Captain Cook's Journey to the Undiscovered Country
Australia has already been discovered by various Dutch, Portuguese and Spanish sailors, but apparently it doesn't count until the English discover it. Captain Cook is sent to Tahiti under secret orders to observe the transit of Venus across the Sun. The next opportunity won't take place for another 100 years. Other nations are suspicious of the British Empire sending ships across the world, so once Captain Cook reaches Tahiti, he opens his SECOND set of secret orders. They read in part...   
- "Whereas there is reason to imagine that a Continent or Land of great extent, may be found to... the Southward of the Track of any former Navigators ... you are to proceed to the southward in order to make discovery of the Continent above mentioned... You are also, with the consent of the natives, to take possession of convenient situations in the country in the name of the King of Great Britain; or, if you find the country uninhabited, take possession for His Majesty by setting up proper marks and inscriptions as first discoverers and possessors." 
'No Liberty! No King!'
It's a massacre as British troops fire into the crowd. 6 are dead. 15 are wounded. It's not Boston. IT'S LONDON! The roots of this riot began in 1763 when John Wilkes published an article that was critical of King George the 3rd. (The actual offense was sedition. It was implied, but obvious enough.) The King issued a general warrant and people were swept up including Wilkes. Wilkes was a member of Parliament so he argued successfully that he retained his free speech rights. He went right on publishing. Parliament then moved to expel Wilkes from the Commons so he fled the country. He was forced to return this year after he ran out of money. He is now in prison, but his supporters have been gathering in protest shouting "No Liberty! No King!". They are read the Riot Act and ordered to disperse. They refuse. Out come the muskets and you know the rest. 
- Encyclopedia Britannica publishes part 1. 100 parts are planned. They will be bound into three volumes, so the parts are short. 
- Dolley Madison is born. She will become First Lady, and during the War of 1812, she will make sure that famous portrait of George Washington is saved before the British come rolling through. 
- Samuel Slater "The Traitor" is born in England. He will bring the Industrial Revolution to the USA! In Great Britain he will be known as "Slater the Traitor!" 
This Year in Wikipedia
Year 1768, Wikipedia.
- "Calico", Asimov's Chronology of Science and Discovery (PDF), Houghton Mifflin. ISBN 0062701134.
- First voyage of James Cook - Wikipedia (2016). Retrieved on 18 April 2016. “The Royal Society, and especially Alexander Dalrymple, believed that it must exist and that Britain's best chance of discovering it and claiming its fabled riches before any other rival European power managed to do so would be by using Cook's Transit of Venus mission (on an inconspicuous small ship such as the Endeavour) as a cover.”
- EXPLORATION through the AGES: James Cook - The First Voyage, 1768-1771. The Mariners' Museum (2016). Retrieved on 17 April 2016. “On April 20, 1770, the Endeavour anchored at Botany Bay. In June of that year, while traveling the coast of Australia, the Endeavour was nearly wrecked; when the ship was examined, it was found that only a large piece of coral was plugging one of the holes. Cook and his crew struggled as they tried to navigate and escape the Great Barrier Reef.”
Mackay, Joseph Angus (July 30, 1768). Cook's Secret Orders. New Zealand Electronic Text Collection,. Retrieved on 17 April 2016. “The full text appears in the Navy Records Society's Naval Miscellanies, Vol. 3, 1928, p. 343 et seq., and the salient points are as follows:
'Whereas the making of discoveries of countries hitherto unknown and the attaining of a knowledge of distant parts, which, though formerly discovered, have yet been imperfectly explored, will redound greatly to the honour of this nation as a Maritime Power, as well as to the dignity of the Crown of Great Britain, and may tend greatly to the advancement of the trade and navigation thereof.
'And, whereas there is reason to imagine that a continent, or land of great extent, may be found to the southward of the tract lately made by Captain Wallis in His Majesty's ship the Dolphin (of which you will herewith receive a copy) or of the tract of any former navigators in pursuits of the like kind; you are, therefore, in pursuance of His Majesty's pleasure, hereby required and directed to put to sea with the bark you command, so soon as the observation of the transit of the planet Venus shall be finished, and observe the following instructions:
'You are to proceed to the southward in order to make discovery of the continent above mentioned until you arrive in the latitude of 40 deg., unless you sooner fall in with it: but, not having discovered it in that run, you are to proceed in search of it to the westward, between the latitude before mentioned and the latitude of 35 deg., until you discover it or fall in with the Eastern side of the land discovered by Tasman and now called New Zealand.
