One Good Turn: A Natural History of the Screwdriver and the Screw (13 page)

Archimedes was a citizen of Syracuse, a wealthy Greek city-state on the island of Sicily. He was born about
287
B.C.
, the son of an astronomer, and was sent as a young man to study mathematics in Alexandria with the successors of the great Euclid. On his return to
Syracuse, he devoted himself to science. He became the foremost mathematician of the ancient world, devising a variety of proofs in both plane and solid geometry, including describing the geometry of the spiral. He wrote several treatises on the equilibrium of planes and established the mathematical foundation for the science of mechanics. In addition, he single-handedly invented the science of hydrostatics, the branch of physics that deals with fluids at rest and under pressure.

Archimedes left instructions that his sepulchral column include a depiction of his favorite proposition: the calculation of the exact ratio between a sphere and the cylinder that circumscribed it. He died at the age of seventy-five. One hundred and fifty years later, Cicero, while serving as Roman administrator of Sicily, sought out the tomb and, finding it neglected, had it restored. Cicero anticipated the interest in Archimedes by later historians such as Diodorus Siculus, Livy, and Plutarch. Of course, they wrote three hundred years (in the case of Plutarch, four hundred years) after the fact; by then, all that was left were stories. One of these concerned Archimedes’ death. During the Second Punic War, Syracuse was attacked by the Roman army, and after a two-year siege the city fell. According to Plutarch, the victorious Roman general, Marcellus, who was an amateur mathematician, sent a soldier to fetch the renowned Archimedes. “As fate would have it, he [Archimedes]
was intent on working out some problem with a diagram, and having fixed his mind and his eyes alike on his investigation, he never noticed the incursion of the Romans nor the capture of the city,” Plutarch writes. “And when a soldier came up to him suddenly and bade him follow to Marcellus, he refused to do so until he had worked out his problem to a demonstration; whereat the soldier was so enraged that he drew his sword and slew him.”
⁸
The remorseful Marcellus is said to have personally erected the mathematician’s tomb. He also appropriated two of Archimedes’ celestial globes, one of which later came into the hands of the astronomer Gallus, who showed it to Cicero.

The most famous story told about Archimedes concerns his solution of the so-called wreath problem. Hieron, the king of Syracuse, commissioned a gold wreath as an offering to the gods. He provided gold to the jeweler, who in due time delivered the finished wreath. Hieron suspected that the gold had been diluted with silver, but could not prove it. The wreath was a consecrated object and could not be tampered with, so a chemical assay was out of the question. Since the goldsmith refused to confess, the king turned to Archimedes. The mathematician pondered the matter and devised a simple experiment. He weighed the wreath, and immersed similar weights of silver and gold in a vessel of water, measuring how much water each displaced. He
discovered that silver displaces more water than gold (the specific gravity of silver is almost half that of gold). Since the immersed wreath caused more water to overflow than the equivalent weight of gold, he deduced the presence of silver and proved that the wreath was indeed impure. According to legend, the idea for the water experiment came to Archimedes as he was plunging himself into a tub in a public bath. Seeing the water overflowing triggered something in his mind. “Transported with joy, he jumped out of the tub and rushed home naked,” writes Vitruvius, “crying out in a loud voice,
‘Heure-ka! Heure-ka!’
[I’ve found it! I’ve found it!].”
⁹

Plutarch wrote that Archimedes “regarded as sordid and ignoble the construction of instruments, and in general every art directed to use and profit, and he only strove after those things which, in their beauty and excellence, remain beyond all contact with the common needs of life.”
¹⁰
Yet there is no doubt that the mathematician had a mechanical bent, no less than Hero or Maudslay. Archimedes’ reputation for cleverness and ingenuity was legendary. The Romans named a popular puzzle, which consisted of various-shaped pieces of ivory that had to be assembled into a square,
Loculus Archimedius
in his honor. His cleverness manifested itself in many practical inventions, all still in use: the compound pulley, whose several sheaves increased lifting power and allowed a single man to raise heavy
weights; the windlass, a rope wound around a drum, which was used as a hoisting device aboard ships and in mines; and the ancestor of the balancing weighing scale, the steelyard. In addition to the celestial globe, he is said to have built a water clock and a hydraulic organ in which air was compressed by water.

Like Leonardo and Ramelli, Archimedes served as a military engineer. During the siege of Syracuse he was called on to build defensive weapons. He designed catapults that threw rocks weighing five hundred pounds, and complicated underwater obstacles that capsized ships. His most renowned weapon was a mirror that beamed the sun’s rays and set the attackers’ ships on fire. To prove the practicality of what had long been considered merely a colorful legend, in
1973,
a Greek engineer named Ioannis Sakas built a working version of the ancient ray gun.
¹¹
He used seventy bronze-coated mirrors, which he aimed at a tarred plywood cutout of a ship. At a distance of
165
feet, approximating the “bow-shot” that is mentioned in the classical text, it took only a few minutes for fire to break out.

