In 1657 the Muscovy Company, renewed its charter for trade in Russia and established a New General Stock. If a man bought a share, he bought freedom of the company. An annual dividend was declared from the annual profits.

Commercial men regularly kept accounts with bankers. Merchants used division to apportion profits or losses to the parties whose capital was involved. Simple and compound interest were used. The concept of contract became a familiar one.

Regular private bankers of London emerged from the Goldsmiths from 1640 to 1675. They issued bank notes and paid checks.

Cromwell increased trade by seizing territories, establishing colonies, and warring with compet.i.tors for master of the seas and trade. In 1649 it was provided that no one who paid his a.s.sessment for soldiers' pay would have to quarter any of them.

Authority was given in 1649 to impress seamen: mariners, sailors, watermen, surgeons, gunners, ship carpenters, caukers, coopers, whoymen, and carmen for carriage of victuals.

English ships were embellished with decoration. Their sail area was increased by triangular fore and aft sails. The Navy increased from 39 to 80 vessels.

After serving in foreign wars, ex-soldiers were allowed in 1654 to practice any trade without serving a seven year apprenticeship.

Colonies New Hampshire and Maine were established in 1635, Connecticut in 1636, and Rhode Island in 1638, as offshoots from other colonies.

In 1649 a corporation was established to teach the Gospel of Jesus Christ in New England to Indians.

About 1650, steel was hardened by repeated quenchings and temperings when the steel had reached certain colors. Bra.s.s was made from copper and zinc alloyed together.

There were power-driven rolls for the coinage from 1657. Strips of silver were pa.s.sed between engraved rolls. Then coins were punched out and their edges serrated.

In the 1650s, Huygens made the first pendulum that worked practically in a mechanical clock. This new clock increased the accuracy of time-keeping tenfold. He also introduced the concept of mathematical expectation into probability theory.

There was a thermometer which used liquid such as water or alcohol in a gla.s.s tube instead of air.

Dutchman Stevinus showed that the pressure at the bottom of a column of liquid is proportional to the height of the column, and not to its bulk, about 1634. He also studied oblique forces, and the balancing of such that could bring about "stable equilibrium".

Evangelista Torricelli, an Italian student of Galileo, discovered in 1643 that any fluid will be supported at a definite height, according to its relative weight, as compared with air. He realized that a mercury column, 30 inches in height, in a long gla.s.s tube inverted in a cup of mercury, was being supported by air pressure exerted on the mercury in the cup. When he observed that this height changed with the weather, he had invented the mercury barometer. In his work, he created and used vacuums.

Blaise Pascal, a French mathematician, physicist, and religious philosopher, was a child prodigy. At the age of 12, he proved Euclid's 32nd theorem that the sum of the angles of a triangle is equal to two right angles. Before age 16, he wrote a book on conic sections. He is famous for his theorem that a hexagon inscribed in a conic section has the property that the three meeting points of the opposed sides are always in a straight line. He constructed a calculator, which could handle nine-digit numbers, in 1644 to a.s.sist his father, also a gifted mathematician, in tax computations he did as a local government official. He had Torricelli's mercury barometer carried up a mountain and found that the height of the column dropped as alt.i.tude increased, and thus that air pressure decreased with alt.i.tude. This showed that the attribution of these effects to nature's abhorrence of a vacuum were due instead solely to the weight and pressure of air. He determined that the height to which the mercury rose was the same regardless of the shape of the vessel containing it. Around 1646, he did experiments with double vacuums and on the results formulated his principle that pressure applied to a confined liquid is transmitted undiminished through the liquid in all directions regardless of the area to which the pressure is applied. Around 1653, he laid the foundations for the theory of probabilities after being asked by a gambling friend why, in playing dice, some frequencies came up more often than others. He developed a means of calculating probabilities with his "Pascal's Triangle" of coefficients of (a+b) raised to the nth power. Each row represents the coefficients of a power one greater than the power of the previous row.

Each number is the sum of the nearest two numbers in the row above it.

He and lawyer and mathematician Pierre Fermat invented the theory of probabilities.

Fermat also proved that the law for refraction (bending) of light results from light's following the path that takes the shortest time. He founded number theory, the study of properties of whole numbers, in 1640. Fermat formulated the notion of a line tangent to a curve and started the development of differential calculus, in which a rate of change is expressed as a function of time in equation form and also as a tangent to the curve a.s.sociated with that equation. This work helped lay the foundation for the mathematics field of a.n.a.lysis. He and German Gottfried Leibniz formulated the principle that an equation with two unknown quant.i.ties can represent a curve. Leibnitz believed that man's mind can arrive at truths about ent.i.ties by pure thought.

