Russian mathematician Paphnutij Chebyshev proved Bertrand’s Postulate, which had been proposed by Frenchman Joseph Bertrand just seven years earlier: if you take a prime number, say 1009, and keep counting until you reach double the prime number, you are guaranteed to encounter at least one prime number along the way.

Ada Lovelace, considered the world’s first computer programmer, dies of cancer at just 36. The ADA programming language will be dedicated to her.

La Spezia. The first American base in Europe is built. It provides logistical support for the American Marines fighting pirates under the protection of the Ottoman Empire. At Camposanto deiGenchi (distortion ofYankee) there is also an American war cemetery (also the first in Europe).

France. Reigns Napoleon III, Emperor of the French, known as Napoleon the Little.

Charles Darwin publishes Barnacles in 4 volumes

Giuseppe Garibaldi lives in New York in Antonio Meucci’s house on Staten Island.

Great Exhibition at Crystal Palace Park in Sydenham, south-east London.

Bukhara, Central Asia. Giovanni Orlandi of Parma is captured and sold as a slave to the emir. He manages to gain his favor by making him a large clock and a telescope. One day, the telescope falls and breaks. The emir summons the Italian to have it repaired, but Orlandi is drunk. He is then threatened with death for the second time unless he converts to Islam. Orlandi refuses, and his throat is slit—but only just beneath the skin, from ear to ear—with the warning that he has one more day to live. The next day, he does not change his mind and is beheaded in Registan Square.

Muslim Western China. Nian Rebellion. It will continue bloodily for nearly two decades.

In France, a coup d’état by Louis Bonaparte (Napoleon III) is launched. The ghost of communism fades throughout Europe, and the power of the bourgeoisie is consolidated everywhere.

Russia. Leo Nikolayevich Tolstoy leaves for the Caucasus, where he joins his older brother Nikolai, an officer in a small garrison. He will remain there until 1854.

England. Second attempt to lay an insulated copper cable between Dover and Calais. This time the cable is composed of four independent insulated wires, protected by layers of hemp and tar, and reinforced with wire. It proves to be more resistant than the previous one.

London. Sir Joseph William Bazalgette draws up a comprehensive plan for new sewers and diversion channels to prevent sewage from being discharged into the River Thames in central London, which has always caused all sorts of problems, including cholera. The work will be completed in 1875.

Duchy of Modena and Reggio. Duke Francis V signed a railway agreement in Rome to run the railway between Modena and Reggio Emilia. He had it run close to his home: between the Ducal Palace and the Villa Ducale Pentetorri, with the train station right in between. That same year, he also filled in the port and built Corso Estense (later Corso Vittorio Emanuele II). He also demolished the walls near Porta Albareto, filled in the canal within the walls, and built the Darsena.

Scotsman James Harrison, who emigrated to Australia in 1837, built a refrigerator based on the vapor compression of ether for an Australian brewery. Harrison and American Alexander Twining, who had simultaneously done much the same thing but with vapor compression, are considered the inventors of commercial refrigeration.

England. William Lassell discovers Uranus’s satellites Ariel and Umbriel (the third and fourth).

Virginia Military Institute, Lexington, Virginia. Professor Thomas Jonathan Jackson (who later became the legendary Stonewall Jackson in the American Civil War) teaches “Natural and Experimental Philosophy.” It’s a physics course, one of the most difficult at the institute, and he’s greatly feared by the students. He covers electricity, magnetism, acoustics, optics, classical mechanics and artillery, celestial mechanics, and astronomy. Jackson memorizes his lectures and then recites them in front of the students. If they ask for explanations, he repeats what he has just said. And he expects the students to do the same when they are questioned. He thus becomes unpopular at the institute.

Prussia, although militarily and politically strong, fails in its attempt to lead a Confederation of German States by riding the wave of widespread unification sentiment, which Austria opposes (Humiliation of Olmutz).

Birth of Charles Doolittle Walcott, America’s most powerful scientific administrator, and discoverer of the Burgess Shale Bestiary

Henry Clay, a Kentuckian and longtime leader of the conservative Whigs, proposed to the Senate a compromise between Northerners and Southerners on the issue of slavery in the new states that had joined the Union. The proposal was met with coldness by both sides.

The population of the United States of America is 23,261,000.

In the United States, 10.67% of the population is illiterate (5.80% of people over 20). In Italy, 78% of the population is illiterate.

In Chicago, where the McCormick reaper has been mass-produced (5,000 a year) for three years, the combined reaper (Combined or Combine Harvester) is also invented.

After Stephenson’s Rocket in 1829 (the first steam locomotive), Western Europe was already a dense railway hub with over 40,000 km of railways. In contrast, Asia, Africa, and South America as a whole still had only 4,000 km of railways combined. The first railway in China was laid in 1876, and was built by Europeans. The Chinese government had it removed the following year.

