Boston Common: October 12, 1713, 10:33:52 AMEdit

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Boston Common
A park in central Boston, founded sometime around 1634 and the site of many public executions. Google Maps

as Jack Ketch stands there
Jack Ketch is the archetypal name for an executioner. It comes from Jack Ketch (died 1686), an English executioner employed by King Charles II. Wikipedia:Jack Ketch

The Puritans gaze
Puritans of the 16th century were a group of Protestants within the Church of England that demanded greater strictness in religious discipline. They were known for being strict on moral and religious matters, to some, excessively so. They made up a sizable proportion of the population of early Massachusetts. Wikipedia:Puritans

a squadron of lobsterbacks
British soldiers were called lobsterbacks because of the distinctive red colour of their uniforms.

a stone powder-house
A powder-house is a building used to store gunpowder, an explosive, safely.

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Sir Isaac Newton's temperature scale
The Newton scale, proposed in the early 1700's, uses the same reference as the Celsius scale: water's freezing point. Wikipedia:Newton scale

Herr Fahrenheit were here with one of his new quicksilver-filled, sealed-tube thermometers"
Fahrenheit is credited with creating one of the first accurate, reproducible instruments for measuring temperature.
This is also one of the first mentions of quicksilver (aka. mercury), an important theme throughout The Baroque Cycle.

he would probably observe something in the Fifties
Fahrenheit proposed his scale in 1724. 50°F is approximately 10°C.

an outmoded rapier
A rapier is a slender sword with a large hilt to protect the hand. Wikipedia:Rapier

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The redcoats
British soldiers. "Redcoat" is a less derogatory term than "lobsterback."

a new burying ground... by the granary
The Boston Granary Burial ground started in 1660. The granary was moved in 1737. City of Boston

Navy's largest men-of-war
A man-of-war is a large ship armed with cannon and propelled by sails. Wikipedia:Man-of-war

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French or Spanish galleons
A galleon is a large sailing ship with multiple decks, used for battle or cargo. Wikipedia:Galleon

one Cartesian number line… plotted out… whatever strange curves
The number line is a line along which a point can be identified uniquely; the rest of the paragraph uses the Cartesian coordinate system as a metaphor. This system is nowadays taken for granted, but was only introduced (formally) by René Descartes in 1637. Wikipedia:Cartesian coordinate system

some carpenter's block-plane
A small tool for shaving pieces of wood. Wikipedia:Block plane

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in most parts of Christendom… tallow-chandler's sons do not go to grammar school
Puritan colonists, quite unlike most other Christian societies, made a point of educating their children. Harvard College was founded in 1636, and in 1647 Massachusetts' law required towns to hire a schoolmaster to teach children.

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I know of the war… A Peace has been signed at Utrecht
The Treaty of Utrecht (April 1713) ended the War of the Spanish Succession between Spain and France against England, the Dutch Republic, and others. Wikipedia:Treaty of Utrecht

You have Barkers here?
The Barkers are a fictional Puritan sect created by Neal Stephenson. Reminiscent of Quakers though, who are historic. 

The Glorious Revolution
Dutch head-of-state William of Orange successfully invaded of England in 1688, overthrew King James II, and ascended to the English throne. James was a Catholic; William, a Protestant. Protestant Christians, such as the Puritans, were tolerated by William's new government, which also made life much harder for English Catholics. Wikipedia:Glorious Revolution

The Civil War
The English Civil War includes a number of conflicts between Kings Charles I and II against supporters of Parliament. The turbulent wars ended with the execution of King Charles and the ascendancy of Oliver Cromwell, a committed Puritan. Wikipedia:English Civil War

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came the Restoration
King Charles II was restored to power in 1660, after the collapse of Oliver Cromwell's government. This was a major setback for Puritan power in England. Wikipedia:English Restoration

speaking of Archbishop Laud
William Laud was Archbishop of Canterbury, a fervent Anglican, and inimical to Puritanism. He was executed in 1645 during the English Civil War. Wikipedia:William Laud

in Charing Cross
A central location in London, England.

caused his ears and nose to be cut off
Archbishop Laud had the ears and noses of many Puritan pamphleteers cut off as punishment for opposing the Anglican Church.

