Wives participated with their husbands in general agricultural chores and did the dairy work including making cheese. Every householder kept chickens because egg production was cheap, their market price being only 1s. for a hundred. Wives also took care of the gardening work and traditionally kept for their own the cash that came in from garden, dairy, and poultry products. A wife made jellies and preserves when the fruit trees, bushes, and vines were bearing. Imported sugar enabled fruit to be preserved as jam in jars sealed with a layer of mutton fat to make them airtight. She was likely to concoct medications from her herbs. Meat had to be smoked or salted when there was not enough fodder to keep animals alive through the winter. She saw to it that the soap was boiled and the candles molded. She cooked the daily meals, did the washing, produced cloth for the family's use, and sewed the family's clothing.
Women had less work and lower pay than men. Since most cottages had a spinning wheel, spinning work was readily available to wives. In the 1670s, a female weaver or spinner was paid 2-4d. per day. A domestic servant, who was usually female, was paid 40-80s. a year. Men in the trades objected to competition from lower-paid women. Aristocratic ladies actively managed their family's household and estates. The only work available to a high middle- class woman who was waiting to get married was to be a governess in another household or a lady-in-waiting to a gentlewoman. Children often worked; this was recommended so that they were under the direct supervision of their parents rather than getting into mischief in the village. The mother typically mingled severity with gentleness, but the father did not dare to err on the side of leniency. Discipline was by whipping. Children were treated as little adults. The lack of a conception of childhood innocence even extended to the practice of adults to tell bawdy jokes in their presence or play with their children's genitals.
About 1660, the Royal Society for science was founded by Charles II, who became its patron. It was formed from a discussion group of the new experimental philosophy. It included the Baconians formerly at Oxford and Cambridge, who were ejected at the Restoration, and a group of Gresham professors of geometry and astronomy. The Royal Society met at Gresham College. Its goal was to compare ideas in mathematics and science and identify specific aims of science. Charles himself had his own laboratory and dabbled in chemistry and anatomy. Similar societies were formed all over the world. Theologicians warned that scientific research was dangerous. But it's advances improved agriculture, manufactures, medicine, surgery, navigation, naval architecture, gunnery, and engineering.
Issac Newton was a genius, who in his childhood designed and built model windmills, water wheels, water clocks, and sundials. He came from a family which had risen from the yeomen ranks to the gentry. For a few years after graduating from Cambridge University in 1665, he secluded himself in the countryside to study. Here, using the work of Wallis, he formulated the binomial theorem that expands (A+B) raised to the nth power, where n is an integer, fraction, or negative number. When n was a negative number, the expansion never terminated; instead of a finite sum, there is an infinite series. He then developed the notion of a number being the limit of an infinite converging series of partial sums, such as the limit of 1+(1/2)+(1/4)+(1/8)…= 2. By considering the state of motion of a mass-point in an infinitely short time under the influence of an external force, he developed rules for finding areas under algebraic curves [integration], such as the hyperbola, and finding tangents to algebraic curves [differentiation], which he recognized as inverse processes. That is, taking the integral and then the differential of a function results in a return to that function.
Newton discovered that colors arose from the separation rather than a modification of white light, that is natural sunlight. He did this using a prism to dissect the white light into its spectrum of constituent colors and then using a prism and lens to recombine the colors to reconstitute white light. The spectrum was the same as that of a rainbow. He determined the angle of refraction of each color by beaming white light through a prism, and then through a hole in a board which isolated one color, to another prism. When he discovered that all colors reflect from a mirror at the same angle, he invented and built the reflecting telescope, which used a parabolic concave mirror and a flat mirror instead of a convex lens, thereby eliminating the distortions and rainbow coloring around the edges that resulted from the refraction of different colors at different angles. He deemed a ray of light to consist of a rapidly moving stream of atomic particles, rather than Robert Hooke's pulses or Christian Huygens' waves, because shadows showed a sharp boundary between the light and the absence of light. He reasoned that if light was made up of pulses or waves, it could spread around obstacles or corners as sound seemed to do. He approximated the speed of sound.
Newton opined that an object moves because of external forces on it rather than by forces internal to the object. He connected the concepts of force and acceleration with a new concept: mass. He found that the acceleration of a body by a force is inversely proportional to its mass, and formulated the equation that force equals mass time acceleration. Another law was his principle of inertia that any body, in so far as it is able, continues its state either of rest or in uniform, rectilinear motion. His next law was that when a body A exerts a force on a body B, then B also exerts a force on A which is equal in amount but opposite in direction.
