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Archimedes and the Simple Machines That Moved the World

Overview

"Give me a place to stand," Archimedes is said to have promised, "and I will move the world." In this perhaps apocryphal quote, the Greek mathematician, scientist, and inventor was discussing the principle of the lever and fulcrum, but he could very well have been describing his whole career. In addition to his mathematical studies and his work on buoyancy, Archimedes contributed to knowledge concerning at least three of the five simple machines—winch, pulley, lever, wedge, and screw—known to antiquity. His studies greatly enhanced knowledge concerning the way things work, and his practical applications remain vital today; thus he is aptly named the "father of experimental science."

Background

Born in the Greek town of Syracuse in Sicily, Archimedes (287?-212 b.c.) was related to one of that city's kings, Hieron II (308?-216 b.c.). Son of an astronomer named Phidias, he went to Alexandria in around 250 b.c. to study under Conon and other mathematicians who had been disciples of Euclid (330?-260? b.c.). He later returned to his hometown, where he lived the remainder of his life.

Though he contributed greatly to understanding of the lever, screw, and pulley, Archimedes did not invent any of these machines. Of these three, the lever is perhaps the oldest, having been used in some form for centuries prior to his writings on the subject. Actually, the more proper name for this simple machine is "lever and fulcrum," since the lever depends on the fulcrum as a pivot. The simplest example of this machine in operation would be the use of a crowbar (lever) balanced on a block of wood (fulcrum), which greatly increases the lifting ability of the operator.

Levers appeared as early as 5000 b.c. in the form of a simple balance scale, and within a few thousand years workers in the Near East and India were using a crane-like lever called the shaduf to lift containers of water. Archimedes's contribution lay in his explanation of the lever's properties, and in his broadened application of the device. Similarly, he used the screw principle to improve on the shaduf and other rudimentary pumping devices.

The shaduf, first used in Mesopotamia in about 3000 b.c., consisted of a long wooden lever that pivoted on two upright posts. At one end of the lever was a counterweight, and at the other a pole with a bucket attached. The operator pushed down on the pole to fill the bucket with water, then used the counterweight to assist in lifting the bucket. By about 500 b.c., other water-lifting devices, such as the water wheel, had come into use.

Another water-lifting device was a bucket chain using a pulley, which is believed to have provided the means of watering the Hanging Gardens of Babylon. Archimedes, for his part, applied the screw principle to the pump, and greatly improved the use of the pulley for lifting. The pulley, too, was ancient in origin: though the first crane device dates to about 1000 b.c., pictorial evidence suggests that pulleys may have been in use as early as the ninth millennium b.c.

Impact

Returning now to the topic of the lever, it should be noted that Archimedes was first of all a mathematician and physicist, and secondarily an inventor. Not only was that his role in history, but that was how he saw himself: like virtually all great thinkers of the Greek and Roman worlds, he viewed the role of the practical scientist as on a level with that of the artisan—and since most artisans were slaves, he considered applied science as something infinitely less noble than pure science. This is of course an irony, given his great contributions to applied science, but it is also essential to understanding his work on the lever and other machines. In each case, his practical contributions sprang from a theoretical explanation.

Where the lever was concerned, Archimedes explained the underlying ratios of force, load, and distance from the fulcrum point, and provided a law governing the use of levers. In Archimedes's formulation, the effort arm was equal to the distance from the fulcrum to the point of applied effort, and the load arm equal to the distance from the fulcrum to the center of the load weight. Thus established, effort multiplied by the length of the effort arm is equal to the load multiplied by the length of the load arm—meaning that the longer the effort end, the less the force required to raise the load. Simply put, if one is trying to lift a particularly heavy stone, it is best to use a longer crow bar, and to place the fulcrum as close as possible to the stone or load.

Some three centuries after Archimedes, Hero of Alexandria (first century a.d.) expanded on his laws concerning levers. Then in 1743 John Wyatt (1700-1766) introduced the idea of the compound lever, in which two or more levers work together to further reduce effort—a principle illustrated in the operation of the nail clipper. Physicists have also applied Archimedes's laws on the operation of levers to situations in which the fulcrum rests beyond the load (as with the wheelbarrow, whose wheel serves as the fulcrum), or beyond the effort (as with tongs, in which the elbow joint serves as fulcrum).