'If you discover the continent above mentioned, either in your run to the southward or to the westward, as above directed, you are to employ yourself diligently in exploring as great an extent of the coast as you can…. You are also to observe the nature of the soil and the products thereof…. You are likewise to observe the genius, temper, disposition and number of the natives, if there be any, and endeavour, by all proper means, to cultivate a friendship and alliance with them, making them presents of such trifles as they may value, inviting them to traffic, and showing them every kind of civility and page 25 regard, taking care, however, not to suffer yourself to be surprised by them, but to be always upon your guard against any accident.
'You are also, with the consent of the natives, to take possession of convenient situations in the country in the name of the King of Great Britain; or, if you find the country uninhabited, take possession for His Majesty by setting up proper marks and inscriptions as first discoverers and possessors.
'But, if you should fail of discovering the continent before mentioned you will, upon falling in with New Zealand, carefully observe the latitude and longitude in which that land is situated and explore as much of the coast as the condition of the bark, the health of her crew, and the state of your provisions will admit of, having always great attention to reserve as much of the latter as will enable you to reach some known Port, where you may procure a sufficiency to carry you to England, either round the Cape of Good Hope, or Cape Horn, as from circumstances you may judge the most eligible way of returning home….
'Given &c the 30th of July, 1768, Ed. Hawke, Py. Brett, C. Spencer.'”
- Charles Green (astronomer) - Wikipedia (2016). Retrieved on 17 April 2016. “Due to Green's death on the homeward voyage, the work of collating and analysing his results fell first to Cook, and ultimately to Nevil Maskelyne. Cook admitted that Green's papers were in a disorganised state, when he inspected them after Green's death, and that some of the timings were inconsistently recorded in various of the astronomer's papers.”
- John Wilkes - Wikipedia (2016). Retrieved on 12 April 2016. “When Wilkes was imprisoned in the King's Bench Prison on 10 May 1768, his supporters appeared before King's Bench, London, chanting 'No liberty, no King.' Troops opened fire on the unarmed men, killing seven and wounding 15, an incident that came to be known as the St George's Fields Massacre. The Irish playwright Hugh Kelly, a prominent supporter of the government, defended the right of the army to use force against rioters, which drew the anger of Wilkes' supporters and they began a riot at the Drury Lane Theatre during the performance of Kelly's new play A Word to the Wise forcing it to be abandoned.”
- Society of Gentlemen Supporters of the Bill of Rights - Wikipedia (2016). Retrieved on 18 April 2016. “On 23 July 1771 the Society published a manifesto calling for annual Parliaments, the exclusion of placemen and pensioners from the House of Commons, outlawing bribery in elections, the 'full and equal representation of the people', the abolition of all excise taxes and for America not to be taxed without her consent.”
- NYPD issues new stop-and-frisk rules. NY Daily News (March 3, 2015). Retrieved on 18 April 2016. “The updated rules hammer home the point that cops can't stop-and-frisk people for merely making 'furtive movements,' such as reaching for their waistband or acting nervous, or for being in a high-crime area — reasons that were allowed in the past.”
- Stop and Frisk Practices. New York Civil Liberties Union (2016). Retrieved on 18 April 2016. “An analysis by the NYCLU revealed that innocent New Yorkers have been subjected to police stops and street interrogations more than 4 million times since 2002, and that black and Latino communities continue to be the overwhelming target of these tactics. Nearly nine out of 10 stopped-and-frisked New Yorkers have been completely innocent, according to the NYPD’s own reports.”
- Writ of assistance (General Warrant) - Wikipedia (2016). Retrieved on 18 April 2016. “In general, customs writs of assistance served as general search warrants that did not expire, allowing customs officials to search anywhere for smuggled goods without having to obtain a specific warrant. These writs became controversial when they were issued by courts in British America in the 1760s, especially the Province of Massachusetts Bay. Controversy over these general writs of assistance inspired the Fourth Amendment to the United States Constitution, which forbids general search warrants in the United States.”
- History of the Encyclopædia Britannica - Wikipedia (2016). Retrieved on 18 April 2016. “Needing an editor, the two chose a 28-year-old scholar named William Smellie who was offered 200 pounds sterling to produce the encyclopedia in 100 parts (called 'numbers' and equivalent to thick pamphlets), which were later bound into three volumes.”
- Dolley Madison - Wikipedia (2016). Retrieved on 18 April 2016. “Popular accounts during and after the war years tended to portray Dolley Madison as the one who removed the painting, and she became a national heroine. Early twentieth-century historians noted that Jean Pierre Sioussat, a Frenchman, had directed the servants in the crisis.”
- Samuel Slater - Wikipedia (2016). Retrieved on 18 April 2016. “Samuel Slater (June 9, 1768 – April 21, 1835) was an early English-American industrialist known as the 'Father of the American Industrial Revolution' (a phrase coined by Andrew Jackson) and the 'Father of the American Factory System.' In the UK he was called 'Slater the Traitor'  because he brought British textile technology to America, modifying it for United States use.”