April 28 – A fire at White's Chocolate House, near St. James's Palace, destroys the historic club and the paintings therein, but is kept from spreading by the fast response of firemen.
June 4 – The English market town of Blandford Forum is destroyed by fire, with the exception of 26 houses. About one-third of the uninsured losses are paid for by the collection of disaster relief money. 
March 21 – The Molasses Act is passed by British House of Commons, which reinforces the negative opinions of the British by American colonists. . The Act then goes to the House of Lords, which consents to it on May 4 and it receives royal assent on May 17.
After British Prime Minister Robert Walpole's proposed excise tax bill results in rioting over the imposition of additional taxes and the use of government agents to collect them, Walpole informs the House of Commons that he will withdraw the legislation. 
June 12 – In Berlin,Prince Frederick of Prussia, the 21-year-old heir to the throne reluctantly marries Duchess Elisabeth Christine of Brunswick-Bevern in order to avoid prosecution for desertion from the Prussian Army and to be guaranteed the throne. Despite the unhappy marriage Frederick and Elisabeth later reign as King and Queen Consort of Prussia.
September 12 – Stanislas Leszczynski, who had been King of Poland from 1704 to 1709 until being driven from the throne by King Augustus II, is returned to office by the vote of the Sejm.  Russia and Austria protest the election, since King Stanislaus is backed by France and Sweden.
December 19 – Unsuccessful in capturing Baghdad from the Ottoman Empire, Persia's ruler Nader Shah signs the Treaty of Baghdad with the Ottoman Governor, Ahmad Khan Pasha, with the Turks and the Iranians agreeing to restore the boundary between the two empires to the lines before the 1732 Ottoman invasion of Iran. 
October 23 – Jamaica's Governor John Ayscough declares martial law to fight the slave rebellion that began in 1733, then drafts 600 men into the colonial army to march into the Blue Mountains. 
October 31 – Chief Tomochichi of the Yamacraw band of the Muscogee Nation ends a successful four and a half month visit to Great Britain, along with Georgia Governor James Oglethorpe and other Yamacraw Indians, after having signed the cession of the area of modern day Savannah, Georgia to the Georgia Company. On June 16, he and the Muscogee delegation (Senauki, Toonahowi, Hillispilli, Umpichi, Apokutchi, Santachi and Stimaletchi) had been welcomed as a guest of King George II. The group departs on HMS Aldborough after completing the visit by the largest delegation of Native Americans since 1616. 
February 3 – All 256 people on board the Dutch East India Company ships Vliegenthart and Anna Catherina die when the two ships sink in a gale off of the Netherlands coast. The wreckage of Vliegenthart remains undiscovered until 1981. 
March 10 – The Russian Empire and Persia sign the Treaty of Ganja, with Russia ceding territories in the Caucasus mountains to Persia, and the two rivals forming a defensive alliance against the Ottoman Empire.
October 3 – An agreement between the European powers brings a ceasefire in the War of the Polish Succession, one week short of the second anniversary of the war. With France and Spain on the side of the reigning monarch, Stanis?aw Leszczy?ski, and Prussia, Russia, and Austria supporting Augustus III, a preliminary peace is signed allowing Stanislaw to reign in Warsaw and Augustus to reign in Krakow, and is ratified in 1738.
April 14 – German adventurer Theodor Stephan Freiherr von Neuhoff is crowned King Theodore of Corsica, 25 days after his arrival on the island on March 20. . His reign ends on November 5 when he flees Corsica.
September 29 – The Gin Act 1736 goes into effect, placing a steep tax on the sale of gin and license requirements for its sale, with the intent of reducing consumption of the liquor in Britain. Widely ignored, the Act is repealed in 1734. 
November 13 – Word of the discovery of silver, south of what is now the U.S.-Mexican border, reaches Sonora Governor Juan Bautista Anza and soon leads to prospectors coming to Nogales to find more silver.  Late in October, a Yaqui Indian prospector, Antonio Siraumea, had discovered large slabs of silver ("Las planchas de plata"), and at the Estancia Arizona, a ranch owned by Captain Bernardo de Urrea. The region, and later the U.S. territory, and state of Arizona are named for Urrea's ranch.
February 27 – French scientists Henri-Louis Duhamel du Monceau and Georges-Louis Leclerc de Buffon publish the first study of correlating past weather conditions with an examination of tree rings), "On the cause of the eccentricity of the woody layers which one perceives when one cuts horizontally the trunk of a tree" (De la cause de l'excentricité des couches ligneuses qu'on apperçoit quand on coupe horisontalement le tronc d'un arbre)
Lots are first advertised for sale in the new town of Richmond, Virginia, by the placement of a notice by William Byrd in the Virginia Gazette. According to the paper, "... on the North Side of James River, near the Uppermost Landing, and a little below the Falls, is lately laid off by Major Mayo, a Town, called Richmond, with Streets 65 Feet wide, in a pleasant and healthy Situation, and well supply'd with Springs of good Water. It lies near the Publick Warehouse at Shoccoe's, and in the midst of great Quantities of Grain, and all kind of Provisions. The Lots will be granted in Fee Simple, on Condition only of building a House in Three Years Time, of 24 by 16 Feet, fronting within 5 Feet of the Street. The Lots to be rated according to the Convenience of their Situation, and to be sold after this April General Court, by me, William Byrd." 
