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1845 ( MDCCCXLV) was a common year starting on Wednesday of the Gregorian calendar and a common year starting on Monday of the Julian calendar, the 1845th year of the Common Era (CE) and (AD) designations, the 845th year of the Anno Domini 2nd millennium, the 45th year of the 19th century, and the 6th year of the 1840s decade. As of the start of 1845, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.
January 23 – The United States Congress establishes a uniform date for federal elections, which will henceforth be held on the first Tuesday after the first Monday in November.
New York Evening Mirror.
February 1 – Anson Jones, President of the Republic of Texas, signs the charter officially creating Baylor University (the oldest university in the State of Texas operating under its original name).
February 7 – In the British Museum, a drunken visitor smashes the Portland Vase, which takes months to repair.
February 28 – The United States Congress approves the annexation of Texas.
March 1 – President John Tyler signs a bill authorizing the United States to annex the Republic of Texas.
March 4 – James K. Polk is sworn in as the 11th President of the United States. ).
March 13 – The by Violin Concerto Felix Mendelssohn premieres in Leipzig, with Ferdinand David as soloist.
March 17 – Stephen Perry patents the rubber band, in the United Kingdom.  March 30 – Due to different transition dates to the Gregorian calendar, Finland (then part of the Russian Empire) is the only place in the world to have Easter day on this particular Sunday.
April 7 – An earthquake destroys part of Mexico City, along with the nearby towns of Tlalpan and Xochimilco.
April 10 – The Great Fire of Pittsburgh destroys much of the American city of Pittsburgh.
April 20 – Ramón Castilla becomes president of Peru.
May – Frederick Douglass's autobiographical is published by the Narrative of the Life of Frederick Douglass, an American Slave Boston Anti-Slavery Society.
May 2 – Yarmouth suspension bridge in Great Yarmouth, England, collapses leaving around 80 dead, mostly children. 
May 19 – HMS and Erebus HMS , with 134 men, comprising Sir Terror John Franklin's expedition to find the Northwest Passage, sail from Greenhithe on the Thames. They will last be seen in the summer, entering Baffin Bay. 
May 25 – A theater fire in Canton, China, kills 1,670.
June 8 – Former U.S. President Andrew Jackson, 78, dies at The Hermitage (Nashville, Tennessee).
Alexander III of Russia
Wilhelm Conrad Röntgen
Gustaf de Laval
January 7 – King Ludwig III of Bavaria (d. 1921)
January 29 – Pyotr Bezobrazov, Russian admiral (d. 1906)
February 2 – Ivan Puluj, Ukrainian physicist, inventor (d. 1918) )
February 15 – Elihu Root, American statesman, diplomat, recipient of the Nobel Peace Prize (d. 1937)
February 25 – Sir George Reid, 4th Prime Minister of Australia (d. 1918)
March 3 – Georg Cantor, German mathematician (d. 1918)
March 4 – Henry Clay Taylor, American admiral (d. 1904)
March 10 – Emperor Alexander III of Russia (d. 1894)
Governor of New South Wales (d.
