The formula for the area of a circle is A = Pi * r 2 where "r" is the radius and the radius is half the diameter. To figure out how much more force you can produce on the large cylinder you have to figure out the area of both cylinders. Suppose you have one cylinder with a piston at the top that is two-inches in diameter and another cylinder that is six-inches in diameter. The press has been used in thousands of industrial applications over the next 150 years.
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When he and a colleague figured out how to build cylinders with matching pistons that were sealed with leather, self-tightening collars, they had the basis of the hydraulic press. He realized that, using Pascal's principle, putting pressure on the top of the narrow cylinder would force the liquid to put a huge amount of pressure on the larger cylinder. Bramah took two cylinders one small and the other large filled both with liquid and connected them by a pipe. In 1795, he patented his "Hydrostatic Machine" to help build another of his inventions, an unpickable lock. Joseph Bramah was an inventor and successful locksmith in England. It took another 140 years and the dawn of the Industrial Revolution for that scientific principle to be applied in a useful way. Pascal's Law says that the same 10 pounds of force would be applied on each and every square inch on the insides of the bottle. Imagine you put 10 pounds of force on the top of a cork in the neck of the bottle. Under this principle, imagine you have a bottle with a one-inch square opening filled with liquid. In other words, if you put pressure on a fluid in one area, it will transmit pressures equally in all directions. What Pascal discovered is that fluids don't compress in the way that air will. He studied fluids, pressures and vacuums in the mid-1600s, four centuries ago. The idea for hydraulic cylinders goes back to the French mathematician Blaise Pascal.
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