March 28 – The British House of Commons votes, 257 to 209, for a resolution in favor of a war with Spain, clearing the way for the 1739 War of Jenkins' Ear after years of lobbying my mariner Robert Jenkins. Basil Williams, The Life of Wiliam Pitt Earl of Chatham (Longmans, Green, and Co., 1913), reprinted by Routledge, 2018
July 10 – Thomas Pellow of Cornwall finally escapes captivity, 23 years after he had been captured by Barbary pirates and held as a slave in Morocco. He arrives in British territory when the ship he is on sails into Gibraltar Bay on July 21, and later recounts his story in the book The Adventures of Thomas Pellow, of Penryn, Mariner: Three and Twenty Years in Captivity Among the Moors. 
December 27 – After setting off from Rotterdam in August with 240 immigrants to America, the British ship Princess Augusta is wrecked near Block Island off of the coast of the colony of Rhode Island.  During the voyage, 200 passengers and seven crew died from illness spread by contaminated water. Another 20 die after the crew leaves rows to shore. The wreck later becomes the subject of the legend of the "Palatine Light" ghost ship and of John Greenleaf Whittier's 1867 poem "The Palatine".
December 30– Months of unseasonably cold weather begin in Ireland, precipitating the Irish Famine of 1740, known as Bliain an Áir ("The Year of Slaughter"). A January 5 dispatch from Dublin to the Stamford Mercury says "Since last Wednesday we have had the most violent cold Weather that was ever known in this Kingdom; hard Frost began that evening, which has continued ever since with a very stormy Wind at South-East."  At least 13% of Ireland's population dies of starvation in the year that follows. 
^ abcde"Fires, Great", in The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance, Cornelius Walford, ed. (C. and E. Layton, 1876) p49
^"List of British Merchant Ships, taken or plundered by the Spaniards", The Political State for the Month of April, 1738' of Great Britain (April 30, 1738) p322
^"The imperial heritage of Peter the Great in the foreign policy of his early successors", by E. V. Anisimov, in Imperial Russian Foreign Policy, ed. by Hugh Ragsdale (Cambridge University Press, 1993) p30
^Thomas Carlyle, History of Friedrich the Second, Called Frederick the Great (Harper & Brothers, 1858) p372
^Douglas M. Gibler, International Military Alliances, 1648-2008, (SAGE Publications, 2008) p.85
^Kaveh Farrokh, Iran at War, 1500-1988 (Bloomsbury Publishing, 2011) pp110-113
^"George II", in An Index of Dates, Comprehending the Principal Facts in the Chronology and History of the World, from the Earliest to the Present Time, by J. Willoughby Rosse (Henry G. Bohn, 1858) p347
^Chris Cook and Philip Broadhead, The Routledge Companion to Early Modern Europe, 1453-1763 (Taylor & Francis, 2012) p.126
^"Fires, Great", in The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance, Cornelius Walford, ed. (C. and E. Layton, 1876) p50
^W. H. Wilkins, Caroline, the Illustrious Queen-Consort of George II. and Sometime Queen-Regent: A Study of Her Life and Time, Volume 2 (Longmans, Green, 1901) p20
^Oscar Peschel and Gustav Leipoldt, Physische Erdkunde: Nach den Hinterlassenen Manuscripten Oscar Peschel's (Physical Geography: According to Oscar Peschel's Surviving Manuscripts (Duncker & Humblot, 1879) p. 152
^Carlos R. Herrera, Juan Bautista de Anza: The King's Governor in New Mexico (University of Oklahoma Press, 2015) p37
^Journal du voyage fait par ordre du roi à l'équateur. Paris. 1751.
^Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio.
^An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst.
^ W. N. Hargreaves-Mawdsley, Eighteenth-Century Spain 1700-1788: A Political, Diplomatic and Institutional History (Palgrave Macmillan UK, 1979)
^Arthur Hassall, The Balance of Power, 1715-1789
By (Macmillan, 1907) p. 119
^Historical Calendar (Philippine National Historical Commission, 1970), p11
^ S.R. Bakshi and O.P. Ralhan, Madhya Pradesh Through the Ages (Sarup & Sons, 2007) p. 384
^Kara Reilly, Automata and Mimesis on the Stage of Theatre History (Springer, 2011) pp83-84
^Richard L. Kagan, Clio and the Crown: The Politics of History in Medieval and Early Modern Spain (Johns Hopkins University Press, 2010) p. 279
^"Subscribing to the Building of a Masonic Temple", in The American Ecclesiastical Review (May 1914) p.606
^"Paul, Lewis", by Justin Corfield, in The Encyclopedia of the Industrial Revolution in World History p710
^Francisco A. Eissa-Barroso, The Spanish Monarchy and the Creation of the Viceroyalty of New Granada (1717-1739) (Brill, 2016) p232
^Bennet Woodcroft, Titles of Patents of Invention, Chronologically Arranged, From March 2, 1617 (14 James I.) to October 1, 1852 (16 Victoriae). 1617 - 1823 (The Queen's Printing Office, 1854) p104-105
^Thomas Pellow, The Adventures of Thomas Pellow, of Penryn, Mariner (reprinted by T. Fisher Unwin, 1890) pp. 813-816
^C. H. von Manstein, Memoirs of Russia, Historical, Political and Military, from the Year 1727 to 1744 (Beckett & DeHondt, 1770) pp203-210
^Pedar Foss and John J. Dobbins, The World of Pompeii (Routledge, 2009) p29
^Jill Farinelli, The Palatine Wreck: The Legend of the New England Ghost Ship (University Press of New England, 2017) pp. 101-105