In
1981
, the redoubtable Sakas tested another Archimedean invention, the
architronito,
or steam cannon. This device was credited to Archimedes by Leonardo da Vinci, whose sketchbooks show a gun barrel with a breech encased in a heated firebox. When water is released from a cistern into the white-hot barrel, the
resulting steam creates sufficient pressure to eject the cannonball. Leonardo wrote that “this machine has driven a ball weighing one talent [about twenty pounds] six stadia [about three thousand feet].”
¹²
Sakas’s scale model successfully fired a cement-filled tennis ball a distance of two hundred feet.
¹³

According to Plutarch, after Archimedes had written a treatise titled “To Move a Given Weight by a Given Force,” in which he claimed that any weight could be moved, Hieron challenged the mathematician to prove his assertion by moving a beached ship loaded with freight. Archimedes set up his apparatus, attached a line to the ship, “and then drew it along, smoothly and evenly as if it were floating in water, not with great labor, but sitting down at a distance.”
¹⁴
It was on that occasion that he made his famous claim: “Just give me somewhere to stand, and I shall move the earth.”
¹⁵
How could Archimedes move a vessel weighing as much as seventy-five tons? According to Plutarch, it was done with a compound pulley; a description by a Byzantine historian mentions a three-sheaved pulley; and Athenaeus, a Greek historian, writes that Archimedes used an endless screw. A. G. Drachmann suggested that it is not unreasonable to assume that the ship was moved by a combination of these machines. He calculated the mechanical advantage of a pulley of five sheaves, pulled by a windlass that was powered by a combination of
endless screws, would be
1
:
125
,
000
.
¹⁶
That is, one pound of force on the rope would translate into a pulling force of more than sixty tons. Even assuming losses for friction, Drachmann argued, Archimedes alone—the different versions are in agreement on this point—could easily move the heavy ship a small distance.

Who was the inventor of the endless screw? Some modern historians credit Archytas of Terentum, a Pythagorean philosopher who lived at the time of Plato, around
400
B.C.
; others point to Apollonius of Perge, a younger contemporary of Archimedes’.
¹⁷
Drachmann champions Archimedes himself, citing not only Athenaeus’ story of moving the ship, but also quoting Eustathius, a Greek scholar who wrote, “Screw is also the name of a sort of machine, which was first invented by Archimedes.”
¹⁸

Drachmann’s claim is all the more plausible since Archimedes’ name is associated with another kind of screw, the water screw, a device for lifting water. The water screw consists of a giant screw about one foot in diameter and ten to fifteen feet long, encased in a watertight wooden tube. The tube, whose ends are left open, is installed at a low angle, with the lower end immersed in water. As the entire apparatus turns, powered by a person walking on cleats fastened to the exterior, the water entering the lower end is moved up by the helical partitions—or threads—of the screw and emerges at
the top. The water screw turns slowly, but its capacity is substantial (the lower the angle, the greater the flow), and its mechanical efficiency has been estimated to be as much as
60
percent, which compares favorably with later water-lifting devices such as waterwheels and bucket conveyor belts.
^I
,
19

The oldest references to the water screw, in the second century
B.C.
, all credit Archimedes with the invention. According to Diodorus, Archimedes invented the water screw while he was a young man in Alexandria.
²⁰
That makes sense. The device is ideal for agricultural irrigation in Egypt: unlike large waterwheels, it can easily be moved from place to place; its lift is not great, but sufficient for the flat delta; and the simple design—there are no moving parts—resists clogging by the silted Nile River water.

Water screw technology spread from Egypt throughout the Mediterranean. Water screws were used for irrigation, but they had other applications. Archimedes is said to have used them to empty bilge water from one of Hieron’s huge ships. Water screws were also used by the Romans to lift water in municipal water systems, and to pump out mines. Several well-preserved wooden water
screws were discovered in the early
1900
s in ancient Roman copper mines in Spain.
²¹
The twelve-foot-long tubes, approximately one foot in diameter, are wrapped in pitched cloth and strengthened with rope; inside, the helical partitions are made of laminated strips of wood, glued and attached with copper nails. Four such water screws in series could lift water a vertical distance of about twenty feet. Diodorus describes how “with constant pumping by turns they throw up the water to the mouth of the pit and thus drain the mine; for this engine is so ingeniously contrived that a vast quantity of water is strangely and with little labor cast out.”
²²

Archimedean screw, from a later edition of Vitruvius,
The Ten Books on Architecture,
first century
B.C.

Diodorus was impressed with the simplicity and effectiveness of the water screw since he compared it to other ancient water-lifting devices such as complicated bucket conveyor belts and waterwheels. A common type of waterwheel was the
tympanum,
a large hollow wheel, ten
to fifteen feet in diameter, divided into eight pie-shaped compartments. As the wheel turned, water flowed into the lowest compartment when it was submerged, and out when the compartment reached the top position. It has been suggested that the
tympanum
may have inspired Archimedes.
²³
Indeed, if the
tympanum
shape is stretched and rotated along its central axis, it produces a cylindrical helix. This three-dimensional extrapolation, although hardly obvious, would not have been difficult for a skilled mathematician. The presumed authorship of Archimedes is supported by another curious fact. The only detailed description of a water screw in all Greek and Latin literature, which is by Vitruvius, specifies a water screw with
eight
helical partitions—the precise number that would be produced if the water screw were inspired by the
tympanum.
²⁴
Vitruvius was presumably describing the original water screw; later Roman engineers, realizing that there is no mechanical advantage to eight partitions—and considerable added cost—reduced their number to two or three.

Whether or not Archimedes was inspired by the
tympanum,
the water screw is yet another example of a mechanical invention that owes its existence to human imagination rather than technological evolution. And imagination is fickle. The ancient Chinese, for example, did not know the water screw; indeed, they didn’t know screws at all: the screw is the only major mechanical
device that they did not independently invent.
²⁵
The Romans, on the other hand, knew about the screw when they invented the auger, yet they never realized that the same principle could solve a major drilling problem: the tendency of deep holes to become clogged with sawdust. Not until the early
1800
s was the so-called spiral auger, whose helical shank cleared the sawdust as the bit turned, invented.