in Star Chamber
Star Chamber was a court of law in Westminster Palace, London. During the reign of King Charles I, it was often used to prosecute Puritan dissenters. Wikipedia:Star Chamber

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The King of Spain's coat of arms stares back at him
Spanish dollars, also known as pieces of eight, are silver coins minted from 1497 until the 19th century. Wikipedia:Spanish dollar

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The same coins that are changing hands…
Spanish pieces of eight were the de facto international currency until the late 18th century, and legal tender in the United States until 1857.

to go a-pirating on the Spanish Main
The Spanish Main were the Spanish territories in America, which included Florida, Mexico, Central America, and the north of South America. During the 16th through 18th centuries, they supplied the vast majority of Spanish silver, gold, spices and &c.; their waters were full of ships laden with riches, excellent opportunities for attack and plunder by pirates.

a matted reticule of taut jute and spokeshaved tree-trunks
Jute is a vegetable fiber which is often made into coarse, dun-coloured burlap cloth. A spokeshave is a woodworking tool used to shape wooden shafts.

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lapping clinkers of their hulls
Clinker ship hulls are built by overlapping wooden planks, held in place by iron plates.

barefoot jacks paying pitch and oakum into troublesome seams
Here, a jack is a sailor. These sailors are applying pitch and oakum, a preparation of tar and fibers used to seal ships against leaks, into the gaps between planks of ships' hulls.

the Lady mounted below the bowsprit
The bowsprit is an extension from the front of a sailboat (its prow) that allows its foremost sail (the forestay) to be anchored farther forward than would be possible otherwise. The Lady is a figurehead, carved or mounted on the prow of a ship.

a gray-eyed woman in a gilded helmet
Minerva is the Roman name for the Greek goddess Athena, virgin goddess of warriors, poetry, medicine, wisdom, and commerce. Wikipedia:Minerva

so he is probably Angolan
African slaves were often used by the Spanish in the Americas. Though the Spanish did use a number of Native American slaves, African slaves were preferred for their resistance to European diseases. It has been suggested that Spanish Jesuits also did not object to the abuse of Africans to the same extent they did the abuse of American natives.

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there was a riot underway
There were a number of riots in American urban centers during early 18th century, many a reaction against English impressment—also known as press-ganging: forcible conscription—and food shortages.

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Natural Philosophers
Natural philosophy was the objective study of the physical universe that was dominant before the development of modern science.

The Royal Society of London
A learned society founded in 1660, which counted among its members some of the best known scientists and philosophers of the age. Wikipedia:Royal Society

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where Harvard College is
Founded in 1636, Harvard College was named after a minister from Charlestown. Its original purpose was to train Puritan ministers, but by 1708 it had begun to become independent from Puritanism. Wikipedia:Harvard College

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The Franklin boy!
Ben is, indeed, young Benjamin Franklin, to be American Founding Father and discoverer of electricity. Wikipedia:Benjamin Franklin

the vis viva is conducted
Vis viva, Latin for "life force," was an early scientific concept alike to kinetic energy: the work necessary to set a body in motion. Wikipedia:Vis viva

And cheafer!
(Typographic error. Should be "cheaper.")
Pepper, though much more common and affordable then ever, was, in 1713, something only the more affluent could afford.

The Massachusetts Bay Colony Institute of Technologickal Arts
This appears to be a fictional institution created by Neal Stephenson, though the name does resemble Massachusetts Institute of Technology (MIT).

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Herr Leibniz… that stole the calculus from Sir Isaac
Gottfried Leibniz, renowned German philosopher and mathematician, and Isaac Newton both claimed to have invented calculus (). This became a major intellectual controversy, and an obsession of Isaac Newton's later years. Wikipedia:Leibniz and Newton calculus controversy

Metaphysickal thinking… a throwback to the Scholastics
The Harvard men here are referring to Leibniz's theory of monads, what he considered to be units of the fundamental element of reality. Scholasticism, a system of thought dominant in Middle Age Europe which attempts to combine Christian theology and ancient Greek philosophy, had lost favour among many intellectuals of the 18th century.

discover new truths through computation!
Leibniz is considered one of the first computer scientists. He discovered the binary system, the foundation of all modern computers, and made or anticipated several advances in logic, computation, and machinery.

accumulation of yellow bile—the humour of anger and ill-temper
In humourism, the ancient Greek theory of human bodies and temperament, an excess of yellow bile was believed to cause "bilious" behaviour such as anger. Wikipedia:Humorism

fairly straining at her hawsers
Hawsers are ropes used to tie ships to shore (to moor them).