From exile in Gaeta (due to the riots that broke out in Rome) Pope Pius IX celebrates the Jubilee

Venice. Cholera, fueled by the lack of drinking water and sanitation, causes 2,788 deaths. The city, besieged by the Austrians for two months, is exhausted. The epidemic and hunger deal the final blow to the populace, who rise up in revolt. Manin signs the surrender on August 22nd. The last embers of the fire that had broken out in Palermo twenty months earlier are extinguished.

Comacchio. 5:00 PM. Garibaldi and his patriots arrive at the Podere Zanetto, owned by the Patrignani family, where Teresa De Carli, wife of Antonio Patrignani (Colonel of the National Guard and Gonfaloniere of Comacchio), is tending to the very precarious condition of poor Anita, who is now dying. Her faithful servant Cinti Zeffirillo, who was on lookout at the lagoon landing stage, raises the alarm: he has spotted boats heading toward the Podere Zanetto.

Comacchio. 11:00 a.m. Garibaldi and his patriots set out, dragging the pregnant and very tired Anita with them. Joined by Filippo Patrignani, they reach the Podere Cavallina farmhouse, where the mother is assisted.

San Marino. The Austrians offer Giuseppe Garibaldi surrender, but Garibaldi, probably rightly, is wary. He leaves San Marino and follows the Rubicon River to Cesenatico, where, arriving at 8:30 PM, he disarms a small Austrian garrison.

The Austrians shot all Garibaldi’s men they managed to capture. D’Aspre’s men, starting with Gorzkowski, spared no effort even in this final phase, shooting all the fugitives, as they had already done, for example, to Captain Basilio Bellotti from Romagna and five others on July 29th. Ciceruacchio was also shot, along with his son Lorenzo, just thirteen years old, and the priest Ramorino (along with five others) on August 10th. Ugo Bassi and Giovanni Livraghi, captured in Comacchio, were taken prisoner to Bologna, and shot there on August 8th. Overall, it can be said that the lieutenant-field marshal made a decisive contribution to the composition of the noblest martyrology of the Italian Risorgimento.

Giuseppe Garibaldi arrives in Arezzo with only 2,000 volunteers, in hostile territory. The city refuses to open its gates and is determined to defend itself. Garibaldi certainly has no intention of attacking the city (on the contrary, he wants it to rise up) and camps near the walls.

Duchy of Modena and Reggio. Duke Francis V institutes elementary education for children: “In every city, capital, and in those towns or villages where it is deemed appropriate, provision is made for the education of children with gymnasiums or elementary schools, unless there are seminaries or public colleges, which in themselves sufficiently provide for them.” On this occasion, the Decimal Metric System is adopted as the official system taught in schools.

Pilsner, Bohemia (now Czechia). Lager beer, with its characteristic pale color, is invented. A few years earlier, also in Bohemia, a method for producing glass on an industrial scale at a low cost had been invented, allowing beer mugs to be sold, made of glass that allows customers to see what they’re drinking. And they don’t like it: the beer often varies in color from dark brown to amber. This will lead to the success of Pilsner beer, with its distinctive, transparent blond color.

Sir George Cayley builds a large glider, complete with vertical tail, rudders, and elevators—all the wing control surfaces of an airplane. Cayley understands the concept of lift caused by the wing’s profile, and drag. Four years later, the glider will carry a boy for 500 meters.

Goffredo Mameli dies from the after-effects of a wound

David Livingstone explores the southern African continent and discovers Victoria Falls

Following the concessions of the Constitutions, around twenty elections are held over a 24-month period in the various Italian states to form their respective parliaments. The vote is always secret, as in France, unlike in England, where it is open.

Russia, Far East. Nevelskoy discovers that Sakhalin is an island and not a peninsula as previously believed. The news is kept secret for several years, and during the Crimean War, it proves useful to the Tsar’s fleet as they escape British warships that believed they had trapped the Russians on the Sakhalin Peninsula.

Gold is discovered in California: peak of the great rush to the West in the United States of America: in 1 year the population of California goes from 14,000 to more than 100,000

Giuseppe Garibaldi and his wife Anita, leading a small group of volunteers, marched up the peninsula towards Venice in an unsuccessful attempt to rekindle revolutionary and independence sentiment for Italy.

Rome. The Roman Republic officially falls to the French.

Rome. After the surrender, Rome lays down its arms, but Garibaldi refuses to surrender to the French and, at the head of 4,000 men, leaves the city for Venice, the last bastion of armed patriots.

Rome. Roman Republic. Garibaldi surrenders to the French siege and leaves the city, delivering his famous speech in St. Peter’s Square, which ends with: “…Whoever loves Italy, follow me!” Garibaldi intends to reach Venice, which is still fighting with the Austrians. The phrase, “I have nothing to offer but blood, toil, tears, and sweat,” has been described as a paraphrase of one uttered on July 2, 1849, by Giuseppe Garibaldi when he gathered his revolutionary forces in Rome: “I offer hunger, thirst, forced marches, battles, and death.” As a young man, Churchill had considered writing a biography of Garibaldi.

