January 8 – An avalanche from the Skafjell mountain causes a massive wave in the Storfjordenfjord in Norway that sinks all boats that happen to be in the water at the time and kills people on both shores.[1]
April 28 – A fire at White's Chocolate House, near St. James's Palace in London, destroys the historic club and the paintings therein, but is kept from spreading by the fast response of firemen.[5]
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.[5]
August 15 – King Frederick William I of Prussia forgives his 19-year-old son, Prince Frederick, who has been confined since November to the town of Küstrin (now Kostrzyn nad Odrą in Poland) for his 1730 attempt to desert from the Prussian Army.[8] Nine years later, having been politically rehabilitated, Prince Frederick succeeds his father as King and is later remembered as "Frederick the Great".
August 23 – The oldest known sports score in history is recorded in the description of a cricket match at Richmond Green in England, when the team of Thomas Chambers of Middlesex defeats the Duke of Richmond's team by 119 to 79.
September – The first successful appendectomy is performed by English surgeon William Cookesley.[9]
October 23 – A fire at Ashburnham House in Westminster destroys 114 irreplaceable manuscripts (including a manuscript of the Anglo-Saxon Chronicle) and damages 98 others (among them the manuscript of Beowulf). Richard Bentley, the King's librarian and the House's owner, saves the only copy of the Codex Alexandrinus, carrying it under one arm as he leaps from a window. Bentley's ten year labor in translating the Greek Testament is ruined by the blaze. The remaining 844 manuscripts later form the heart of the collections of the British Library.[10][5]
Swiss mathematician Leonhard Euler announces his use of the irrational number e (approximately 2.71828) as the base for the concept of the natural logarithm, describing it in a letter to German mathematician Christian Goldbach.
Patrona Halil, an ethnic Albanian and a janissary who instigated a mass uprising in 1730 within the Ottoman Empire that brought Mahmud I to power as the new Sultan, is strangled to death in Mahmud's presence after the rebellion is suppressed.
^"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.
^ abcd"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
^Hubert Howe Bancroft, History of Alaska, 1730-1865 (A. L. Bancroft & Co., 1886) p45
^ Orcutt Frost, Bering: The Russian Discovery of America (Yale University Press, 2003) p67
^Durant Will and Ariel (1965). The Story of Civilization, Volume IX: The Age of Voltaire. Simon & Schuster.
^Selley, Peter (2016). "William Cookesley, William Hunter and the first patient to survive removal of the appendix in 1731". Journal of Medical Biography. 24 (2): 180–3. doi:10.1177/0967772015591717. PMID26758584. S2CID1708483.