Archimedes of Syracuse, Sicily, was a mathematician and inventor of ancient Greece who lived about 287 to 212 BCE. His On Floating Bodies is the earliest known work on hydrostatics, and it covers the floating of solids in a fluid. Archimedes is recognized as the founder of that field. A popular story says Archimedes found buoyancy while bathing and then ran shouting "Eureka!" through the streets. The story was recorded in writing in the first century BC, well after he lived, and the method it describes is doubted by some scholars. In 1586, at age 22, Galileo wrote a short treatise, La Bilancetta ("The Little Balance"), which doubted Vitruvius's story of how Archimedes tested the crown and proposed a method of Galileo's own using water.
Vitruvius's overflow method is hard to use. Had a 1000-gram wreath been 30 percent silver, the water in a container 20 centimeters across would have risen only about 0.41 millimeters higher than it would for pure gold. Archimedes' principle says a body in a fluid at rest feels an upward push matching the weight of the fluid pushed aside by the body (displaced). The reasoning goes like this: imagine the object removed and its space filled with water. The surrounding water held that water up, so the buoyant force on the object must match that water's weight. Pressure rising with depth is the source of buoyancy, because the upward force on the bottom of a submerged object is greater than the downward force on its top, and the difference is the buoyant force.
When the buoyant force exceeds an object's weight, the object rises and floats; when it falls short, the object sinks; and when the two match, it hangs in place. Depth itself does not matter: a thing floating in 2 feet of water also floats in 2000 feet. A launched ship sinks until the weight of the water it displaces equals its own weight, then sinks deeper as cargo is added. The part of a hull below the water must be big enough for the water it pushes aside to equal the weight of the fully loaded ship. The ship then floats no lower than its design waterline. The fraction of a floating object that is under the surface equals its specific gravity.
Density measures the mass packed into a given amount of space (volume). To find an odd-shaped object's density, weigh it in air and then in water. The loss of weight is the weight of water displaced, which gives its volume (1 gram of water per cubic centimeter). Mass divided by volume gives density, and a coin can be tested the same way. Body density is one indicator of a person's percent body fat. In a "fat tank" a person is weighed completely under water, with the air left in the lungs measured separately and corrected for. A hydrometer, a weighted bulb on a glass stem, is another way to read density. Etched markings on it turn the height at which it floats into the liquid's relative density (also called specific gravity).
Water reaches its greatest density near 39°F (4°C), so within a lake, water at its densest settles below colder water. This keeps lakes from freezing from the bottom up. Measured in grams per cubic centimeter, water at 4.0°C is at its peak of 1.00000. At 32°F (0°C) the figure is 0.99987, and at 212°F (100°C) it is 0.95865, so the changes are small but real. Ice has its molecules in an open, spread-out arrangement with plenty of space separating the molecules, so ice has lower density than the liquid. Buoyancy works in gases too, and air pushes up on a helium balloon the way water pushes up on a floating cork. Floating is not only about water, since lava rises in a volcano and mountain ranges rest on crust and mantle that are denser than they are.
Load marks on ships are old. Ships from Venice were marked with a cross as long ago as the 12th century, but only in the 19th century did load lines become widespread, after ships called "coffin ships" were overloaded. Lloyd's Register, a classification society, made an early attempt at safety marks in 1835, and it covered only the ships the society itself classed. Unloaded, a ship floats higher than the same ship carrying a full load of cargo, and salt water has more density than fresh water, so a ship, loaded or empty, sits higher in the sea than it would in a river or in a lake of fresh water.
In 1870 British MP Samuel Plimsoll began investigating ship safety. Load lines became compulsory under a law of 1876, and the line's position was fixed by law in 1894. Painted along a ship's side, the Plimsoll line marks how deep a ship may safely sit. The Plimsoll mark is a circle with a horizontal line through its center, and it is recognised worldwide. Where the water may reach on the line depends on how warm and how salty the water is, the season and the place. Life jackets help people float, and children and everyone in a boat should wear them. Child sizes exist because an adult-sized jacket may fail a child. The U.S. Coast Guard says that for most adults, between 7 and 12 pounds of buoyancy, which is 31 to 53 newtons, is enough to keep the head above water. Whenever you swim or play in water, a grown-up should watch, and you should ask first.
Words to know
- displaces: pushes aside
- hydrostatics: fluids at rest
- buoyant: pushing upward
- density: mass per volume