Newton had a radically novel idea that equated instantaneous acceleration to the gravity force which provoked it. He theorized that the same gravity force that pulled an apple down from a tree extended out to the moon hold it in its orbit around the earth. He connected these movements by imagining a cannon on a mountain shooting a series of cannonballs parallel to the earth's surface. The first shot had only a tiny charge of explosive, and the cannonball barely makes it out of the muzzle before falling to the ground. The second shot is propelled by a larger charge, and follows a parabolic arc as it falls, The next shots, fired with increasingly more propellant, eventually disappear over the horizon as they fall. Lastly, with enough gunpowder, a speeding cannonball would completely circle the earth without hitting it. He combined the inductive and deductive methods of inquiry, first making observations, and then generalizing them into a theory, and finally deducing consequences from the theory which could be tested by observation. He carried mathematization of data from experiments as far as possible. His universal theory of gravitation is based on the idea of forces between objects rather than from one object to another; e.g. the apple exerts a force toward the earth as well as receiving a force from the earth. His law of gravitation explains how the whole universe is held together. This law holds that every object in the universe attracts every other object with a single gravitational force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Newton had first believed in the Cartesian system of celestial vortices of aether than swirled the planets and comets around their orbits. The gross features of the universe led to his recognition that the attraction between two bodies decreased inversely to the square of the distance between them. Then he came to accept Hooke's hypothesis that planets are kept in their orbits by the combination of an attractive power of the sun and of motion in a straight line that was tangential to their orbits. From astronomical data, he calculated this centrifugal acceleration of each planet to be the inverse square of its distance from the sun. He also calculated the "centripetal" accelerations necessary to bring the planets into their orbits. His experiments had shown that he centripetal force in a circular orbit was equal to the mass of the body times the square of its velocity, all divided by the radius of the circular path. He used calculus and differential equations to determine centripetal forces of elliptical orbits, where the distance from the sun, the velocity, and the acceleration were variables. He correlated the moon's orbit with the measured acceleration of gravity on the surface of the earth. Then he formulated the idea that the ultimate agent of nature was a force acting between bodies rather than a moving body itself. Gravity did not act in proportion to the surfaces of bodies, but in proportion to quantity of matter, its penetration to the very center of all bodies without diminution, its propagation to immense distances decreasing in exact proportion to the square of the distance. Newton showed that a single gravitational force could account for the way falling objects descend to the ground, the parabolic trajectory of projectiles, the motion of the moon in its orbit around the earth, the course of the tides every twelve hours, the lower densities of the earth's atmosphere at greater heights, the paths of Jupiter's satellites, and the ellipitical motions of the planets in their orbits around the sun. It had been thought that invisible angels moved the planets. He proved from his law of gravitation and his three laws of motion the truth of Kepler's laws of ellipitical planetary motion. He demonstrated from data collected from the comet of 1680 that comets moved according to his law of gravitation. Non-periodic comets were observed to follow hyperbolic paths. He used the concept of a common center of gravity as a reference point for other motions. The fact that the center of gravity of the solar system was within the body of the sun verified that the sun was indeed at the center of it.
Newton's "Principia Mathematica Philosophia Naturalis", was published in 1687. The church denounced it as being against the scripture of the Bible. Newton did not agree with the established church on many points, such as the trinity, and was considered a heretic. He had his own interpretations of the Bible and doubted the divinity of Jesus. But it was accepted for dissenters like Newton to qualify for full civil rights by maintaining an outward conformity and taking the sacrament in the established church once a year. Newton was given a royal dispensation from taking holy orders as prescribed by the rules for tenure of fellows of his college at Cambridge University. He did believe in a God who created the universe and who had a ubiquitous presence in all space. When Catholic King James II tried to have a Catholic monk admitted to the degree of a Master of Arts at Cambridge University without taking the oath of adherence to the established Protestant church, in order to participate in the business of the university, Newton was active in the opposition that defeated this attempt.
When Newton's laws were applied to the paths of the moons of Jupiter, it was noticed that the moons were a few minutes ahead of time at that time of year when Jupiter was nearest to the earth and a few minutes behind time when Jupiter was farthest from the earth. Olaus Roemer, a Danish astronomer, postulated that Jupiter's eclipses of its moons lasted seconds longer the farther away Jupiter was from the earth because it took their light longer to reach the earth. He concluded that light does not travel instantaneously, but at a certain speed, which he calculated in 1676.
In 1668, Christian Huygens formulated the law of conservation of momentum [mass times velocity], which held that when objects collide, they may each change direction, but the sum of all their velocities will remain the same. Huygens also recognized the conservation of what was later called "kinetic energy", which is associated with movement. In 1690, he posited the theory that light consists of a series of waves. It states that all points of a wave front of light in a vacuum may be regarded as new sources of wavelets that expand in every direction at a rate depending on their velocities. He thought this a better explanation of bending and interference of light than Newton's particle theory.