Archimedes’ legacy: inventions and discoveries

Archimedes is the perfect embodiment of a man ahead of his time. Even amongst peers that practiced philosophy and the arts as well as established democracy, Archimedes of Syracuse outshined them all. A true polymath, Archimedes was active in the fields of astronomy, geometry, logic, physics, and mathematics, and was recognized as the best engineer and inventor of his time. As a part of his grand legacy, many of his inventions and discoveries from over 2,000 years ago are still in use today.

Archimedes’ screw

This ingeniously contrived device was invented by Archimedes to help poor farmers irrigate their crops. The device consists of a screw mechanism inside a hollow casing. When the screw is rotated, either by a windmill or manual labor, the bottom end of the screw scoops water, then moves it through the casing against gravity until it escapes through the last thread to reach irrigation canals.

Today, the same principle is used in modern machinery for drainage and irrigation, and also in some types of high-speed tools. It can also be applied for handling light, loose materials such as grain, sand, and ashes. Of course, these look more impressive. Since 1980, Texas City, TX, USA uses eight 12-ft.-diameter Archimedes screws to manage rainstorm runoff. Each screw is powered by a 750-hp diesel engine and can pump up to 125,000 gallons per minute. The SS Archimedes was a ship named after the great inventor, which was the first steamship to come with a screw propeller.

Burning mirrors

Throughout his career as an inventor, Archimedes would frequently be commissioned by the rulers of Syracuse to invent war machines to protect their fair city. Such is the case with his “burning mirrors” – a system of large mirrors placed on the walls of the city that concentrated solar power in order to burn any ships foolish enough to sail against Syracuse. The story is extremely controversial, and even to this day historians and engineers alike debate whether this is a fact or myth.

The earliest account of Archimedes’ ancient death ray was written in the 12th century by Zonares and Tzetzes who were quoting an earlier, but now lost work called The Siege of Syracuse.

When Marcellus [The Roman General] had placed the ships a bow shot off, the old man [Archimedes] constructed a sort of hexagonal mirror. He placed at proper distances from the mirror other smaller mirrors of the same kind, which were moved by means of their hinges and certain plates of metal. He placed it amid the rays of the sun at noon, both in summer and winter. The rays being reflected by this, a frightful fiery kindling was excited on the ships, and it reduced them to ashes, from the distance of a bow shot. Thus the old man baffled Marcellus, by means of his inventions.

Crafty old man, indeed, but did it really happen? The ability of mirrors to concentrate the sun and obtain high temperatures is no myth, as any kid who used a magnifying glass to burn scraps can attest. This year, Morocco opened the largest concentrated solar power (CSP) plant in the world which will generate enough electricity to power the homes of one million people. CSP plants typically use 12m high parabolic mirrors that reflect sunlight onto pipework that contains a heat transfer fluid (HTF), typically thermal oil. This increases the temperature of the fluid to almost 400°C. The HTF is then used to heat steam in a standard turbine generator. Some CSPs heat the target tower to temperatures in excess of 1,000 degrees Fahrenheit (537 degrees Celsius), so it’s easy to imagine how Archimedes might have pulled something similar to burn enemy ships.

The real question isn’t whether it’s possible per se, but whether Archimedes actually made a burning mirror system using the tools and resources at his disposal two thousand years ago.

Apparently, in 1973 a Greek scientist, Dr. Ioannis Sakkas, became curious about whether Archimedes could really have used a “burning glass” to destroy the Roman fleet, so he set up an experiment involving 60 Greek sailors each using an oblong 3′ by 5′ flat mirror to focus light on a wooden rowboat 160 feet away. The boat was set on fire fairly quickly, though it’s worth mentioning the boat was coated in tar paint, which is highly flammable. Tar paint was used frequently to coat ships back in Archimedes’ time. However, more recently, when the Mythbusters made their own reenactment, things didn’t go quite as smoothly. In 2010, 500 flat mirrors controlled by 500 volunteer middle and high school students were focused on the sail of a ship, which should have combusted at 500°F. After an hour, no more than 230°F could be reached, so the team classified this as ‘inconclusive’. Jamie Hyneman, who was stationed on the mock boat for the duration of the experiment, did say that he could barely see, however. He suggests that Archimedes’ burning mirrors might have been real, but perhaps were used more for dazzling enemies than burning boats.