March 27 – Wilhelm Röntgen, German physicist, Nobel Prize laureate (d. 1923)
April 4 – František Plesnivý, Austro-Hungarian architect (d. 1918)
April 5 – Jules Cambon, French diplomat (d. 1935)
April 22 – Carlo Caneva, Italian general (d. 1922)
April 24 – Carl Spitteler, Swiss writer, Nobel Prize laureate (d. 1924)
May 4 – William Kingdon Clifford, English mathematician, philosopher (d. 1879)
May 9 – Gustaf de Laval, Swedish engineer, inventor (d. 1913)
May 12 – Gabriel Fauré, French composer (d. 1924)
May 14 – Charles J. Train, American admiral (d. 1906)
May 15 – Élie Metchnikoff, Russian microbiologist, recipient of the Nobel Prize in Physiology or Medicine (d. 1916)
May 17 – Jacint Verdaguer, Catalan poet (d. 1902)
May 25 – Eugène Grasset, Swiss-born artist (d. 1917)
May 30 – King Amadeo I of Spain (d. 1890)
May 31 – R. E. B. Crompton, British electrical engineer, industrialist and inventor (d. 1940)
June 7 – Leopold Auer, Hungarian violinist, composer (d. 1930)
June 18 – Charles Louis Alphonse Laveran, French physician, recipient of the Nobel Prize in Physiology or Medicine (d. 1922) June 22 – Richard Seddon, 15th Prime Minister of New Zealand (d. 1906)
July 4 – Thomas John Barnardo, Irish philanthropist (d. 1905)
July 19 – Horatio Nelson Young, American naval hero (d. 1913)
August 9 – André Bessette, Canadian religious leader and saint (d. 1937)
August 10 – Abai Qunanbaiuly, Kazakh poet (d. 1904)
August 19 – Edmond James de Rothschild, French philanthropist (d. 1934)
Roman Catholic religious professed and saint (d.
August 21 – William Healey Dall, American naturalist, biologist and explorer (d. 1927)
August 25 – King Ludwig II of Bavaria (d. 1886)
September 1 – Paul Methuen, 3rd Baron Methuen, British field marshal (d. 1932)
September 9 – Warner B. Bayley, United States Navy rear admiral (d. 1928)
Emile Baudot, French telegraph engineer and inventor (d.
October 13 – Charles Stockton, American admiral (d. 1924)
William McKendree Carleton, American poet (d.
November 3 – Inoue Yoshika, Japanese admiral (d. 1929)
November 4 – Vasudev Balwant Phadke, Indian revolutionary (d. 1883)
November 10 – Sir John Thompson, 4th Prime Minister of Canada (d. 1894)
November 13 – Marta Abreu, Cuban philanthropist (d. 1909)
José Maria de Eça de Queirós, Portuguese writer (d.
December 9 – Joel Chandler Harris, American writer (d. 1908) December 24 – George I of Greece (d. 1913)
January 11 – Etheldred Benett, British geologist (b. 1776)
January 24 – Emiliano Madriz, acting Supreme Director of Nicaragua (b. 1800)
January 28 – Mary Ann Browne, British poet and writer of musical scores (b. 1812)
February 13 – Henrik Steffens, Norwegian philosopher (b. 1773)
February 22 – William Wellesley-Pole, 3rd Earl of Mornington, British politician (b. 1763) March –
Nicolás Espinoza, Head of State of El Salvador (b. 1795)
March 13 – Charles-Guillaume Étienne, French playwright (b. 1778)
March 18 – Johnny Appleseed, American pioneer (b. 1774)
April 10 – Dr. Thomas Sewall, American anatomist (b. 1786)
April 20 – Seku Amadu, founder of the Fula Massina Empire (b. 1773)
May 15 – Braulio Carrillo Colina, Costa Rican Head of State (b. 1800)
June 4 – Lasse-Maja, notorious Swedish criminal (b. 1785) June 8 – Andrew Jackson, 7th President of the United States (b. 1767)
Charlotte Ann Fillebrown Jerauld
July 17 – Charles Grey, 2nd Earl Grey, Prime Minister of the United Kingdom (b. 1764)
Heinrich Graf von Bellegarde, Austrian field marshal, statesman (b.
Charlotte Ann Fillebrown Jerauld, American poet and story writer (b.
August 23 – Rafael Urdaneta, hero of the Latin American War of Independence (b. 1788)
October 12 – Elizabeth Fry, British humanitarian (b. 1780)
October 18 – Jacques Dominique, comte de Cassini, French astronomer (b. 1748)
October 26 – Lady Nairne, Scottish songwriter (b. 1766)
November 17 – Sir Salusbury Pryce Humphreys, British admiral (b. 1778) November 18 – King Aleamotuʻa of Tonga (b. 1738)