the precious clove is obtained, from the Moluccas and bring them to the French colony of Mauritius. From there, the plant will spread throughout the East African coast, especially to Zanzibar, where cloves

Industrial Revolution: Richard Arkwright develops the hydraulic loom

Peter III of Russia becomes Tsar

William Harrison takes his father John’s H-3 and H-4 watches from London to Port Royal, Jamaica and back: in 81 days at sea, the H-4 loses only 5 seconds!

Leonhard Euler, the most prolific mathematician in history, publishes Euler’s Formula: in a regular polyhedron F-E+V=2, where F is the number of faces, E is the number of edges, and V is the number of vertices. It will later be generalized to F-E+V=2-2g, where g

Shropshire, England. At Abraham Darby’s foundry in Coalbrookdale, Richard Ford adjusted the amount of coal and coke added to the iron ore to obtain steel of varying strength. A wide variety of applications were born, from beams to railway tracks (chemin de fer, Eisenbahn, via

Genoa was liberated from the Austrian troops who had occupied it for several months with Piedmontese support.

Chemist and director of the Swedish Mint, Georg Brandt, realized that enamel was not a compound of arsenic and known metals, as was believed at the time, but rather a compound of a new metal, cobalt. The name derives from Kobold, an underground demon from

Abraham De Moivre discovers the famous “Gaussian” bell curve or Normal Distribution.

Fissure volcanic eruption at Timanfaya on the island of Lanzarote, Canary Islands; the eruption is described by the priest of Yaiza, Don Andres Lorenzo Curbelo.

George Frideric Handel composed most of his pieces at the London court as “Composer of Musick”

The Sea-Clock method and the Lunar Distance method compete for estimation of longitude at sea

Irish philosopher George Berkeley sailed for Newport, Rhode Island. He intended to found an academy there, but the funds never arrived, and in 1731 he returned to England. The Americans, however, did not forget his concern for the education of their ancestors, and named a

The Amish, a religious sect founded by Jakob Amman, and a breakaway from the Mennonites of Menno Simmons, fled to the United States to avoid military service in German-speaking Switzerland.

After the Marseille epidemic, plague slowly disappeared from Western Europe, perhaps because the spread of the brown rat deprived the black rat (or common rat) of its food resources. It remained in the Balkans and the Levant.

Marseille. Last serious outbreak of bubonic plague in Europe.

China. The Qing Dynasty allowed Moscow to establish a Russian Orthodox ecclesiastical mission in Beijing, which ultimately served as the Russian embassy in China. It would remain the only foreign mission of its kind in China for over a century.

War between the Ottoman Empire and Venice.

England. The House of Hanover reigns, with six sovereigns: George I, George II, George III, George IV, William IV, and Victoria. Queen Victoria has nine children, including the future King Edward VII, who, however, inheriting his father’s name, Prince Albert of Saxe-Coburg-Gotha, is considered a

South Africa. A smallpox epidemic wipes out the San population shortly after the arrival of Europeans.

Posthumous publication of Ars Conjectandi by Jakob Bernoulli, a Swiss mathematician and physicist, with which Probability Theory reaches full maturity.

Irish philosopher George Berkeley publishes A Treatise Concerning the Principles of Human Knowledge, in which he argues that matter does not exist, that it is no more real than a rainbow.

The French attack the city of Rio de Janeiro, initially defeated but then the Portuguese surrender to the besiegers and pay a substantial ransom in gold, sugar and cattle; during the return journey two French ships sink during a violent storm and a good part

Battle of Poltava: Sweden’s Baltic Empire falls and Russia occupies its eastern territories; the king in Sweden is the young Charles XII.

Epidemics of the “Picardy sweats” raged in France. The disease eventually disappeared completely, long before modern medicine could diagnose it.

Coalbrookdale, England. First blast furnace for smelting iron (in the West: the first ever was in China in 200 BC).

Irish philosopher George Berkeley publishes An Essay towards a New Theory of Vision, in which he approaches the problem of explaining how we judge the distance and size of the objects we see.

Scotland and England, with a specific Treaty of Union, officially formed the Kingdom of Great Britain. The kingdoms of Scotland and England had already been united dynastically since 1603.

Eruption of Mount Fuji in Japan.

Upper State, New York. A molar from an American mastodon is shipped to London. The bones will be studied in 1739. Further bones will be found in Ohio. The interpretation of these finds is mixed: some suggest they belong to giants who lived in ancient

The Great Storm of England devastates the British Isles; the Royal Navy alone loses 1,200 men in the shipwrecks.

Isaac Newton is voted a fellow and then chosen as president of the Royal Society, thus saving it from decline.

Robert Hooke, Isaac Newton’s archenemy, dies; this event will convince the reticent Newton to publish his particle theory of light in 1704, after several decades. Hooke and Newton have been privately and publicly engaged for years in a double dispute: over light and gravitation.

South Africa. First clash between the Dutch and the black Bantu people. The Dutch arrived in South Africa in 1652, starting from Cape Town, but encountered little organized resistance from the natives, only a few Khoisan villages. The Bantus, coming from Nigeria and Cameroon, stopped

Isaac Newton: 2nd edition of “Principia Mathematica”: Calculation of the lunar orbit with an error of 10 arc minutes

Maria Kirch (wife of Gottfried Kirch, who was the first to use a telescope to discover and observe a comet) was the first woman to discover a comet. It was the “Comet of 1702.”

Isaac Newton was the right man in the right place at the right time to settle an age-old controversy, born of ignorance of statistics: the Pyx Test to monitor the variability of the weight of silver coins at the end of the minting process. But

Johann Sebastian Bach is a 15-year-old boy at the Michaelisschule in the city of Luneburg, 50 km from Hamburg.

Berlin is a cosmopolitan city: one in five Berliners is a French Huguenot refugee, followed by Protestants from Salzburg, Waldensians, Mennonites, Scottish Presbyterians, Jews, Catholics, and openly agnostics. Freedom and the presence of so many foreigners have caused a prodigious cultural explosion. There is also

Early origins of the London Stock Exchange

Florence. The Medici inventory of musical instruments already mentions “a harpicembalo by Bartolomeo Cristofori, of a new invention, which plays both piano and forte.” However, the first surviving piano was made by Cristofori himself in 1720 and is now at the Metropolitan Museum of Art