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a specimen of white phosphorus that had suddenly burst into flame
Phosphorus is a chemical element that is highly flammable. White phosphorus emits a glow when exposed to oxygen, and can ignite when in open air. Wikipedia:Phosphorus

Bitte, mein herr…
German for "Please, my Lord…"

heard by their future Queen
In 1713, Sophia of Hanover was heiress presumptive to her first cousin Queen Anne of England. The letter that so impresses the Harvard men bears Sophia's seal.

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In Grantham lived an apothecary, name of Clarke
William Clarke was an apothecary who provided lodgings for a young Isaac Newton whilst he attended King's School in Grantham.

The Peace of Westphalia… The end of the Thirty Years' War
Signed in October of 1648, the diplomatic congress at Westphalia ended The Thirty Years' War, which was initially a conflict between Catholics and Protestants. Peace negotiations were held in the cities of Münster and Osnabrück because Protestant and Catholic leaders refused to meet. Wikipedia:Peace of Westphalia

to look in on a Mr. Huygens in the Hague
Christiaan Huygens was a Dutch mathematician and physicist, known for inventing the pendulum clock. Wikipedia:Christiaan Huygens

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as if reciting a catechism
A catechism is a short summary of religious doctrine, traditionally used in Christian teaching. They typically are in question-and-answer format, between teacher and student. Wikipedia:Catechism

Killed a great many Irishmen
Cromwell led an invasion of Ireland in 1649 against an alliance of Irish Catholics and English royalists. The invasion was marked by a number of massacres of Irish soldiers, civilians, and Catholic priests. Many Irish were sold into slavery. Wikipedia:Cromwellian conquest of Ireland

The answer is: the Navigation Act
Passed in October 1651, the Navigation Act banned non-English ships from transporting goods from to England. This angered the Dutch, as the Act was used as a pretext for British pirates to legally take any Dutch ship they encountered. This led to the First Anglo-Dutch War.

Rich Tories, no less!
Tories were one of the two the most influential political groups in Britain (the other being the Whigs). Tories were typically members of the landed upper classes, loyal to the King and faithful to the Anglican Church.

We did not begin calling people Tories until a good bit later.
Though the ideological foundations of the Tory Party were set during the English Civil War, the term was not in common use until 1678.

approach called Alchemy
Alchemy is considered both an early form of science—the investigation of nature—and speculative philosophy, with elements of chemistry and mysticism. Alchemical projects include the search for methods of transmuting baser metals into gold, a universal solvent, and an elixir of life. Wikipedia:Alchemy

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with Monsieur LeFebure, was was the apothecary to the French Court
May be based on Nicasius le Febure. He was the demonstrator of chemistry at the Jardin du Roi in Paris and in 1660 he was appointed Professor of Chemistry to Charles II of England and Apothecary in Ordinary to the Royal Family. He was elected a Fellow of the Royal Society in 1663. Wikipedia: Nicasius le Febure

Cromwell and his New Model Army
The New Model Army was formed in 1645 by the Parliamentarians in the English Civil War. It differed from other armies of the time in that its soldiers were full-time professionals, not tied to a single area or garrison. Its officers were also professional soldiers, not having seats in Parliament and therefore not linked to any political or religious faction. Wikipedia:New Model Army

pay a call on John Wilkins
John Wilkins was a founding member of the Royal Society, and is known primarily for his attempt to create a universal language for the use of philosophers. Wikipedia:John Wilkins

pick up some copies of Cryptonomicon
The Cryptonomicon is a fictional book on cryptography and cryptanalysis. It is also the title of a book by Neal Stephenson which may be considered part of The Baroque Cycle. Wikipedia:Cryptonomicon

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Experimental Philosophical Clubb met. Christopher Wren, Robert Boyle, Robert Hooke…
The Clubb was, presumably, a predecessor of the Royal Society. The names Enoch lists all became Fellows of the Society.