Jean Ray from France concluded from his experiments that every piece of material has a given weight, including air and fire. Otto von Guericke from Germany discovered that, in a vacuum, sound does not travel, fire is extinguished, and animals stop breathing.

At a time when mathematics was only a business of traders, merchants, seamen, carpenters, and surveyors, mathematician John Wallis, the son of a minister, studied sections of cones [circles, ellipses, parabola, and hyperbolas] as curves of the second algebraic degree, i.e. with an exponent of two, i.e. y = (a (x squared)) + b. He also worked with negative and fractional exponents. Around 1655 he invented the infinite arithmetic and introduced the symbol for infinity. He determined that the area under any curve defined by the equation y = (x to the nth power), was x to the (n+1)th power divided by n+1. He introduced the concept of the limit of a string of numbers. He wrote a treatise on algebra which was historical as well as practical. He also decoded enemy cyphers for the sovereign.

Some English gentlemen interested in the new scientific methods originated by Galileo had meetings beginning about 1645 to discuss scientific topics. One group met at Gresham College and was headed by Wallis. Another group was led by Robert Boyle, a philosopher, physicist, and chemist. They wrote in English instead of Latin. These meetings later gave rise to the Royal Society for science.

Since the Puritans forbade music in churches, but enjoyed it in domestic circ.u.mstances, much secular music was composed, published, and played. There were many musical clubs. The violin became very popular.

Solo songs were much sung. The first English opera: "The Siege of Rhodes" was written and performed with women on stage. Writers of the time included John Milton, political philosopher James Harrington, poet Edmund Waller, Thomas Fuller, poet Abraham Cowley, and biographer Issak Walton. John Aubrey wrote anecdotes about famous men. Jeremy Taylor, chaplain to Charles I, wrote on theology. People still read French romances translated into English. Dancing was still popular. Coffee houses came into prominence as places of social discourse. The first coffee house was established in London in 1652; ten years later, there were 82 coffee houses in the City. There were elegant pleasure gardens, with a fee for access. They were used for promenades and picnics. Ladies and their gallants rendezvoused there. Cromwell introduced the habit of port drinking to England.

In 1657, one general Post Offices was established with one Postmaster General for all of England. No other person could have the horsing of the through-posts. It cost 2d. for a letter to or from 80 miles of London and 3d. for one outside 80 miles of London.

The Society of Friends was founded by the son of a weaver. They greeted everyone as "friend" and did not bow; remove their hat, as was the custom when before the king or an earl; or otherwise show any reverence to anyone. From 1650, they were called Quakers because they trembled when religiously stirred. They reverted to the ancient "thou" and "thee"

appellations. Their dress was particularly simple, with no b.u.t.tons, lace, ruffles, or embroidery. They hated ritual so much that they rejected baptism and communion. They did not observe the Sabbath as a special day different from other days. They derided the holiness of churches. No clergy were admitted into their sect. When they met for divine worship, each rose to deliver extemporaneous inspirations of the Holy Ghost. Women were admitted to teach the brethren and were considered proper vehicles to convey the dictates of the spirit. Quakers believed that every man, in his own life, could be fully victorious over sin. They denied any clerical authority and all texts. They believed in the separation of church and state. They refused to swear to any oath, e.g. in court, or to partic.i.p.ate in war. They refused to take off their hats to anyone but G.o.d. It was their practice to turn the other cheek when one cheek had been struck. If asked for his cloak, a Quaker would give it. He never asked more for his wares than the precise sum which he was determined to accept. The Quakers encouraged widows and widowers to provide for children from a first spouse when remarrying. They carefully selected masters and mistresses who wanted to take on child apprentices for their suitability for such responsibility. The education of Quaker women did not decline, as it did for other women. From the fervor of their zeal, the Quakers broke into churches, disturbed public worship, and hara.s.sed the clergyman and audience with railing and reproaches.

When brought before a magistrate, they show no reverence but treated him as an equal. Sometimes they were thrown into mad house or prisons and sometimes whipped or pilloried. They endured stoically under this suffering. Mary Fisher from Yorkshire introduced Quakerism to colonial New England.