There was a thermometer which used liquid such as water or alcohol in a glass 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".
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 as curves of the second algebraic degree. He 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. ,
Blaise Pascal, a French mathematician, physicist, and religious philosopher, constructed a calculator in 1644 to assist his father, who was involved in local administration, in tax computations. Around 1646, he proved his law 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, including the creation of "Pascal's Triangle" of coefficients of (a=b) raised to the nth power. 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. 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 associated with that equation.. This work helped lay the foundation for analysis. He and German Gottfried Leibniz formulated the principle that an equation with two unknown quantities can represent a curve. Leibnitz believed that man's mind can arrive at truths about entities by pure thought.
Since the Puritans forbade music in churches, but enjoyed it in domestic circumstances, 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.
There was continual problem with Catholics. Where Papists or others had caused rebellion and insurrection and plundered, robbed, pillaged, murdered and raped, mayor, Justices and capital burgesses of such towns were given the power in 1642 to call, assemble, train, and arm soldiers for defense. The Committee of the Militia of London was given authority in 1647 to search all houses and places for Papists and to search for and seize any arms, ammunition, and war materials in custody of such persons. In 1648, all Papists and soldiers of fortune who had borne arms against Parliament were ordered to depart from within twenty miles of London and Westminster or be imprisoned as traitors. In 1657 convicted Papists and people marrying convicted Papists were required to take an oath renouncing the pope and Catholic Church or lose two-thirds of their lands and estate, retaining their house on the remaining one-third. If one went to mass in an ambassador's house, the fine was 100 pounds and imprisonment for six months, one half going to the informer. In 1659 all householders in London and Westminster had to give a list of persons lodging in their house, and the horses and arms there. But the laws against Catholics practicing their religion were not rigorously enforced, nor were those against adherents of the formerly established Church of England.
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 buttons, 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. The 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 participate in war. They refused to take off their hats to anyone but God. 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 developed a value of making provision 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 harassed 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 New England.
In 1653 there were separation agreements between spouses as to property, e.g. support and maintenance.
Cromwell had bad experiences with Parliaments. The Rump Parliament was a remnant of the Long Parliament. The army and then Cromwell, although a member, came to believe that its members were self- interested, preoccupied with perpetuating themselves in seats of power, and corrupt. They thought that their own hopes of reform in the law, in the church, and in public finances were being deliberately frustrated. Cromwell came to doubt that it would ever give the people adequate government and protection. He started to believe that one man as chief executive could do this better. Cromwell dismissed the Rump Parliament in 1653. A new constitution created a Puritan "Parliament of Saints". These men were nominated in various ways, such as by church parishes, and selected by Cromwell. This one-house Parliament of Saints in 1653 made Cromwell Lord Protector for life with executive power of the state, with responsibility for making peace and establishing order after a decade of civil strife and political chaos. He was to administer the government and be the chief magistrate. It also provided for triennial Parliaments (consisting of one house), and religious freedom for all except Roman Catholics and adherents of the formerly established Church of England. Cromwell did not tolerate the ritual of the formerly established English church nor allow any of its adherents to have any office under him. His was a purely Puritan government. He did not sell offices. The Parliament of Saints challenged many vested interests in property such as sales of delinquents' and Papists' lands. It clashed severely over the continuation of tithes to the church. It became disorderly when some declared the Parliament dissolved and left. Others remained in their seats. To avoid a Parliamentary crisis, Cromwell had soldiers close the Parliament of Saints and lock its doors. The people supported this action because they were dissatisfied with the state of public affairs. The next Parliament that was tried was elected on a new constitutional basis of men with 200 pounds, but these men voted to make Parliament sovereign without a chief executive, thereby abolishing the protectorate. Cromwell was distressed that this Parliament had also voted themselves to be the sole determinors of atheism and blasphemy instead of advancing liberty of religious conscience and religious toleration as Cromwell had advocated. dissolved this Parliament, declaring that it was not acting for the public good. A last Parliament was also dissolved by Cromwell for tending to loosen the bonds of government and thereby threatening the peace of the nation.