| 1799–1825 | [maths] | The French mathematician and physicist Pierre-Simon Laplace publishes the five-volume Traité de mécanique céleste/Celestial Mechanics, which applies calculus to the motions of celestial bodies and Isaac Newton's theories of the Solar System to show how its stability is implicit in the law of gravitation. |
| 1800–1850 | USA [consumer products] | A revolution in retail and wholesale trade occurs: specialization transforms the urban retail market, replacing the general store with individual stores for hardware, groceries, dry goods, furnishing, books, tobacco, and so on. Cash-only sales policies are instituted around 1806. |
| 1810–1859 | USA [agriculture] | US cotton production, the vast majority of which is grown in the southern states, rises from 171,000 bales in 1810 to just under 5.4 million in 1859. |
| 1819–1826 | UK [other structures] | Scottish engineer Thomas Telford constructs the 177 m/580 ft Menai suspension bridge over the Menai Straits between Bangor, Wales and the island of Anglesey. The first modern suspension bridge, it uses chains of wrought-iron links suspended from masonry towers at either end. Lacking stiffening girders it is vulnerable to high winds. |
| 1821–1830 | USA, UK, Ireland [statistics and demography] | Emigration to the USA from Britain is 27,489, and from Ireland, 54,338. |
| 1825 | [maths] | French physicist André Ampère publishes Electrodynamics, in which he formulates the mathematical laws governing electric currents and magnetic fields. It lays the foundation for electromagnetic theory. |
| 1825 | USA [railways] | US engineer John Stevens constructs the first steam locomotive to run on rails in the USA. It runs on a short circular track at his home in Hoboken, New Jersey. |
| 1825 | England [painting] | The English artist John Constable paints Leaping Horse. |
| 4 May 1825 | England [births and deaths] | Thomas Henry Huxley, English biologist known for his defence of Darwinian evolution, born in Ealing, Middlesex, England (–1895). |
| 25 August 1825 | Uruguay, Brazil [decolonization] | Uruguay declares itself independent of Brazil. |
| 27 September 1825 | UK [railways] | The Stockton to Darlington railway line in England opens. Built by George Stephenson, it is the world's first public railway to carry steam trains. |
| 10 October 1825 | Southern Africa [births and deaths] | Paul Kruger, Boer statesman who founds the Afrikaaner nation and is instrumental in initiating the Second Anglo-Boer War, born in Cradock district, Cape Colony, Southern Africa (–1904). |
| 25 October 1825 | Austria [births and deaths] | Johann Strauss, Austrian composer of Viennese waltzes and operettas, born in Vienna, Austria (–1899). |
| 25 October 1825 | USA [canals] | The canal boat Seneca Chief opens the Erie Canal. Linking the Great Lakes with the Hudson River, it opens the Midwest to settlement. |
| 1 December 1825 | Russia [administration] | Alexander I, emperor of Russia 1801–25 who was instrumental in defeating the French emperor Napoleon I, dies in Taganrog, Russia, and is succeeded by Nicholas I, his younger brother. |