Rome. The defenders must evacuate the Villa del Vascello. Manara falls in the final battles. His last writing reads: “We must die to bring the Forty-Eight to a serious close. For our example to be effective, we must die.”

Rome. The French breached the walls, but Garibaldi and Manara incredibly managed to dig in a few hundred meters behind, prolonging the battle. But the battle’s fate was sealed, and with it that of the Roman Republic, attacked by those who should have been its allies, nipping in the bud a story of Italian unity that could have been very different and perhaps more straightforward.

Rome. The French gain the upper hand on Janiculum Hill, the key to Rome. The Republicans report more than a thousand casualties among their volunteers.

Rome. The truce suggested by Mazzini and rejected by Garibaldi has allowed French General Oudinot to organize a veritable army corps of 30,000 men. The French attack on the Italian volunteers begins. The defenders have no hope.

Venice. Under the energetic leadership of the Neapolitan Girolamo Ulloa, the Venetians put up tenacious resistance to the Austrians. It was decided to cut the bridge connecting the city to the coast: the Ponte di Sant’Antonio. A large artillery battery, the Batteria di Sant’Antonio, was placed on the bridge’s section. The Austrian cannons failed to hit the city, but the Batteria di Sant’Antonio was far enough advanced to strike the Austrians. The Austrians tried everything: they mounted the cannons on special supports to fire at 45 degrees, heated cannonballs to start fires, attempted bombing from hot air balloons, and even attempted a swimming attack on the Batteria di Sant’Antonio, but all their efforts were in vain. A city in the middle of the sea had little to fear.

The moderate liberals of Western Europe made two important discoveries: that revolution was dangerous and that to achieve some of their demands, they could do without it. The bourgeoisie thus ceased to be a revolutionary force. The revolution was defeated throughout Europe: the popular and revolutionary wing was silenced. At the same time, the more reactionary “black” wing was excluded from the decision-making process (blacks or pigtails convinced that liberalism and democracy had led the country to ruin). Thus, the moderate bourgeois element seized power.

Sicily. Bourbon troops finally enter Palermo, where the last bastion of Sicilian independence was held out by a resistance led by a Polish soldier: Ludwig Mieroslawski.

The Austrians conquer Livorno and put an end to the Tuscan rebellion

Palestrina, Lazio. Roman Republic. Ferdinand II’s Bourbon army, with 12,000 well-trained men (veteran of the victorious campaign against the Sicilian rebels), clashes with Italian volunteers. The attack of two Bourbon columns is repelled, one by Manara’s bersaglieri, the other by Garibaldi’s legionaries supported by a battalion of university students. Garibaldi tries to continue the counterattack once more but is stopped by Pisacane. The Bourbons flee into the night. In effect, a powerful army is routed by “a few brigands.” From this point on, the Bourbons will develop a certain respect for Garibaldi.

Piedmont. Massimo D’Azeglio becomes prime minister and remains so for over three and a half years. Together with King Victor Emmanuel II, he will be the guarantor and promoter of a liberal regime, uniquely maintaining in force, among the Italian states, the Constitution and Statute granted in 1848.

Venice. The Austrians begin work to besiege the Marghera fort, the most important Venetian stronghold outside the lagoon.

Rome. Roman Republic. The first phase of the French attack ends with a substantial victory for the defenders. Garibaldi wants to continue the counterattack to sweep away the French, but Mazzini (who initially distrusted the adventurer) stops him, hoping to reach an agreement with France, which is still considered a potential ally due to its supposed republican ideals.

Manara, founder of the Bersaglieri, formed around his 124 volunteers in Milan, wrote to Fanny Bonacini shortly before his fall in Rome: “We must die to bring the Forty-Eight to a serious close; for our example to be effective, we must die.”

Rome. Roman Republic. French warships drop anchor off Civitavecchia. 7,000 elite men, the best of the French army, disembark, led by General Oudinot, with the mission of “liberating” Rome. On paper, the republicans have 14,000 volunteers, but they are scattered from Bologna to Ancona, all the way down to the border with the Bourbon Kingdom. In Rome, there are university units, 600 riflemen under Luciano Manara, and Giuseppe Garibaldi’s Italian Legion.

Kingdom of Naples. Annibale de Gasparis, an astronomer (and also a revolutionary sympathizer), from the Capodimonte astronomical observatory in Naples, discovers the first of a series of asteroids: 10 Hygea, followed by 11 Parthenope, 13 Egeria, 15 Eunomia, 16 Psyche (incredibly composed almost entirely of metal, perhaps a naked planetary nucleus), 20 Massalia, 24 Themis, 63 Ausonia, and 83 Beatrix. The number before the name represents the order of discovery, after Ceres (or Ceres), which was the first in 1801.

Genoa. The Piedmontese army’s defeat against the Austrians humiliates everyone, but especially the “reds” (liberals, democrats, revolutionaries) of Genoa. The population revolts, and after a few hours, the garrison captain surrenders. The city is free again. But only briefly.