The gold crown and “Eureka!”

According to the Roman architect Vitruvius, the Syracusan king Hiero II commissioned a gold crown shaped like a laurel wreath to be placed in a temple. The king himself weighed the gold and gave the goldsmith the material to turn it into a piece of art. On the appointed day, the goldsmith presented his masterpiece — a gold crown shaped like a laurel wreath, exactly as the king ordered. When it was weighed, it had exactly the same mass as measured earlier. The king was pleased, but only days before the temple ceremony, he heard rumors that the goldsmith had cheated him and given him a crown not of pure gold, but of gold that had silver mixed with it.

Hiero believed there was only one man in Syracuse capable of discovering the truth and solving his problem — his cousin, Archimedes, a young man of 22 who already distinguished himself in the fair city for his work in mathematics, physics, and engineering.

When faced with the challenge, Archimedes devised a clever science experiment to get to the bottom of things, but not until after thoroughly pondering the situation.
Legend has it that Archimedes was thinking about the golden crown while bathing in the public baths one day. As he began to enter a cold bathtub for his final dip, he noticed water started dripping on the sides. As he continued to lower his body into the bath, even more water ran out over the sides of the tub. In this instant, he recognized the solution to Hiero’s problem, jumped out of the tub at once, and ran all the way home without remembering to put his clothes on, all the while shouting, ‘Eureka, Eureka!’ – which in Greek means, ‘I have found it! I have found it!’

Alas, the “Eureka!” story itself is likely a fabrication, but Archimedes is genuinely credited as the first to state the laws of buoyancy. The Achimedes Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object.

He knew that if the crown was pure gold, its volume would be the same as that of the lump of gold (which he had made sure weighed the same as the crown), regardless of shape, and it would displace the same amount of water as the gold. If the goldsmith had indeed cheated and replaced some of the gold with silver, then the volume of gold and silver would be greater, and thus the crown would displace more water. According to Vitruvius, Archimedes used this method and found the goldsmith had indeed cheated.

Skeptics weren’t convinced, however. As far back as 1586, Galileo wrote a short treatise called La Bilancetta, or The Little Balance, in which he argued this method could not work because the differences in gold and silver volumes are too small. Instead, he suggested Archimedes used a similar, but more crafty technique. In short, Archimedes probably suspended the gold crown on one end of a scale, and a lump of gold of equal mass on the other end. 

The scale would have been then submerged in water, with both contents still on the ends of the scale. Since a body immersed in water is buoyed up by a force equal to the weight of the water displaced by the body, the denser body, which has a smaller volume for the same weight, would sink lower in the water than the less dense one. If the crown was pure gold, the scales would continue to balance even underwater.

The Iron Claw

We continue with yet another war machine designed by Archimedes: the so-called Iron Claw. True to its name, this mechanical device was installed on the walls of the old city of Syracuse. The exact design has been lost in time, but we know its purpose was to topple eager Roman ships. Once the claw fastened itself to a ship’s underbelly, it would be tugged in an upward fashion and then released from a distance. In 2005, the producers of Discovery Channel’s Superweapons of the Ancient World challenged engineers to replicate this arcane device on the condition they’d use only techniques and materials known to be available in the 3rd century BC. Within seven days, they were able to test their creation, and they did succeed in tipping over a model of a Roman ship to make it sink.

The Odometer

The same Vitruvius who accounted Archimedes’ “Eureka!” moment also reported Archimedes to have “mounted a large wheel of known circumference in a small frame, in much the same fashion as the wheel is mounted on a wheelbarrow; when it was pushed along the ground by hand it automatically dropped a pebble into a container at each revolution, giving a measure of the distance traveled. It was, in effect, the first odometer,” according to Encyclopedia Britannia. This mechanism is said to have been invented by Archimedes during the First Punic War.  It seems to have been used until the time of Emperor Commodus (192A.D.) and then was lost in Europe until the middle of the fifteenth century.

