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Quantities in Context

A quantity typically does not mean much unless it is expressed in terms of a unit. Which is longer, 1 or 10000? It is hard to tell. Perhaps the 1 refers to a kilometer, while the 10000 refers to millimeters. Units in use have changed over the years. This section explores some of those units.

Origin of Units

Time

Major units of time were the product of astronomical phenomena. The dayrepresented the rotation of the Earth with respect to the Sun. The monthrepresented the full cycle of lunar phases. The yearrepresented the full orbit of the Earth about the Sun. It is the inclination of the Earth with respect to its orbital plane that results in the seasons, which were of tremendous importance for growing crops, seasonal migrations and many other matters of importance to survival. These units are still with us and fairly universal among humans throughout history, although the exact magnitude of the unit varies over time and across societies. Of course, their names vary considerably.

Shorter units such as the hour, minute and second are considerably more arbitrary in origin, although their modern definitions may be quite precise.

Mass, Weight and Volume

Units of mass and weight were sometimes derived from the means of measuring these quantities. For example, a cup is a unit of volume obviously derived from a physical cup. Other units were based on how much a hand could hold., or how much a typical person could carry in a hand-held container. Other units were based on the amount of a typical object being measured.

Length

Some units of length were based upon human physical characteristics, such as the length of a hand or arm. Other units were based on how far a typical person or horse could walk or fun in an hour or day.

 

Ancient Units

The following examples of historical and modern weights is not comprehensive.

Egypt

“Egyptian cubit developed around 3000 BC. Based on the human body, it was taken to be the length of an arm from the elbow to the extended fingertips. Since different people have different lengths of arm, the Egyptians developed a standard royal cubit which was preserved in the form of a black granite rod against which everyone could standardise their own measuring rods.”[1]

“The digit was the smallest basic unit, being the breadth of a finger. There were 28 digits in a cubit, 4 digits in a palm, 5 digits in a hand, 3 palms (so 12 digits) in a small span, 14 digits (or a half cubit) in a large span, 24 digits in a small cubit, and several other similar measurements.”[1]

Babylonia

The Babylonians developed measures  around 1700 BC. “Their basic unit of length was … the cubit. The Babylonian cubit (530 mm), however, was very slightly longer than the Egyptian cubit (524 mm). The Babylonian cubit was divided into 30 kus which is interesting since the kus must have been about a finger’s breadth but the fraction ¹/₃₀ is one which is also closely connected to the Babylonian base 60 number system. A Babylonian foot was ²/₃ of a Babylonian cubit.”[1]

India

“Harappan civilisation flourished in the Punjab between 2500 BC and 1700 BC. An analysis of the weights discovered in excavations suggests that they had two different series [of weights and measures], both decimal in nature, with each decimal number multiplied and divided by two. The main series has ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Several scales for the measurement of length were also discovered during excavations. One was a decimal scale based on a unit of measurement of 1.32 inches (3.35 centimetres) which has been called the “Indus inch”. Of course ten units is then 13.2 inches (33.5 centimetres) which is quite believable as the measure of a “foot”. Another scale was discovered when a bronze rod was found to have marks in lengths of 0.367 inches. …Now 100 units of this measure is 36.7 inches (93 centimetres) which is about the length of a stride”[1]

Ancient Greece

“The Greeks used as their basic measure of length the breadth of a finger (about 19.3 mm), with 16 fingers in a foot, and 24 fingers in a Greek cubit. These units of length, as were the Greek units of weight and volume, were derived from the Egyptian and Babylonian units. Trade, of course, was the main reason why units of measurement were spread more widely than their local areas. In around 400 BC Athens was a centre of trade from a wide area.”[1]

Ancient Rome

“The Romans adapted the Greek system. They had as a basis the foot which was divided into 12 inches (or ounces for the words are in fact the same). The Romans did not use the cubit but, perhaps because most of the longer measurements were derived from marching, they had five feet equal to one pace (which was a double step, that is the distance between two consecutive positions of where the right foot lands as one walks). Then 1,000 paces measured a Roman mile which is reasonably close to the British mile as used today.”[1]

 

Early Europe

“The Angles, Saxons, and Jutes brought measures such as the perch, rod and furlong. The fathom has a Danish origin, and was the distance from fingertip to fingertip of outstretched arms while the ell was originally a German measure of woollen cloth.”[1]

 

Modern Units

English

• Ounce, Pound
• Inch, Foot, Yard, Mile
• Ounce, Cup, Pint, Quart, Gallon

Metric

• Length: Meter
• Mass: Kilogram
• Volume: \(Meters^3\) or Liters
• Energy: Joules
• Power: Watts
• Time: Seconds

 

References

1. U. of St. Andrews, The history of measurement
2. Russ Rowlett, English Customary Weights and Measures
3. U.S. National Institute of Standards and Technology (NIST), Definitions and historical context of SI

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