With regard to the screw, Archimedes provided a theoretical underpinning, in this case with a formula for a simple spiral, and translated this into the highly practical Archimedes screw, a device for lifting water. The invention consists of a metal pipe in a corkscrew shape that draws water upward as it revolves. It proved particularly useful for lifting water from the hold of a ship, though in many countries today it remains in use as a simple pump for drawing water out of the ground.

Some historians maintain that Archimedes did not invent the screw-type pump, but rather saw an example of it in Egypt. In any case, he developed a practical version of the device, and it soon gained application throughout the ancient world. Archaeologists discovered a screw-driven olive press in the ruins of Pompeii, destroyed by the eruption of Mount Vesuvius in a.d. 79, and Hero later mentioned the use of a screw-type machine in his Mechanica. Certainly the screw is a widely used device in modern times, and though its invention cannot be attributed to Archimedes, it is certain that he influenced the broadening of its applications. Thus in 1838, when the Swedish-American engineer John Ericsson (1803-1899) demonstrated the use of a screw-driven ship's propeller, he did so on a craft he named the Archimedes.

Again, in the case of the pulley, Archimedes improved on an established form of technology by providing a theoretical explanation. He showed that a pulley, which may be defined as any wheel supporting a rope or other form of cable for the transferring of motion and energy, operates according to much the same principle as a lever—that is, the pulley provides the operator with a mechanical advantage by reducing the effort required to move the object.

A single pulley provides little mechanical advantage, but by about 400 b.c. the Greeks had put to use compound pulleys, or ones that contained several wheels. Again, Archimedes perfected the existing technology, creating the first fully realized block-and-tackle system using compound pulleys and cranes. This he demonstrated, according to one story, by moving a fully loaded ship single-handedly while remaining seated some distance away. In the late modern era, compound pulley systems would find application in such everyday devices as elevators and escalators.

Archimedes's studies in fluid mechanics gave rise to the most famous story associated with him. It was said that while trying to weigh the gold in the king's crown, Archimedes discovered the principle of buoyancy: when an object is placed in water, it loses exactly as much weight as the weight of the water it has displaced. Supposedly he made his discovery in the bath, and was so excited that he ran naked through the streets of Syracuse shouting "Eureka!" or "I have found it." Again, the story itself may be apocryphal, but the application is very real: thanks to Archimedes's principle, shipbuilders understood that a boat should have a large enough volume to displace enough water to balance its weight.

In the realm of mathematics, Archimedes developed the first reliable figure for π, and in his work with curved surfaces used a method similar to calculus, which would only be developed some 2,000 years later by Isaac Newton (1642-1727) and Gottfried Wilhelm Leibniz (1646-1716). As an astronomer, he developed an incredibly accurate self-moving model of the Sun, Moon, and constellations, which even showed eclipses in a time-lapse manner. The model used a system of screws and pulleys to move the globes at various speeds and on different courses. In addition, he conducted important studies on gravity, balance, and equilibrium that grew out of his work with levers.

During the Second Punic War (218-201 b.c.), Archimedes worked as a military engineer for Syracuse in its efforts against the Romans and either invented or improved upon a device that would remain one of the most important forms of warfare technology for almost two millennia: the catapult. He is also said to have created a set of lenses that, using the light of the Sun, could set ships on fire at a distance. But Archimedes may have been a bit too successful in his wartime efforts: he was killed by a Roman soldier, no doubt as retribution, when Rome took Syracuse.

Archimedes remains one of the towering figures both of pure and applied science. He developed the three-step process of trial and experimentation that helped form the basis for scientific work in subsequent centuries: first, that principles continue to work even with large changes in the size of application; second, that mechanical toys and laboratory experiments may yield practical applications; and third, that a rational, step-by-step logic must be applied in solving mechanical problems and designing equipment. In so doing, he created the machines that transformed the world, and his impact remains powerful today.

JUDSON KNIGHT