The block and tackle pulley system

“Give me a place to stand on, and I can move the earth,” Archimedes once said speaking of the power of the lever. While he did not invent the lever, he gave an explanation of the principle involved in his work On the Equilibrium of Planes.

Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline toward the weight which is at the greater distance, states Archimedes’ law of the lever.

If, when weights at certain distances are in equilibrium, something is added to one of the weights, they are not in equilibrium but incline towards that weight to which the addition was made.

Similarly, if anything is taken away from one of the weights, they are not in equilibrium but inclined towards the weight from which nothing was taken.
When equal and similar plane figures coincide if applied to one another, their centers of gravity similarly coincide.[/panel]

The familiar king Hieron was very impressed by this statement and asked Archimedes to prove it. The occasion seemed very fitting because Syracuse at the time was biting off more than it could chew. The city built a magnificent 55-meter-long ship called the Syracusia packed with a sumptuous decor of exotic woods and marble along with towers, statues, a gymnasium, a library, and even a temple. Oh, and the ship was designed by Archimedes. According to Plutarch, Archimedes managed to set the Syracuse out of harbor using an intricate system of pulleys, although his account seems a bit too poetic.

“[Archimedes] had stated [in a letter to King Hieron] that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labour and many men; and, loading her with many passengers and a full freight, sitting himself the while far off, with no great endeavour, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea.”

“Archimedes chose for his demonstration a three-masted merchantman of the royal fleet, which had been hauledashore with immense labour by a large gang of men, and he proceeded to have the ship loaded with her usual freight and embarked a large number of passengers. He then seated himself at some distance away and without using any noticeable force, but merely exerting traction with his hand through a complex system of pulleys, he drew the vessel towards him with as smooth and even a motion as if she were gliding through the water.,” Plutarch.

The geometry of spheres and cylinders

According to Plutarch, the famous Greek biographer, Archimedes had a low opinion of the mechanical contraptions he invented and for which he was recognized in the entire ancient world. Instead, he relished in his theoretical explorations of mathematics and physics. Archimedes is credited for nine extant treatises, among which is the two-volume On the Sphere and Cylinder. In this fantastic work, Archimedes determined the surface area of any sphere of radius r is four times that of its greatest circle (in modern notation, S = 4πr²) and that the volume of a sphere is two-thirds that of the cylinder in which it is inscribed ( V = ⁴/₃πr³). Archimedes was so proud of this achievement that he left instructions for his tomb to be inscribed with “a sphere inscribed in a cylinder.” Marcus Tullius Cicero (106–43 bce) found the tomb, overgrown with vegetation, a century and a half after Archimedes’ death.

The measurement of the circle

Determining the area of a circle was once considered a great mathematical challenge. Archimedes found a way to approximate it with a method called “squaring the circle”. He first created a square inscribed inside of the circle (inscribed means that it exactly fits inside, with its vertices just touching the edge of the circle). Since he knew the area of the square is (the product of two sides), it was clear that the area of the circle is bigger than the area of that inscribed square. He then fitted a polygon with six sides instead of four within the circle and computed its area; he gradually worked his way up with more complex polygons to get even closer to the circle’s true area.

Eventually, Archimedes got really good at this and discovered π (pi) — the ratio of the circumference to the diameter of a circle. His calculations use an astonishing 96–sided polygon to suggest that pi lies “between the limits of 3 and 10/71 and 3 and 1/7”. In other words, he calculated an estimate that was equal to pi to two digits (3.14). Until the advent of calculus and computing infinite series 1,500 years later, not many digits were added to the ones found by Archimedes. A major breakthrough was made in 1655 when the English mathematician derived a formula for pi as the product of an infinite series of ratios.