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.
About 1650, steel was hardened by repeated quenchings and temperings when the steel had reached certain colors. Brass was made from copper and zinc alloyed together.
There were power-driven rolls for the coinage from 1657. Strips of silver were passed 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 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".
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, 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 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.