# 1.4 Units and the Metric System

The subject of measurement has a rich and fascinating history. Ever since humans have traded goods, they have needed a standard system of weights and measures. Many of our familiar units are part of the English system, which dates back to the Middle Ages. For example, length units were based on the human body: an inch is the length of the end joint of a thumb, a foot is of course the length of a foot, a yard is the distance from the tip of the nose to the end of an outstretched arm, and a fathom is the distance between the fingertips of two arms held straight out. However, these units are variable, since people are different sizes! As early as 1215, King John of England recognized the need for standardization in the Magna Carta, "There shall be standard measures of wine, corn, and ale throughout the kingdom."

Even after standardization, the English system of units is a mess. It consists of a welter of different units, many of which are divided by different amounts. There are 8 pints in a gallon, 12 inches in a foot, and 16 ounces in a pound. Many units are accidents of history, but the use of these multiples came about because very few people have ever been numerate. It is easy to divide up objects when they are contained in groups of 8 (= 2 × 2 × 2) or 12 (= 2 × 2 × 3) or 16 (= 2 × 2 × 2 × 2).

The metric system was established by the French Academy of Sciences in 1791. It grew out of the French Revolution and a desire to rationalize many aspects of human affairs. The goal was to create a measurement system based on invariable quantities in nature, rather than on parts of the human body. Thus, the meter was defined to be 1 ten-millionth of the distance from the Earth’s equator to the North Pole, the gram was defined to be the mass of a cubic centimeter of water at 4º C, and the second was defined to be 1/86,400 of a solar day (1/60 × 1/60 × 1/24). The metric system makes a lot of sense. There is only one basic unit for each quantity and all subdivisions and multiples are powers of ten. Thomas Jefferson was impressed by the metric system and pushed for its adoption in the United States. Finally, the United States and sixteen other countries signed the Treaty of the Meter in 1879. But as you look around, you will see that we are not metric in everyday life. In this regard, the United States is almost a lone holdout — not even the English use the English system any more!

Scientists have embraced the metric system completely. Here are the conversion factors between some familiar quantities in the English system and their counterparts in the metric system:

• 1 m = 39.37 in and the reverse 1 in = 0.0254 m = 25.4 mm

• 1 m = 1.094 yd and the reverse 1 yd = 0.914 m = 914 mm

• 1 km = 0.621 mi and the reverse 1 mi = 1.609 km = 8/5 km

• 1 g = 0.0353 oz and the reverse 1 oz = 28.3 g = 0.0283 kg

• 1 kg = 2.205 lb and the reverse 1 lb = 0.454 kg = 454 g

• 1 liter = 1.06 qt and the reverse 1 qt = 0.94 liters = 940 cm^{3}

• 1 liter = 0.264 gal and the reverse 1 gal = 3.79 liters = 3790 cm^{3}

• 1 W = 0.00134 hp and the reverse 1 horsepower = 745.7 W

• 1 J = 0.00024 cal and the reverse 1 calorie = 4186 J

These are just a few of the most common units from the English system. There are many more. You can be glad you do not have to remember the distinctions between cubits and furlongs and pecks and pottles and bushels and jacks and jills! Here are other important quantities that can all be derived from the fundamental units of mass, length, and time:

• Frequency: measured in cycles/s or Hertz (Hz)

• Force: measured in kg m/s^{2} or Newton (N)

Photograph of William Thomson,?Lord Kelvin: a Scottish-Irish physicist famous for his work on thermodynamics. Click herefor original source URL.

• Energy: measured in kg m^{2}/s^{2} or Joules (J)

• Power: measured in J/s or Watts (W)

• Temperature: measured in K or Kelvin (K)

In science, temperature is given on the Kelvin scale, named after the Scottish physicist William Thomson, Lord Kelvin. The Kelvin scale is measured with reference to absolute zero — the temperature at which an object contains no heat and all atomic motions are frozen. Some scientists also use the Celsius scale, named after the Swedish astronomer Anders Celsius. The Celsius scale is also called the centigrade scale, since it is based on the division of the range from the freezing to the boiling points of water into 100 equal degrees. A third temperature scale was named after German physicist Gabriel Fahrenheit, who made the first successful mercury thermometer in 1720. The Fahrenheit scale is not used by scientists, and it is only used in the United States.

The information below gives some important temperature markers and tells you how to convert from one temperature scale to another.

• Absolute zero: 0 K = -273 °C = -459 °F

• Water freezes: 273 K = 0 °C = 32 °F

• Water boils: 373 K = 100°C = 212 °F

• Surface of the Sun: 5700 K = 5427 °C = 9797 °F

• Any level: °C + 273 = 5/9(°F-32) = (9/5)°C+32

Despite the variety of measurements we can make in the natural world, there are three fundamental properties that cannot be described in any simpler terms. These fundamental properties are mass, length, and time. Every quantity you see in basic astronomy can be expressed as some combination of these three. For example, velocity is distance (or length) divided by time, and density is mass divided by volume (orlength cubed).

The metric system has been refined over time. The modern version of the metric system was agreed on in 1960; it is called the International System of Units (SI). We now have fundamental and extremely precise definitions of the units of mass, length, and time. The standard unit for mass is the kilogram (kg). The "true" kilogram is a metal cylinder kept at the International Bureau of Weights and Measures in Paris. The standard unit of length is the meter (m). The meter is defined to be the distance that light travels in 1/299,792,458 seconds; this definition is precise because we have measured the speed of light very accurately. The standard unit of time is the second (s). One second is defined as the length of time required for 9,192,631,770 vibrations of the cesium-133 atom. These exact definitions are not important — scales and rulers and clocks work well enough in everyday life. But it is important to know that metric units have precise definitions.